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Sample records for abelian family symmetry

  1. Quasi-degenerate neutrinos from an abelian family symmetry

    SciTech Connect

    Binetruy, P. |; Lavignac, S.; Petcov, S. |; Ramond, P.

    1996-12-31

    The authors show that models with an abelian family symmetry which accounts for the observed hierarchies of masses and mixings in the quark sector may also accommodate quasi-degeneracies in the neutrino mass spectrum. Such approximate degeneracies are, in this context, associated with large mixing angles. The parameters of this class of models are constrained. The authors discuss their phenomenological implications for present and foreseen neutrino experiments.

  2. Bilarge neutrino mixing and Abelian flavor symmetry

    NASA Astrophysics Data System (ADS)

    Ding, Gui-Jun; Morisi, S.; Valle, J. W. F.

    2013-03-01

    We explore two bilarge neutrino mixing Anzätze within the context of Abelian flavor symmetry theories: (BL1) sin⁡θ12˜λ, sin⁡θ13˜λ, sin⁡θ23˜λ, and (BL2) sin⁡θ12˜λ, sin⁡θ13˜λ, sin⁡θ23˜1-λ. The first pattern is proposed by two of us and is favored if the atmospheric mixing angle θ23 lies in the first octant, while the second one is preferred for the second octant of θ23. In order to reproduce the second texture, we find that the flavor symmetry should be U(1)×Zm, while for the first pattern the flavor symmetry should be extended to U(1)×Zm×Zn with m and n of different parity. Explicit models for both mixing patterns are constructed based on the flavor symmetries U(1)×Z3×Z4 and U(1)×Z2. The models are extended to the quark sector within the framework of SU(5) grand unified theory in order to give a successful description of quark and lepton masses and mixing simultaneously. Phenomenological implications are discussed.

  3. Yukawa textures with an anomalous horizontal abelian symmetry

    SciTech Connect

    Binetruy, P.; Lavignac, S.; Ramond, P.

    1996-01-01

    The observed hierarchy of quark and lepton masses and mixings may be obtained by adding an abelian family symmetry to the Minimal Supersymmetric Model and coupling quarks and leptons to an electroweak singlet scalar field. In a large class of such models, this symmetry suffers from anomalies which must be compensated by the Green-Schwarz mechanism; this in turn fixes the electroweak mixing angle to be sin{sup 2}{theta}{sub W} = 3/8 at the string scale, without any assumed GUT structure. The analysis is extended to two distinct generalizations of the Standard Model: neutrino masses and mixings and R-parity violating interactions. (author). 31 refs., 2 tabs.

  4. On discrete symmetries for a whole Abelian model

    SciTech Connect

    Chauca, J.; Doria, R.

    2012-09-24

    Considering the whole concept applied to gauge theory a nonlinear abelian model is derived. A next step is to understand on the model properties. At this work, it will be devoted to discrete symmetries. For this, we will work based in two fields reference systems. This whole gauge symmetry allows to be analyzed through different sets which are the constructor basis {l_brace}D{sub {mu}},X{sup i}{sub {mu}}{r_brace} and the physical basis {l_brace}G{sub {mu}I}{r_brace}. Taking as fields reference system the diagonalized spin-1 sector, P, C, T and PCT symmetries are analyzed. They show that under this systemic model there are conservation laws driven for the parts and for the whole. It develops the meaning of whole-parity, field-parity and so on. However it is the whole symmetry that rules. This means that usually forbidden particles as pseudovector photons can be introduced through such whole abelian system. As result, one notices that the fields whole {l_brace}G{sub {mu}I}{r_brace} manifest a quanta diversity. It involves particles with different spins, masses and discrete quantum numbers under a same gauge symmetry. It says that without violating PCT symmetry different possibilities on discrete symmetries can be accommodated.

  5. Discrete Abelian gauge symmetries and axions

    NASA Astrophysics Data System (ADS)

    Honecker, Gabriele; Staessens, Wieland

    2015-07-01

    We combine two popular extensions of beyond the Standard Model physics within the framework of intersecting D6-brane models: discrete ℤn symmetries and Peccei-Quinn axions. The underlying natural connection between both extensions is formed by the presence of massive U(1) gauge symmetries in D-brane model building. Global intersecting D6-brane models on toroidal orbifolds of the type T6/ℤ2N and T6/ℤ2 × ℤ2M with discrete torsion offer excellent playgrounds for realizing these extensions. A generation-dependent ℤ2 symmetry is identified in a global Pati-Salam model, while global left-right symmetric models give rise to supersymmetric realizations of the DFSZ axion model. In one class of the latter models, the axion as well as Standard Model particles carry a non-trivial ℤ3 charge.

  6. Projected Entangled Pair States with non-Abelian gauge symmetries: An SU(2) study

    NASA Astrophysics Data System (ADS)

    Zohar, Erez; Wahl, Thorsten B.; Burrello, Michele; Cirac, J. Ignacio

    2016-11-01

    Over the last years, Projected Entangled Pair States have demonstrated great power for the study of many body systems, as they naturally describe ground states of gapped many body Hamiltonians, and suggest a constructive way to encode and classify their symmetries. The PEPS study is not only limited to global symmetries, but has also been extended and applied for local symmetries, allowing to use them for the description of states in lattice gauge theories. In this paper we discuss PEPS with a local, SU(2) gauge symmetry, and demonstrate the use of PEPS features and techniques for the study of a simple family of many body states with a non-Abelian gauge symmetry. We present, in particular, the construction of fermionic PEPS able to describe both two-color fermionic matter and the degrees of freedom of an SU(2) gauge field with a suitable truncation.

  7. Non-Abelian symmetries of the half-infinite XXZ spin chain

    NASA Astrophysics Data System (ADS)

    Baseilhac, Pascal; Belliard, Samuel

    2017-03-01

    The non-Abelian symmetries of the half-infinite XXZ spin chain for all possible types of integrable boundary conditions are classified. For each type of boundary conditions, an analog of the Chevalley-type presentation is given for the corresponding symmetry algebra. In particular, two new algebras arise that are, respectively, generated by the symmetry operators of the model with triangular and special Uq (gl2)-invariant integrable boundary conditions.

  8. Field theories for gauged symmetry-protected topological phases: Non-Abelian anyons with Abelian gauge group Z2⊗3

    NASA Astrophysics Data System (ADS)

    He, Huan; Zheng, Yunqin; von Keyserlingk, Curt

    2017-01-01

    Dijkgraaf-Witten (DW) theories are of recent interest to the condensed matter community, in part because they represent topological phases of matter, but also because they characterize the response theory of certain symmetry protected topological (SPT) phases. However, as yet there has not been a comprehensive treatment of the spectra of these models in the field theoretic setting even for Abelian gauge groups, the goal of this work is to fill the gap in the literature, especially for a selection of DW models with Abelian gauge groups but non-Abelian topological order. Particularly, we focus on the appearance of non-Abelian statistics in type-III twisted DW theories with Abelian gauge groups Z2⊗3. There are only 22 distinguishable line operators, and their fusion rules and correlation functions are calculated. The flux insertion operators have quantum dimension 2, which clearly demonstrates the non-Abelian topological order of type-III twisted DW theories.

  9. Symmetry-protected non-Abelian braiding of Majorana Kramers pairs

    NASA Astrophysics Data System (ADS)

    Gao, Pin; He, Ying-Ping; Liu, Xiong-Jun

    2016-12-01

    We develop a complete theory for symmetry protected non-Abelian statistics of Majorana Kramers' pairs (MKPs) in time-reversal (TR) invariant topological superconductors, with fundamental results being uncovered. By introducing an effective Hamiltonian approach to describe the braiding of MKPs, we show that the non-Abelian braiding is protected when the effective Hamiltonian exhibits a new TR-like antiunitary symmetry, which is satisfied if the system is free of dynamical noise. Importantly, even the dynamical noise cannot cause error in braiding, unless the noise correlation function breaks a dynamical TR symmetry. This is a profound result and generalizes the TR symmetry protection of MKPs to the dynamical regime. Moreover, the resulted error by noise is shown to be a higher-order effect, compared with the decoherence of Majorana qubits without TR symmetry protection. This study completes the theory of symmetry-protected non-Abelian statistics of MKPs, and shows that the non-Abelian braiding of MKPs is well observable and may have versatile applications to future quantum computation technologies.

  10. Breaking an Abelian gauge symmetry near a black hole horizon

    SciTech Connect

    Gubser, Steven S.

    2008-09-15

    I argue that coupling the Abelian Higgs model to gravity plus a negative cosmological constant leads to black holes which spontaneously break the gauge invariance via a charged scalar condensate slightly outside their horizon. This suggests that black holes can superconduct.

  11. Abelian symmetries in the two-Higgs-doublet model with fermions

    SciTech Connect

    Ferreira, P. M.; Silva, Joao P.

    2011-03-15

    We classify all possible implementations of an Abelian symmetry in the two-Higgs-doublet model with fermions. We identify those symmetries which are consistent with nonvanishing quark masses and a Cabibbo-Kobayashi-Maskawa quark-mixing matrix (CKM), which is not block-diagonal. Our analysis takes us from a plethora of possibilities down to 246 relevant cases, requiring only 34 distinct matrix forms. We show that applying Z{sub n} with n{>=}4 to the scalar sector leads to a continuous U(1) symmetry in the whole Lagrangian. Finally, we address the possibilities of spontaneous CP violation and of natural suppression of the flavor-changing neutral currents. We explain why our work is relevant even for non-Abelian symmetries.

  12. Holographic nonlinear hydrodynamics from AdS/CFT with multiple/non-abelian symmetries

    NASA Astrophysics Data System (ADS)

    Torabian, Mahdi; Yee, Ho-Ung

    2009-08-01

    We study viscous hydrodynamics of hot conformal field theory plasma with multiple/non-Abelian symmetries in the framework of AdS/CFT correspondence, using a recently proposed method of directly solving bulk gravity in derivative expansion of local plasma parameters. Our motivation is to better describe the real QCD plasma produced at RHIC, incorporating its U(1)Nf flavor symmetry as well as SU(2)I non-Abelian iso-spin symmetry. As concrete examples, we choose to study the STU model for multiple U(1)3 symmetries, which is a sub-sector of 5D N=4 gauged SUGRA dual to N=4 Super Yang-Mills theory, capturing Cartan U(1)3 dynamics inside the full R-symmetry. For SU(2), we analyze the minimal 4D N=3 gauged SUGRA whose bosonic action is simply an Einstein-Yang-Mills system, which corresponds to SU(2) R-symmetry dynamics on M2-branes at a Hyper-Kahler cone. By generalizing the bosonic action to arbitrary dimensions and Lie groups, we present our analysis and results for any non-Abelian plasma in arbitrary dimensions.

  13. Non-Abelian discrete flavor symmetries of 10D SYM theory with magnetized extra dimensions

    NASA Astrophysics Data System (ADS)

    Abe, Hiroyuki; Kobayashi, Tatsuo; Ohki, Hiroshi; Sumita, Keigo; Tatsuta, Yoshiyuki

    2014-06-01

    We study discrete flavor symmetries of the models based on a ten-dimensional supersymmetric Yang-Mills (10D SYM) theory compactified on magnetized tori. We assume non-vanishing non-factorizable fluxes as well as the orbifold projections. These setups allow model-building with more various flavor structures. Indeed, we show that there exist various classes of non-Abelian discrete flavor symmetries. In particular, we find that S 3 flavor symmetries can be realized in the framework of the magnetized 10D SYM theory for the first time.

  14. Multi-Higgs model with Abelian and non-Abelian discrete symmetries

    NASA Astrophysics Data System (ADS)

    Machado, A. C. B.; Pleitez, V.

    2008-11-01

    Usually in the context of the standard model and its multi-Higgs extensions the fermions mass matrices has the form Mαβ = Σi(Γi)αβlangleΦ0irangle, where Γi, denotes an arbitrary complex dimensionless 3 x 3 matrices (for Majorana it is symmetric), and langleΦ0irangle denotes the set of vacuum expectation values (VEVs) of one or more neutral scalar field. The mixing matrix and the mass pattern of each charged sector depend on the structure of the respective Γi's. It is well known that explicit, and predictive, forms of these matrices can be obtained by imposing flavor symmetries. Here we will turn the problem upside down. Mass matrices will be of the form Mαβ = f()αβ, where f denotes some dimensionless (Script O(1)) parameters. In general we need at most two f's and αβ is a matrix built with the VEVs of several scalar fields. At first sight, there is no gain in predictive power, we are just changing a dimensionless general matrix ΓαAbT by another one with mass dimension ()αβ. However it seems easier, at least in principle, to explain patterns of dynamical variables like VEVs, than dimensionless numbers. The value of the former can be explained by the dynamics (for instance by studying the scalar potential) and extra flavor symmetries that we can impose to the model. Therefore, we propose a multi-Higgs extension of the standard model with A4 otimes Z3 otimes Z'3 otimes Z''3 symmetries in which the mass matrices of the charged fermions, obtained from renormalizable interactions, are diagonal. Corrections induced by non-renormalizable interactions deviate these matrices from the diagonal form. Active neutrinos acquire mass only from non-renormalizable interactions. The main entries of the neutrino mass matrix arise only through dimension five operators, while the diagonal entries arise only from dimension six operators. The basic idea is to consider SU(2)l fermions doublets in the triplet representation of the A4 symmetry and Higgs doublets or right

  15. Phase structure of one-dimensional interacting Floquet systems. I. Abelian symmetry-protected topological phases

    NASA Astrophysics Data System (ADS)

    von Keyserlingk, C. W.; Sondhi, S. L.

    2016-06-01

    Recent work suggests that a sharp definition of "phase of matter" can be given for some quantum systems out of equilibrium, first for many-body localized systems with time-independent Hamiltonians and more recently for periodically driven or Floquet localized systems. In this work, we propose a classification of the finite Abelian symmetry-protected phases of interacting Floquet localized systems in one dimension. We find that the different Floquet phases correspond to elements of ClG×AG , where ClG is the undriven interacting classification, and AG is a set of (twisted) one-dimensional representations corresponding to symmetry group G . We will address symmetry-broken phases in a subsequent paper C. W. von Keyserlingk and S. L. Sondhi, following paper, Phys. Rev. B 93, 245146 (2016), 10.1103/PhysRevB.93.245146.

  16. Dual-BRST symmetry: 6D Abelian 3-form gauge theory

    NASA Astrophysics Data System (ADS)

    Kumar, R.; Krishna, S.; Shukla, A.; Malik, R. P.

    2012-04-01

    Within the framework of the Becchi-Rouet-Stora-Tyutin (BRST) formalism, we demonstrate the existence of the novel off-shell nilpotent (anti-)dual-BRST symmetries in the context of a six (5+1)-dimensional (6D) free Abelian 3-form gauge theory. Under these local and continuous symmetry transformations, the total gauge-fixing term of the Lagrangian density remains invariant. This observation should be contrasted with the off-shell nilpotent (anti-)BRST symmetry transformations, under which, the total kinetic term of the theory remains invariant. The anticommutator of the above nilpotent (anti-)BRST and (anti-)dual-BRST transformations leads to the derivation of a bosonic symmetry in the theory. There exists a discrete symmetry transformation in the theory which provides a thread of connection between the nilpotent (anti-)BRST and (anti-)dual-BRST transformations. This theory is endowed with a ghost-scale symmetry, too. We discuss the algebra of these symmetry transformations and show that the structure of the algebra is reminiscent of the algebra of de Rham cohomological operators of differential geometry.

  17. Non-Abelian Gauge Symmetry in the Causal Epstein-Glaser Approach

    NASA Astrophysics Data System (ADS)

    Hurth, Tobias

    Non-Abelian gauge symmetry in (3 + 1)-dimensional space-time is analyzed in the causal Epstein-Glaser framework. In this formalism, the technical details concerning the well-known UV and IR problem in quantum field theory are separated and reduced to well-defined problems, namely the causal splitting and the adiabatic switching of operator-valued distributions. Non-Abelian gauge invariance in perturbation theory is completely discussed in the well-defined Fock space of free asymptotic fields. The LSZ formalism is not used in this construction. The linear operator condition of asymptotic gauge invariance is sufficient for the unitarity of the S matrix in the physical subspace and the usual Slavnov-Taylor identities. We explicitly derive the most general specific coupling compatible with this condition. By analyzing only tree graphs in the second order of perturbation theory we show that the well-known Yang-Mills couplings with anticommuting ghosts are the only ones which are compatible with asymptotic gauge invariance. The required generalizations for linear gauges are given.

  18. Nilpotent Symmetries for Matter Fields in Non-Abelian Gauge Theory:

    NASA Astrophysics Data System (ADS)

    Malik, R. P.

    In the framework of superfield approach to Becchi-Rouet-Stora-Tyutin (BRST) formalism, the derivation of the BRST and anti-BRST nilpotent symmetry transformations for the matter fields, present in any arbitrary interacting gauge theory, has been a long-standing problem. In our present investigation, the local, covariant, continuous and off-shell nilpotent (anti-)BRST symmetry transformations for the Dirac fields (ψ ,bar ψ ) are derived in the framework of the augmented superfield formulation where the four (3 + 1)-dimensional (4D) interacting non-Abelian gauge theory is considered on the six (4 + 2)-dimensional supermanifold parametrized by the four even space-time coordinates xμ and a couple of odd elements (θ and bar θ ) of the Grassmann algebra. The requirement of the invariance of the matter (super)currents and the horizontality condition on the (super)manifolds leads to the derivation of the nilpotent symmetries for the matter fields as well as the gauge and the (anti)ghost fields of the theory in the general scheme of augmented superfield formalism.

  19. Origin of Abelian gauge symmetries in heterotic/F-theory duality

    SciTech Connect

    Cvetič, Mirjam; Grassi, Antonella; Klevers, Denis; Poretschkin, Maximilian; Song, Peng

    2016-04-07

    Here, we study aspects of heterotic/F-theory duality for compactifications with Abelian gauge symmetries. We consider F-theory on general Calabi-Yau manifolds with a rank one Mordell-Weil group of rational sections. By rigorously performing the stable degeneration limit in a class of toric models, and also derive both the Calabi-Yau geometry and the spectral cover describing the vector bundle in the heterotic dual theory. We carefully investigate the spectral cover employing the group law on the elliptic curve in the heterotic theory. We find in explicit examples that there are three different classes of heterotic duals that have U(1) factors in their low energy effective theories: split spectral covers describing bundles with S(U(m) x U(1)) structure group, spectral covers containing torsional sections that seem to give rise to bundles with SU(m) x Z_k structure group and bundles with purely non-Abelian structure groups having a centralizer in E_8 containing a U(1) factor. In the former two cases, it is required that the elliptic fibration on the heterotic side has a non-trivial Mordell-Weil group. And while the number of geometrically massless U(1)'s is determined entirely by geometry on the F-theory side, on the heterotic side the correct number of U(1)'s is found by taking into account a Stuckelberg mechanism in the lower-dimensional effective theory. Finally, in geometry, this corresponds to the condition that sections in the two half K3 surfaces that arise in the stable degeneration limit of F-theory can be glued together globally.

  20. Origin of Abelian gauge symmetries in heterotic/F-theory duality

    DOE PAGES

    Cvetič, Mirjam; Grassi, Antonella; Klevers, Denis; ...

    2016-04-07

    Here, we study aspects of heterotic/F-theory duality for compactifications with Abelian gauge symmetries. We consider F-theory on general Calabi-Yau manifolds with a rank one Mordell-Weil group of rational sections. By rigorously performing the stable degeneration limit in a class of toric models, and also derive both the Calabi-Yau geometry and the spectral cover describing the vector bundle in the heterotic dual theory. We carefully investigate the spectral cover employing the group law on the elliptic curve in the heterotic theory. We find in explicit examples that there are three different classes of heterotic duals that have U(1) factors in theirmore » low energy effective theories: split spectral covers describing bundles with S(U(m) x U(1)) structure group, spectral covers containing torsional sections that seem to give rise to bundles with SU(m) x Z_k structure group and bundles with purely non-Abelian structure groups having a centralizer in E_8 containing a U(1) factor. In the former two cases, it is required that the elliptic fibration on the heterotic side has a non-trivial Mordell-Weil group. And while the number of geometrically massless U(1)'s is determined entirely by geometry on the F-theory side, on the heterotic side the correct number of U(1)'s is found by taking into account a Stuckelberg mechanism in the lower-dimensional effective theory. Finally, in geometry, this corresponds to the condition that sections in the two half K3 surfaces that arise in the stable degeneration limit of F-theory can be glued together globally.« less

  1. SL(2, z) Action on Three-Dimensional Conformal Field Theories with Abelian Symmetry

    NASA Astrophysics Data System (ADS)

    Witten, Edward

    On the space of three-dimensional conformal field theories with U(1) symmetry and a chosen coupling to a background gauge field, there is a natural action of the group SL(2, Z). The generator S of SL(2, Z) acts by letting the background gauge field become dynamical, an operation considered recently by Kapustin and Strassler in explaining three-dimensional mirror symmetry. The other generator T acts by shifting the Chern-Simons coupling of the background field. This SL(2, Z) action in three dimensions is related by the AdS/CFT correspondence to SL(2, Z) duality of low energy U(1) gauge fields in four dimensions.

  2. Discrete symmetry enhancement in non-Abelian models and the existence of asymptotic freedom

    NASA Astrophysics Data System (ADS)

    Patrascioiu, Adrian; Seiler, Erhard

    2001-09-01

    We study the universality between a discrete spin model with icosahedral symmetry and the O(3) model in two dimensions. For this purpose we study numerically the renormalized two-point functions of the spin field and the four point coupling constant. We find that those quantities seem to have the same continuum limits in the two models. This has far reaching consequences, because the icosahedron model is not asymptotically free in the sense that the coupling constant proposed by Lüscher, Weisz, and Wolff [Nucl. Phys. B359, 221 (1991)] does not approach zero in the short distance limit. By universality this then also applies to the O(3) model, contrary to the predictions of perturbation theory.

  3. An Introduction to Non-Abelian Discrete Symmetries for Particle Physicists

    NASA Astrophysics Data System (ADS)

    Ishimori, Hajime; Kobayashi, Tatsuo; Ohki, Hiroshi; Okada, Hiroshi; Shimizu, Yusuke; Tanimoto, Morimitsu

    1.C.<FamilyName>LuhnFamilyName>S.<FamilyName>NasriFamilyName>P.<FamilyName>RamondName>2007J. Math. Phys.4807350123376822007JMP....48g3501L10.1063/1.2734865arXiv:hep-th/0701188 Luhn, C., Nasri, S., Ramond, P.: J. Math. Phys. 48, 073501 (2007). arXiv:hep-th/0701188 1.A.<FamilyName>BovierFamilyName>M.<FamilyName>LulingFamilyName>D.<FamilyName>WylerName>1981J. Math. Phys.2215366285271981JMP....22.1536B0501.2000510.1063/1.525095 Bovier, A., Luling, M., Wyler, D.: J. Math. Phys. 22, 1536 (1981) 2.A.<FamilyName>Bovier

  4. Supersymmetric parameter space of family symmetries

    SciTech Connect

    Velasco-Sevilla, L.

    2008-11-23

    In this talk I have emphasized the effects of considering departures from the minimal flavour violation conditions, in the context of CMSSM-like theories, introduced by boundary conditions at GUT scale from Family Symmetries. In [1] we have shown the results of running these conditions down to EW, where constraints from fermion masses and CKM matrix elements have been used. Only when the expansion parameter in the sdown-squark sector is relatively large it is possible to relax the lower limit from b{yields}s{gamma} on the universal gaugino mass. The expansion parameter associated with the slepton sector needs to be smaller than the analogous in the sdown-squark sector in order to satisfy the bound imposed by the decay of {tau}{yields}{mu}{mu}.

  5. Leptonic mixing, family symmetries, and neutrino phenomenology

    SciTech Connect

    Medeiros Varzielas, I. de; Gonzalez Felipe, R.; Serodio, H.

    2011-02-01

    Tribimaximal leptonic mixing is a mass-independent mixing scheme consistent with the present solar and atmospheric neutrino data. By conveniently decomposing the effective neutrino mass matrix associated to it, we derive generic predictions in terms of the parameters governing the neutrino masses. We extend this phenomenological analysis to other mass-independent mixing schemes which are related to the tribimaximal form by a unitary transformation. We classify models that produce tribimaximal leptonic mixing through the group structure of their family symmetries in order to point out that there is often a direct connection between the group structure and the phenomenological analysis. The type of seesaw mechanism responsible for neutrino masses plays a role here, as it restricts the choices of family representations and affects the viability of leptogenesis. We also present a recipe to generalize a given tribimaximal model to an associated model with a different mass-independent mixing scheme, which preserves the connection between the group structure and phenomenology as in the original model. This procedure is explicitly illustrated by constructing toy models with the transpose tribimaximal, bimaximal, golden ratio, and hexagonal leptonic mixing patterns.

  6. Supersymmetric musings on the predictivity of family symmetries

    SciTech Connect

    Kadota, Kenji; Kersten, Joern; Velasco-Sevilla, Liliana

    2010-10-15

    We discuss the predictivity of family symmetries for the soft supersymmetry breaking parameters in the framework of supergravity. We show that unknown details of the messenger sector and the supersymmetry breaking hidden sector enter into the soft parameters, making it difficult to obtain robust predictions. We find that there are specific choices of messenger fields which can improve the predictivity for the soft parameters.

  7. SU(3) family gauge symmetry and the axion

    SciTech Connect

    Appelquist, Thomas; Bai Yang; Piai, Maurizio

    2007-04-01

    We analyze the structure of a recently proposed effective field theory (EFT) for the generation of quark and lepton mass ratios and mixing angles, based on the spontaneous breaking of an SU(3) family gauge symmetry at a high scale F. We classify the Yukawa operators necessary to seed the masses, making use of the continuous global symmetries that they preserve. One global U(1), in addition to baryon number and electroweak hypercharge, remains unbroken after the inclusion of all operators required by standard model fermion phenomenology. An associated vacuum symmetry insures the vanishing of the first-family quark and charged-lepton masses in the absence of the family gauge interaction. If this U(1) symmetry is taken to be exact in the EFT, broken explicitly by only the QCD-induced anomaly, and if the breaking scale F is taken to lie in the range 10{sup 9}-10{sup 12} GeV, then the associated Nambu-Goldstone boson is a potential QCD axion.

  8. Gauge symmetry and non-Abelian topological sectors in a geometrically constrained model on the honeycomb lattice.

    PubMed

    Fendley, Paul; Moore, Joel E; Xu, Cenke

    2007-05-01

    We study a constrained statistical-mechanical model in two dimensions that has three useful descriptions. They are (i) the Ising model on the honeycomb lattice, constrained to have three up spins and three down spins on every hexagon, (ii) the three-color and fully packed loop model on the links of the honeycomb lattice, with loops around a single hexagon forbidden, and (iii) three Ising models on interleaved triangular lattices, with domain walls of the different Ising models not allowed to cross. Unlike the three-color model, the configuration space on the sphere or plane is connected under local moves. On higher-genus surfaces there are infinitely many dynamical sectors, labeled by a noncontractible set of nonintersecting loops. We demonstrate that at infinite temperature the transfer matrix admits an unusual structure related to a gauge symmetry for the same model on an anisotropic lattice. This enables us to diagonalize the original transfer matrix for up to 36 sites, finding an entropy per plaquette S/k{B} approximately 0.3661 ... centered and substantial evidence that the model is not critical. We also find the striking property that the eigenvalues of the transfer matrix on an anisotropic lattice are given in terms of Fibonacci numbers. We comment on the possibility of a topological phase, with infinite topological degeneracy, in an associated two-dimensional quantum model.

  9. Symmetry-broken states in a system of interacting bosons on a two-leg ladder with a uniform Abelian gauge field

    NASA Astrophysics Data System (ADS)

    Greschner, S.; Piraud, M.; Heidrich-Meisner, F.; McCulloch, I. P.; Schollwöck, U.; Vekua, T.

    2016-12-01

    We study the quantum phases of bosons with repulsive contact interactions on a two-leg ladder in the presence of a uniform Abelian gauge field. The model realizes many interesting states, including Meissner phases, vortex fluids, vortex lattices, charge density waves, and the biased-ladder phase. Our work focuses on the subset of these states that breaks a discrete symmetry. We use density matrix renormalization group simulations to demonstrate the existence of three vortex-lattice states at different vortex densities and we characterize the phase transitions from these phases into neighboring states. Furthermore, we provide an intuitive explanation of the chiral-current reversal effect that is tied to some of these vortex lattices. We also study a charge-density-wave state that exists at 1/4 particle filling at large interaction strengths and flux values close to half a flux quantum. By changing the system parameters, this state can transition into a completely gapped vortex-lattice Mott-insulating state. We elucidate the stability of these phases against nearest-neighbor interactions on the rungs of the ladder relevant for experimental realizations with a synthetic lattice dimension. A charge-density-wave state at 1/3 particle filling can be stabilized for flux values close to half a flux quantum and for very strong on-site interactions in the presence of strong repulsion on the rungs. Finally, we analytically describe the emergence of these phases in the low-density regime, and, in particular, we obtain the boundaries of the biased-ladder phase, i.e., the phase that features a density imbalance between the legs. We make contact with recent quantum-gas experiments that realized related models and discuss signatures of these quantum states in experimentally accessible observables.

  10. Families of Quintic Calabi Yau 3 Folds with Discrete Symmetries

    NASA Astrophysics Data System (ADS)

    Doran, Charles; Greene, Brian; Judes, Simon

    2008-06-01

    At special loci in their moduli spaces, Calabi Yau manifolds are endowed with discrete symmetries. Over the years, such spaces have been intensely studied and have found a variety of important applications. As string compactifications they are phenomenologically favored, and considerably simplify many important calculations. Mathematically, they provided the framework for the first construction of mirror manifolds, and the resulting rational curve counts. Thus, it is of significant interest to investigate such manifolds further. In this paper, we consider several unexplored loci within familiar families of Calabi Yau hypersurfaces that have large but unexpected discrete symmetry groups. By deriving, correcting, and generalizing a technique similar to that of Candelas, de la Ossa and Rodriguez Villegas, we find a calculationally tractable means of finding the Picard Fuchs equations satisfied by the periods of all 3 forms in these families. To provide a modest point of comparison, we then briefly investigate the relation between the size of the symmetry group along these loci and the number of nonzero Yukawa couplings. We include an introductory exposition of the mathematics involved, intended to be accessible to physicists, in order to make the discussion self contained.

  11. Optical Abelian lattice gauge theories

    SciTech Connect

    Tagliacozzo, L.; Celi, A.; Zamora, A.; Lewenstein, M.

    2013-03-15

    We discuss a general framework for the realization of a family of Abelian lattice gauge theories, i.e., link models or gauge magnets, in optical lattices. We analyze the properties of these models that make them suitable for quantum simulations. Within this class, we study in detail the phases of a U(1)-invariant lattice gauge theory in 2+1 dimensions, originally proposed by P. Orland. By using exact diagonalization, we extract the low-energy states for small lattices, up to 4 Multiplication-Sign 4. We confirm that the model has two phases, with the confined entangled one characterized by strings wrapping around the whole lattice. We explain how to study larger lattices by using either tensor network techniques or digital quantum simulations with Rydberg atoms loaded in optical lattices, where we discuss in detail a protocol for the preparation of the ground-state. We propose two key experimental tests that can be used as smoking gun of the proper implementation of a gauge theory in optical lattices. These tests consist in verifying the absence of spontaneous (gauge) symmetry breaking of the ground-state and the presence of charge confinement. We also comment on the relation between standard compact U(1) lattice gauge theory and the model considered in this paper. - Highlights: Black-Right-Pointing-Pointer We study the quantum simulation of dynamical gauge theories in optical lattices. Black-Right-Pointing-Pointer We focus on digital simulation of abelian lattice gauge theory. Black-Right-Pointing-Pointer We rediscover and discuss the puzzling phase diagram of gauge magnets. Black-Right-Pointing-Pointer We detail the protocol for time evolution and ground-state preparation in any phase. Black-Right-Pointing-Pointer We provide two experimental tests to validate gauge theory quantum simulators.

  12. The Lorentz extension as consequence of the family symmetry

    SciTech Connect

    Wang Haijun

    2008-05-15

    In this paper, we postulate an algebraic model to explain how the symmetry of three lepton species plays its role in the Lorentz extension. Inspired by the two-to-one mapping between the SL(2,C) group and the Lorentz group, we design a mapping between the SL(3,C) group, which displays the family symmetry, and a generalized Lorentz group. Following the conventional method, we apply the mapping results to the Dirac equation to discuss its transformation invariance, and it turns out that only when the vertex matrix {gamma}{sub {mu}} is extended to the combination c{sub 1}{gamma}{sub {mu}}+c{sub 2}{gamma}{sub 5}{gamma}{sub {mu}} can the Dirac-equation form be reserved. At the same time, we find that the Lorentz group has to be extended with an additional generator {gamma}{sub 5}. The generalized vertex matrix is helpful in understanding the axial-like form of weak interaction and the neutrino oscillations.

  13. Tribimaximal mixing, discrete family symmetries, and a conjecture connecting the quark and lepton mixing matrices

    NASA Astrophysics Data System (ADS)

    Low, Catherine I.; Volkas, Raymond R.

    2003-08-01

    Neutrino oscillation experiments (excluding the Liquid Scintillator Neutrino Detector experiment) suggest a tribimaximal form for the lepton mixing matrix. This form indicates that the mixing matrix is probably independent of the lepton masses, and suggests the action of an underlying discrete family symmetry. Using these hints, we conjecture that the contrasting forms of the quark and lepton mixing matrices may both be generated by such a discrete family symmetry. This idea is that the diagonalization matrices out of which the physical mixing matrices are composed have large mixing angles, which cancel out due to a symmetry when the CKM matrix is computed, but do not do so in the MNS case. However, in the cases where the Higgs bosons are singlets under the symmetry, and the family symmetry commutes with SU(2)L, we prove a no-go theorem: no discrete unbroken family symmetry can produce the required mixing patterns. We then suggest avenues for future research.

  14. Infrared Abelian dominance without Abelian projection

    NASA Astrophysics Data System (ADS)

    Raval, Haresh; Yajnik, Urjit A.

    2015-04-01

    Maximal Abelian gauge has been a particular choice to study dynamical generation of off-diagonal gluon masses in QCD. This gauge is a special case of an Abelian projection. Abelian dominance is characterized by off-diagonal gluons acquiring masses in the relevant phase. Here we propose a gauge condition which is quadratic in fields and which does not fall in the class of an Abelian projection. We explore the possible vacua of the gauge-fixed effective action of the theory and find evidence that ghost bilinears may be subject to condensation, which would signal acquisition of masses by off-diagonal gluons. Such a vacuum satisfies the requirement of Abelian dominance, providing an example of the hypothesis through a mechanism other than Abelian projection.

  15. On the use of Abelian point group symmetry in density-fitted local MP2 using various types of virtual orbitals

    SciTech Connect

    Köppl, Christoph; Werner, Hans-Joachim

    2015-04-28

    Electron correlation methods based on symmetry-adapted canonical Hartree-Fock orbitals can be speeded up significantly in the well known group theoretical manner, using the fact that integrals vanish unless the integrand is totally symmetric. In contrast to this, local electron correlation methods cannot benefit from such simplifications, since the localized molecular orbitals (LMOs) generally do not transform according to irreducible representations of the underlying point group symmetry. Instead, groups of LMOs become symmetry-equivalent and this can be exploited to accelerate local calculations. We describe an implementation of such a symmetry treatment for density-fitted local Møller-Plesset perturbation theory, using various types of virtual orbitals: Projected atomic orbitals, orbital specific virtuals, and pair natural orbitals. The savings by the symmetry treatment are demonstrated by calculations for several large molecules having different point group symmetries. Benchmarks for the parallel execution efficiency of our method are also presented.

  16. Virtually Abelian quantum walks

    NASA Astrophysics Data System (ADS)

    Mauro D'Ariano, Giacomo; Erba, Marco; Perinotti, Paolo; Tosini, Alessandro

    2017-01-01

    We study discrete-time quantum walks on Cayley graphs of non-Abelian groups, focusing on the easiest case of virtually Abelian groups. We present a technique to reduce the quantum walk to an equivalent one on an Abelian group with coin system having larger dimension. This method allows one to extend the notion of wave-vector to the virtually Abelian case and study analytically the walk dynamics. We apply the technique in the case of two quantum walks on virtually Abelian groups with planar Cayley graphs, finding the exact solution in terms of dispersion relation.

  17. Neutrinos and flavor symmetries

    SciTech Connect

    Tanimoto, Morimitsu

    2015-07-15

    We discuss the recent progress of flavor models with the non-Abelian discrete symmetry in the lepton sector focusing on the θ{sub 13} and CP violating phase. In both direct approach and indirect approach of the flavor symmetry, the non-vanishing θ{sub 13} is predictable. The flavor symmetry with the generalised CP symmetry can also predicts the CP violating phase. We show the phenomenological analyses of neutrino mixing for the typical flavor models.

  18. Generalized gauge U(1) family symmetry for quarks and leptons

    NASA Astrophysics Data System (ADS)

    Kownacki, Corey; Ma, Ernest; Pollard, Nicholas; Zakeri, Mohammadreza

    2017-03-01

    If the standard model of quarks and leptons is extended to include three singlet right-handed neutrinos, then the resulting fermion structure admits an infinite number of anomaly-free solutions with just one simple constraint. Well-known examples satisfying this constraint are B- L, Lμ-Lτ, B- 3Lτ, etc. We derive this simple constraint, and discuss two new examples which offer some insights to the structure of mixing among quark and lepton families, together with their possible verification at the Large Hadron Collider.

  19. The Abelian heterotic conifold

    NASA Astrophysics Data System (ADS)

    Halmagyi, Nick; Israël, Dan; Svanes, Eirik

    2016-07-01

    We study heterotic supergravity on the conifold and its ℤ 2 orbifold with Abelian gauge fields and three-form flux. By taking a limit of large five brane charge, we are able suppress non-linear curvature corrections and construct exact supersymmetric solutions. At large distances, these solutions are generically locally Ricci-flat, have a magnetic flux through the two-sphere at infinity as well as non-zero five-brane charge. For a given flux, our family of solutions has three real parameters, the size of the pair of two spheres in the IR and the dilaton zero mode. We present an explicit analytic solution for a decoupled near horizon region which is not asymptotically locally Ricci-flat and where for a given flux, the size of the cycles is frozen and the only parameter is the dilaton zero mode. We also present an exactly solvable worldsheet CFT for this near horizon region. When one of the two cycles has vanishing size, the near horizon region no longer exists but nonetheless we obtain a solution on the (unorbifolded) resolved conifold.

  20. Non-Abelian bubbles in microstate geometries

    NASA Astrophysics Data System (ADS)

    Ramírez, Pedro F.

    2016-11-01

    We find the first smooth bubbling microstate geometries with non-Abelian fields. The solutions constitute an extension of the BPS three-charge smooth microstates. These consist in general families of regular supersymmetric solutions with non-trivial topology, i.e. bubbles, of {N}=d , d = 5 Super-Einstein-Yang-Mills theory, having the asymptotic charges of a black hole or black ring but with no horizon. The non-Abelian fields make their presence at the very heart of the microstate structure: the physical size of the bubbles is affected by the non-Abelian topological charge they carry, which combines with the Abelian flux threading the bubbles to hold them up. Interestingly the non-Abelian fields carry a set of adjustable continuous parameters that do not alter the asymptotics of the solutions but modify the local geometry. This feature can be used to obtain a classically infinite number of microstate solutions with the asymptotics of a single black hole or black ring.

  1. On spectroscopy for a whole Abelian model

    SciTech Connect

    Chauca, J.; Doria, R.

    2012-09-24

    Postulated on the whole meaning a whole abelian gauge symmetry is being introduced. Various physical areas as complexity, statistical mechanics, quantum mechanics are partially supporting this approach where the whole is at origin. However, the reductionist crisis given by quark confinement definitely sustains this insight. It says that fundamental parts can not be seen isolatedely. Consequently, there is an experimental situation where the parts should be substituted by something more. This makes us to look for writing the wholeness principle under gauge theory. For this, one reinterprets the gauge parameter where instead of compensating fields it is organizing a systemic gauge symmetry. Now, it introduces a fields set {l_brace}A{sub {mu}I}{r_brace} rotating under a common gauge symmetry. Thus, given a fields collection {l_brace}A{sub {mu}I}{r_brace} as origin, the effort at this work is to investigate on its spectroscopy. Analyze for the abelian case the correspondent involved quanta. Understand that for a whole model diversity replaces elementarity. Derive the associated quantum numbers as spin, mass, charge, discrete symmetries in terms of such systemic symmetry. Observe how the particles diversity is manifested in terms of wholeness.

  2. Bell diagonal states with maximal Abelian symmetry

    SciTech Connect

    Chruscinski, Dariusz; Kossakowski, Andrzej

    2010-12-15

    We provide a simple class of 2-qudit states for which one is able to formulate necessary and sufficient conditions for separability. As a by-product, we generalize the well-known construction provided by Horodecki et al. [Phys. Rev. Lett. 82, 1056 (1999)] for d=3. It is hoped that these states with known separability and entanglement properties may be used to test various notions in entanglement theory.

  3. Gravitating non-Abelian cosmic strings

    NASA Astrophysics Data System (ADS)

    de Pádua Santos, Antônio; Bezerra de Mello, Eugênio R.

    2015-08-01

    In this paper, we study regular cosmic string solutions of the non-Abelian Higgs model coupled with gravity. In order to develop this analysis, we constructed a set of coupled non-linear differential equations. Because there is no closed solution for this set of equations, we solve it numerically. The solutions we are interested in asymptote to a flat spacetime with a planar angle deficit. The model under consideration presents two bosonic sectors, besides the non-Abelian gauge field. The two bosonic sectors may present a direct coupling, so we investigate the relevance of this coupling on the system, specifically in the linear energy density of the string and on the planar angle deficit. We also analyze the behaviors of these quantities as a function of the energy scale where the gauge symmetry is spontaneously broken.

  4. Discrete flavour symmetries from the Heisenberg group

    NASA Astrophysics Data System (ADS)

    Floratos, E. G.; Leontaris, G. K.

    2016-04-01

    Non-abelian discrete symmetries are of particular importance in model building. They are mainly invoked to explain the various fermion mass hierarchies and forbid dangerous superpotential terms. In string models they are usually associated to the geometry of the compactification manifold and more particularly to the magnetised branes in toroidal compactifications. Motivated by these facts, in this note we propose a unified framework to construct representations of finite discrete family groups based on the automorphisms of the discrete and finite Heisenberg group. We focus in particular, on the PSL2 (p) groups which contain the phenomenologically interesting cases.

  5. Non-Abelian statistics of vortices with non-Abelian Dirac fermions.

    PubMed

    Yasui, Shigehiro; Hirono, Yuji; Itakura, Kazunori; Nitta, Muneto

    2013-05-01

    We extend our previous analysis on the exchange statistics of vortices having a single Dirac fermion trapped in each core to the case where vortices trap two Dirac fermions with U(2) symmetry. Such a system of vortices with non-Abelian Dirac fermions appears in color superconductors at extremely high densities and in supersymmetric QCD. We show that the exchange of two vortices having doublet Dirac fermions in each core is expressed by non-Abelian representations of a braid group, which is explicitly verified in the matrix representation of the exchange operators when the number of vortices is up to four. We find that the result contains the matrices previously obtained for the vortices with a single Dirac fermion in each core as a special case. The whole braid group does not immediately imply non-Abelian statistics of identical particles because it also contains exchanges between vortices with different numbers of Dirac fermions. However, we find that it does contain, as its subgroup, genuine non-Abelian statistics for the exchange of the identical particles, that is, vortices with the same number of Dirac fermions. This result is surprising compared with conventional understanding because all Dirac fermions are defined locally at each vortex, unlike the case of Majorana fermions for which Dirac fermions are defined nonlocally by Majorana fermions located at two spatially separated vortices.

  6. Topologies on Abelian Groups

    NASA Astrophysics Data System (ADS)

    Zelenyuk, E. G.; Protasov, I. V.

    1991-04-01

    A filter phi on an abelian group G is called a T-filter if there exists a Hausdorff group topology under which phi converges to zero. G{phi} will denote the group G with the largest topology among those making phi converge to zero. This method of defining a group topology is completely equivalent to the definition of an abstract group by defining relations. We shall obtain characterizations of T-filters and of T-sequences; among these, we shall pay particular attention to T-sequences on the integers. The method of T-sequences will be used to construct a series of counterexamples for several open problems in topological algebra. For instance there exists, on every infinite abelian group, a topology distinguishing between sequentiality and the Fréchet-Urysohn property (this solves a problem posed by V.I. Malykhin) we also find a topology on the group of integers admitting no nontrivial continuous character, thus solving a problem of Nienhuys. We show also that on every infinite abelian group there exists a free ultrafilter which is not a T-ultrafilter.

  7. Symmetry constraints on many-body localization

    NASA Astrophysics Data System (ADS)

    Potter, Andrew C.; Vasseur, Romain

    2016-12-01

    We derive general constraints on the existence of many-body localized (MBL) phases in the presence of global symmetries, and show that MBL is not possible with symmetry groups that protect multiplets (e.g., all non-Abelian symmetry groups). Based on simple representation theoretic considerations, we derive general Mermin-Wagner-type principles governing the possible alternative fates of nonequilibrium dynamics in isolated, strongly disordered quantum systems. Our results rule out the existence of MBL symmetry-protected topological phases with non-Abelian symmetry groups, as well as time-reversal symmetry-protected electronic topological insulators, and in fact all fermion topological insulators and superconductors in the 10-fold way classification. Moreover, extending our arguments to systems with intrinsic topological order, we rule out MBL phases with non-Abelian anyons as well as certain classes of symmetry-enriched topological orders.

  8. Abelian embedding formulation of the Stueckelberg model and its power-counting renormalizable extension

    NASA Astrophysics Data System (ADS)

    Quadri, Andrea

    2006-03-01

    We elucidate the geometry of the polynomial formulation of the non-Abelian Stueckelberg mechanism. We show that a natural off-shell nilpotent Becchi-Rouet-Stora-Tyutin (BRST) differential exists allowing to implement the constraint on the σ field by means of BRST techniques. This is achieved by extending the ghost sector by an additional U(1) factor (Abelian embedding). An important consequence is that a further BRST-invariant but not gauge-invariant mass term can be written for the non-Abelian gauge fields. As all versions of the Stueckelberg theory, also the Abelian embedding formulation yields a nonpower-counting renormalizable theory in D=4. We then derive its natural power-counting renormalizable extension and show that the physical spectrum contains a physical massive scalar particle. Physical unitarity is also established. This model implements the spontaneous symmetry breaking in the Abelian embedding formalism.

  9. Spontaneous magnetization through non-Abelian vortex formation in rotating dense quark matter

    NASA Astrophysics Data System (ADS)

    Vinci, Walter; Cipriani, Mattia; Nitta, Muneto

    2012-10-01

    When a color superconductor of high density QCD is rotating, superfluid vortices are inevitably created along the rotation axis. In the color-flavor locked phase realized at the asymptotically large chemical potential, there appear non-Abelian vortices carrying both circulations of superfluid and color magnetic fluxes. A family of solutions has a degeneracy characterized by the Nambu-Goldstone modes CP2, associated with the color-flavor locked symmetry spontaneously broken in the vicinity of the vortex. In this paper, we study electromagnetic coupling of the non-Abelian vortices and find that the degeneracy is removed with the induced effective potential. We obtain one stable vortex solution and a family of metastable vortex solutions, both of which carry ordinary magnetic fluxes in addition to color magnetic fluxes. We discuss quantum mechanical decay of the metastable vortices by quantum tunneling and compare the effective potential with the other known potentials, the quantum mechanically induced potential and the potential induced by the strange quark mass.

  10. D{sub 6} family symmetry and cold dark matter at CERN LHC

    SciTech Connect

    Kajiyama, Yuji; Kubo, Jisuke; Okada, Hiroshi

    2007-02-01

    We consider a nonsupersymmetric extension of the standard model with a family symmetry based on D{sub 6}xZ{sub 2}xZ{sub 2}, where one of Z{sub 2}'s is exactly conserved. This Z{sub 2} forbids the tree-level neutrino masses and simultaneously ensures the stability of cold dark matter candidates. From the assumption that cold dark matter is fermionic we can single out the D{sub 6} singlet right-handed neutrino as the best cold dark matter candidate. We find that an inert charged Higgs with a mass between 300 and 750 GeV decays mostly into an electron (or a positron) with a large missing energy, where the missing energy is carried away by the cold dark matter candidate. This will be a clean signal at LHC.

  11. Active error correction for Abelian and non-Abelian anyons

    NASA Astrophysics Data System (ADS)

    Wootton, James R.; Hutter, Adrian

    2016-02-01

    We consider a class of decoding algorithms that are applicable to error correction for both Abelian and non-Abelian anyons. This class includes multiple algorithms that have recently attracted attention, including the Bravyi-Haah RG decoder and variants thereof. They are applied to both the problem of correcting a single burst of errors (with perfect syndrome measurements) and active correction of continuously occurring errors (with noisy syndrome measurements). For Abelian models we provide a threshold proof in both cases for all decoders in this class, showing that they can arbitrarily suppress errors when the noise rate is under a finite threshold. For non-Abelian models such a proof is found for a single burst of errors. The reasons why the proof cannot be applied to the case of continuously occurring errors are discussed.

  12. Theory of nodal s±-wave pairing symmetry in the Pu-based 115 superconductor family

    SciTech Connect

    Das, Tanmoy; Zhu, Jian -Xin; Graf, Matthias J.

    2015-02-27

    The spin-fluctuation mechanism of superconductivity usually results in the presence of gapless or nodal quasiparticle states in the excitation spectrum. Nodal quasiparticle states are well established in copper-oxide, and heavy-fermion superconductors, but not in iron-based superconductors. Here, we study the pairing symmetry and mechanism of a new class of plutonium-based high-Tc superconductors and predict the presence of a nodal s⁺⁻ wave pairing symmetry in this family. Starting from a density-functional theory (DFT) based electronic structure calculation we predict several three-dimensional (3D) Fermi surfaces in this 115 superconductor family. We identify the dominant Fermi surface “hot-spots” in the inter-band scattering channel, which are aligned along the wavevector Q = (π, π, π), where degeneracy could induce sign-reversal of the pairing symmetry. Our calculation demonstrates that the s⁺⁻ wave pairing strength is stronger than the previously thought d-wave pairing; and more importantly, this pairing state allows for the existence of nodal quasiparticles. Finally, we predict the shape of the momentum- and energy-dependent magnetic resonance spectrum for the identification of this pairing symmetry.

  13. Theory of nodal s±-wave pairing symmetry in the Pu-based 115 superconductor family

    DOE PAGES

    Das, Tanmoy; Zhu, Jian -Xin; Graf, Matthias J.

    2015-02-27

    The spin-fluctuation mechanism of superconductivity usually results in the presence of gapless or nodal quasiparticle states in the excitation spectrum. Nodal quasiparticle states are well established in copper-oxide, and heavy-fermion superconductors, but not in iron-based superconductors. Here, we study the pairing symmetry and mechanism of a new class of plutonium-based high-Tc superconductors and predict the presence of a nodal s⁺⁻ wave pairing symmetry in this family. Starting from a density-functional theory (DFT) based electronic structure calculation we predict several three-dimensional (3D) Fermi surfaces in this 115 superconductor family. We identify the dominant Fermi surface “hot-spots” in the inter-band scattering channel,more » which are aligned along the wavevector Q = (π, π, π), where degeneracy could induce sign-reversal of the pairing symmetry. Our calculation demonstrates that the s⁺⁻ wave pairing strength is stronger than the previously thought d-wave pairing; and more importantly, this pairing state allows for the existence of nodal quasiparticles. Finally, we predict the shape of the momentum- and energy-dependent magnetic resonance spectrum for the identification of this pairing symmetry.« less

  14. Theory of nodal s±-wave pairing symmetry in the Pu-based 115 superconductor family

    PubMed Central

    Das, Tanmoy; Zhu, Jian-Xin; Graf, Matthias J.

    2015-01-01

    The spin-fluctuation mechanism of superconductivity usually results in the presence of gapless or nodal quasiparticle states in the excitation spectrum. Nodal quasiparticle states are well established in copper-oxide, and heavy-fermion superconductors, but not in iron-based superconductors. Here, we study the pairing symmetry and mechanism of a new class of plutonium-based high-Tc superconductors and predict the presence of a nodal s+− wave pairing symmetry in this family. Starting from a density-functional theory (DFT) based electronic structure calculation we predict several three-dimensional (3D) Fermi surfaces in this 115 superconductor family. We identify the dominant Fermi surface “hot-spots” in the inter-band scattering channel, which are aligned along the wavevector Q = (π, π, π), where degeneracy could induce sign-reversal of the pairing symmetry. Our calculation demonstrates that the s+− wave pairing strength is stronger than the previously thought d-wave pairing; and more importantly, this pairing state allows for the existence of nodal quasiparticles. Finally, we predict the shape of the momentum- and energy-dependent magnetic resonance spectrum for the identification of this pairing symmetry. PMID:25721375

  15. Feynman rules for a whole Abelian model

    SciTech Connect

    Chauca, J.; Doria, R.; Soares, W.

    2012-09-24

    Feynman rules for an abelian extension of gauge theories are discussed and explicitly derived. Vertices with three and four abelian gauge bosons are obtained. A discussion on an eventual structure for the photon is presented.

  16. Two-component Abelian sandpile models.

    PubMed

    Alcaraz, F C; Pyatov, P; Rittenberg, V

    2009-04-01

    In one-component Abelian sandpile models, the toppling probabilities are independent quantities. This is not the case in multicomponent models. The condition of associativity of the underlying Abelian algebras imposes nonlinear relations among the toppling probabilities. These relations are derived for the case of two-component quadratic Abelian algebras. We show that Abelian sandpile models with two conservation laws have only trivial avalanches.

  17. Automata representation for Abelian groups

    NASA Astrophysics Data System (ADS)

    Fong, Wan Heng; Gan, Yee Siang; Sarmin, Nor Haniza; Turaev, Sherzod

    2013-04-01

    A finite automaton is one of the classic models of recognition devices, which is used to determine the type of language a string belongs to. A string is said to be recognized by a finite automaton if the automaton "reads" the string from the left to the right starting from the initial state and finishing at a final state. Another type of automata which is a counterpart of sticker systems, namely Watson-Crick automata, is finite automata which can scan the double-stranded tapes of DNA strings using the complimentary relation. The properties of groups have been extended for the recognition of finite automata over groups. In this paper, two variants of automata, modified deterministic finite automata and modified deterministic Watson-Crick automata are used in the study of Abelian groups. Moreover, the relation between finite automata diagram over Abelian groups and the Cayley table is introduced. In addition, some properties of Abelian groups are presented in terms of automata.

  18. Introducing Abelian Groups Using Bullseyes and Jenga

    ERIC Educational Resources Information Center

    Smith, Michael D.

    2016-01-01

    The purpose of this article is to share a new approach for introducing students to the definition and standard examples of Abelian groups. The definition of an Abelian group is revised to include six axioms. A bullseye provides a way to visualize elementary examples and non-examples of Abelian groups. An activity based on the game of Jenga is used…

  19. BRST symmetry in the Schrödinger picture

    NASA Astrophysics Data System (ADS)

    Lee, Hyuk-Jae; Yee, Jae Hyung

    1993-05-01

    We show that the effective Lagrangian including the gauge-fixing and ghost terms of the non-Abelian gauge theories can be derived in the functional Schrödinger picture by using the residual symmetry of the gauge-fixed Lagrangian. This residual gauge symmetry is shown to be equivalent to the well-known Becchi-Rouet-Stora-Tyutin symmetry.

  20. Importance of C2 symmetry for the device performance of a newly synthesized family of fused-ring thiophenes

    PubMed Central

    He, Mingqian; Li, Jianfeng; Tandia, Adama; Sorensen, Michael; Zhang, Feixia; Fong, Hon Hang; Pozdin, Vladimir A.; Smilgies, Detlef-M.; Malliaras, George G.

    2010-01-01

    We investigated the relationship between molecular structure and field-effect hole mobility in a family of fused-ring polythiophene copolymers that we designed recently. The results suggest that a repeat unit that possesses a C2 axis perpendicular to the conjugation plane is important to achieve a high-mobility. Our finding is supported by a review of literature data: Many polymer semiconductors showing a hole or electron mobility >0.1 cm2/V·s feature a repeat unit with C2 symmetry; however exceptions have been found from some push – pull polymer structures. PMID:20526456

  1. Vortex states in a non-Abelian magnetic field

    NASA Astrophysics Data System (ADS)

    Nikolić, Predrag

    2016-08-01

    A type-II superconductor survives in an external magnetic field by admitting an Abrikosov lattice of quantized vortices. This is an imprint of the Aharonov-Bohm effect created by the Abelian U(1) gauge field. The simplest non-Abelian analog of such a gauge field, which belongs to the SU(2) symmetry group, can be found in topological insulators. Here we discover a superconducting ground state with a lattice of SU(2) vortices in a simple two-dimensional model that presents an SU(2) "magnetic" field (invariant under time reversal) to attractively interacting fermions. The model directly captures the correlated topological insulator quantum well, and approximates one channel for instabilities on the Kondo topological insulator surface. Due to its simplicity, the model might become amenable to cold atom simulations in the foreseeable future. The vitality of low-energy vortex states born out of SU(2) magnetic fields is promising for the creation of incompressible vortex liquids with non-Abelian fractional excitations.

  2. Discretized Abelian Chern-Simons gauge theory on arbitrary graphs

    NASA Astrophysics Data System (ADS)

    Sun, Kai; Kumar, Krishna; Fradkin, Eduardo

    2015-09-01

    In this paper, we show how to discretize the Abelian Chern-Simons gauge theory on generic planar lattices/graphs (with or without translational symmetries) embedded in arbitrary two-dimensional closed orientable manifolds. We find that, as long as a one-to-one correspondence between vertices and faces can be defined on the graph such that each face is paired up with a neighboring vertex (and vice versa), a discretized Abelian Chern-Simons theory can be constructed consistently. We further verify that all the essential properties of the Chern-Simons gauge theory are preserved in the discretized setup. In addition, we find that the existence of such a one-to-one correspondence is not only a sufficient condition for discretizing a Chern-Simons gauge theory but, for the discretized theory to be nonsingular and to preserve some key properties of the topological field theory, this correspondence is also a necessary one. A specific example will then be provided, in which we discretize the Abelian Chern-Simons gauge theory on a tetrahedron.

  3. Ermakov's Superintegrable Toy and Nonlocal Symmetries

    NASA Astrophysics Data System (ADS)

    Leach, P. G. L.; Karasu Kalkanli, A.; Nucci, M. C.; Andriopoulos, K.

    2005-11-01

    We investigate the symmetry properties of a pair of Ermakov equations. The system is superintegrable and yet possesses only three Lie point symmetries with the algebra sl(2, R). The number of point symmetries is insufficient and the algebra unsuitable for the complete specification of the system. We use the method of reduction of order to reduce the nonlinear fourth-order system to a third-order system comprising a linear second-order equation and a conservation law. We obtain the representation of the complete symmetry group from this system. Four of the required symmetries are nonlocal and the algebra is the direct sum of a one-dimensional Abelian algebra with the semidirect sum of a two-dimensional solvable algebra with a two-dimensional Abelian algebra. The problem illustrates the difficulties which can arise in very elementary systems. Our treatment demonstrates the existence of possible routes to overcome these problems in a systematic fashion.

  4. From physical symmetries to emergent gauge symmetries

    NASA Astrophysics Data System (ADS)

    Barceló, Carlos; Carballo-Rubio, Raúl; Di Filippo, Francesco; Garay, Luis J.

    2016-10-01

    Gauge symmetries indicate redundancies in the description of the relevant degrees of freedom of a given field theory and restrict the nature of observable quantities. One of the problems faced by emergent theories of relativistic fields is to understand how gauge symmetries can show up in systems that contain no trace of these symmetries at a more fundamental level. In this paper we start a systematic study aimed to establish a satisfactory mathematical and physical picture of this issue, dealing first with abelian field theories. We discuss how the trivialization, due to the decoupling and lack of excitation of some degrees of freedom, of the Noether currents associated with physical symmetries leads to emergent gauge symmetries in specific situations. An example of a relativistic field theory of a vector field is worked out in detail in order to make explicit how this mechanism works and to clarify the physics behind it. The interplay of these ideas with well-known results of importance to the emergent gravity program, such as the Weinberg-Witten theorem, are discussed.

  5. Non-abelian T-duality and consistent truncations in type-II supergravity

    NASA Astrophysics Data System (ADS)

    Itsios, Georgios; Lozano, Yolanda; Colgáin, Eoin Ó.; Sfetsos, Konstadinos

    2012-08-01

    For a general class of SO(4) symmetric backgrounds in type-II supergravity, we show that the action of non-Abelian T-duality can be described via consistent truncation to seven dimensional theories with seemingly massive modes. As such, any solution to these theories uplifts to both massive type IIA and IIB supergravities presenting an invertible map between the two. For supersymmetric backgrounds, we show that for spinors transforming under SO(4) the non-Abelian T-duality transformation breaks the original supersymmetry by half. We use these mappings to generate the non-Abelian T-duals of the maximally supersymmetric pp-wave, the Lin, Lunin, Maldacena geometries and spacetimes with Lifshitz symmetry.

  6. Unification of gauge, family, and flavor symmetries illustrated in gauged SU(12) models

    DOE PAGES

    Albright, Carl H.; Feger, Robert P.; Kephart, Thomas W.

    2016-04-25

    In this study, to explain quark and lepton masses and mixing angles, one has to extend the standard model, and the usual practice is to put the quarks and leptons into irreducible representations of discrete groups. We argue that discrete flavor symmetries (and their concomitant problems) can be avoided if we extend the gauge group. In the framework of SU(12) we give explicit examples of models having varying degrees of predictability obtained by scanning over groups and representations and identifying cases with operators contributing to mass and mixing matrices that need little fine- tuning of prefactors. Fitting with quark andmore » lepton masses run to the GUT scale and known mixing angles allows us to make predictions for the neutrino masses and hierarchy, the octant of the atmospheric mixing angle, leptonic CP violation, Majorana phases, and the effective mass observed in neutrinoless double beta decay.« less

  7. Unification of gauge, family, and flavor symmetries illustrated in gauged SU(12) models

    SciTech Connect

    Albright, Carl H.; Feger, Robert P.; Kephart, Thomas W.

    2016-04-25

    In this study, to explain quark and lepton masses and mixing angles, one has to extend the standard model, and the usual practice is to put the quarks and leptons into irreducible representations of discrete groups. We argue that discrete flavor symmetries (and their concomitant problems) can be avoided if we extend the gauge group. In the framework of SU(12) we give explicit examples of models having varying degrees of predictability obtained by scanning over groups and representations and identifying cases with operators contributing to mass and mixing matrices that need little fine- tuning of prefactors. Fitting with quark and lepton masses run to the GUT scale and known mixing angles allows us to make predictions for the neutrino masses and hierarchy, the octant of the atmospheric mixing angle, leptonic CP violation, Majorana phases, and the effective mass observed in neutrinoless double beta decay.

  8. Non-Abelian gauge fields

    NASA Astrophysics Data System (ADS)

    Gerbier, Fabrice; Goldman, Nathan; Lewenstein, Maciej; Sengstock, Klaus

    2013-07-01

    Building a universal quantum computer is a central goal of emerging quantum technologies, which has the potential to revolutionize science and technology. Unfortunately, this future does not seem to be very close at hand. However, quantum computers built for a special purpose, i.e. quantum simulators , are currently developed in many leading laboratories. Many schemes for quantum simulation have been proposed and realized using, e.g., ultracold atoms in optical lattices, ultracold trapped ions, atoms in arrays of cavities, atoms/ions in arrays of traps, quantum dots, photonic networks, or superconducting circuits. The progress in experimental implementations is more than spectacular. Particularly interesting are those systems that simulate quantum matter evolving in the presence of gauge fields. In the quantum simulation framework, the generated (synthetic) gauge fields may be Abelian, in which case they are the direct analogues of the vector potentials commonly associated with magnetic fields. In condensed matter physics, strong magnetic fields lead to a plethora of fascinating phenomena, among which the most paradigmatic is perhaps the quantum Hall effect. The standard Hall effect consists in the appearance of a transverse current, when a longitudinal voltage difference is applied to a conducting sample. For quasi-two-dimensional semiconductors at low temperatures placed in very strong magnetic fields, the transverse conductivity, the ratio between the transverse current and the applied voltage, exhibits perfect and robust quantization, independent for instance of the material or of its geometry. Such an integer quantum Hall effect, is now understood as a deep consequence of underlying topological order. Although such a system is an insulator in the bulk, it supports topologically robust edge excitations which carry the Hall current. The robustness of these chiral excitations against backscattering explains the universality of the quantum Hall effect. Another

  9. New Solutions for Non-Abelian Cosmic Strings

    NASA Astrophysics Data System (ADS)

    Hindmarsh, Mark; Rummukainen, Kari; Weir, David J.

    2016-12-01

    We study the properties of classical vortex solutions in a non-Abelian gauge theory. A system of two adjoint Higgs fields breaks the SU(2) gauge symmetry to Z2 , producing 't Hooft-Polyakov monopoles trapped on cosmic strings, termed beads; there are two charges of monopole and two degenerate string solutions. The strings break an accidental discrete Z2 symmetry of the theory, explaining the degeneracy of the ground state. Further symmetries of the model, not previously appreciated, emerge when the masses of the two adjoint Higgs fields are degenerate. The breaking of the enlarged discrete symmetry gives rise to additional string solutions and splits the monopoles into four types of "semipole": kink solutions that interpolate between the string solutions, classified by a complex gauge-invariant magnetic flux and a Z4 charge. At special values of the Higgs self-couplings, the accidental symmetry broken by the string is continuous, giving rise to supercurrents on the strings. The SU(2) theory can be embedded in a wide class of grand unified theories (GUTs), including SO(10). We argue that semipoles and supercurrents are generic on GUT strings.

  10. Symmetries and vanishing couplings in string-derived low energy effective field theory

    SciTech Connect

    Kobayashi, Tatsuo

    2012-07-27

    We study 4D low-energy effective field theory, derived from heterotic string theory on the orbifolds. In particular, we study Abelian and non-Abelian discrete symmetries and their anomalies. Furthermore, stringy computations also provide with stringy coupling selection rules.

  11. Tunable electron interactions and robust non-Abelian quantum Hall states in graphene and other Dirac materials

    NASA Astrophysics Data System (ADS)

    Abanin, Dmitry

    2013-03-01

    Discovery of the fractional quantum Hall effect inspired a concept of quasiparticles with non-Abelian exchange statistics. However, a major limitation for experimental studies of non-Abelian quasiparticles in traditional GaAs-based 2d systems is their lack of tunability: the effective electron interactions in such systems are fixed at values which make non-Abelian states either absent of very fragile. Therefore it is desirable to find alternative, tunable 2d systems that host robust non-Abelian quantum Hall states. In this talk, we will discuss the phase diagram of fractional quantum Hall states in recently discovered 2d Dirac materials (graphene, bilayer graphene, topological insulators). We will show that the effective interactions in these materials can be naturally tuned in a broad range, in contrast to GaAs. This tunability is achieved by external fields that control the mass gap of Dirac fermions. Alternatively, the effective interactions can be controlled by engineering the dielectric environment of the 2d Dirac electron gas. We will demonstrate that the tunability of interactions in Dirac materials allows one to stabilize non-Abelian states, as well as to drive phase transitions between various correlated phases (quantum Hall states, Fermi-liquid-like states, and states with broken translational symmetry) in a controlled manner. Connecting to experiments, we will argue that a very promising candidate material for tuning interactions and stabilizing non-Abelian states is bilayer graphene, where the gap can be naturally controlled by perpendicular electric field. Our study provides a realistic route towards engineering robust fractional and non-Abelian quantum Hall states in graphene and other Dirac materials. This work was supported by DOE Grant DE-SC0002140Discovery of the fractional quantum Hall effect inspired a concept of quasiparticles with non-Abelian exchange statistics. However, a major limitation for experimental studies of non-Abelian

  12. Spontaneous breaking of the BRST symmetry in the ABJM theory

    NASA Astrophysics Data System (ADS)

    Faizal, Mir; Upadhyay, Sudhaker

    2014-09-01

    In this paper, we will analyze the ghost condensation in the ABJM theory. We will perform our analysis in N=1 superspace. We show that in the Delbourgo-Jarvis-Baulieu-Thierry-Mieg gauge the spontaneous breaking of BRST symmetry can occur in the ABJM theory. This spontaneous breaking of BRST symmetry is caused by ghost-anti-ghost condensation. We will also show that in the ABJM theory, the ghost-anti-ghost condensates remain present in the modified abelian gauge. Thus, the spontaneous breaking of BRST symmetry in ABJM theory can even occur in the modified abelian gauge.

  13. Family nonuniversal U(1){sup '} gauge symmetries and b{yields}s transitions

    SciTech Connect

    Barger, Vernon; Everett, Lisa; Jiang Jing; Langacker, Paul; Liu Tao; Wagner, Carlos E. M.

    2009-09-01

    We present a correlated analysis for the {delta}B=1, 2 processes which occur via b{yields}s transitions within models with a family nonuniversal U(1){sup '}. We take a model-independent approach and only require family universal charges for the first and second generations and small fermion mixing angles. The results of our analysis show that within this class of models, the anomalies in B{sub s}-B{sub s} mixing and the time-dependent CP asymmetries of the penguin-dominated B{sub d}{yields}({pi},{phi},{eta}{sup '},{rho},{omega},f{sub 0})K{sub S} decays can be accommodated.

  14. Family non-universal U(1)' gauge symmetries and b {r_arrow} s transitions.

    SciTech Connect

    Barger, V.; Everett, L.; Jiang, J.; Langacker, P.; Liu, T.; Wagner, C .E. M.; High Energy Physics; Univ. of Chicago; Univ. of Wisconsin at Madison; Inst. for Advanced Study

    2009-01-01

    We present a correlated analysis for the {Delta}B = 1, 2 processes which occur via b {yields} s transitions within models with a family nonuniversal U(1){prime}. We take a model-independent approach and only require family universal charges for the first and second generations and small fermion mixing angles. The results of our analysis show that within this class of models, the anomalies in B{sub s}-B{sub s}{sup -} mixing and the time-dependent CP asymmetries of the penguin-dominated B{sub d} {yields} ({pi},{psi},{eta}{prime},{rho},{omega},f{sub 0})K{sub S} decays can be accommodated.

  15. Double Weyl points and Fermi arcs of topological semimetals in non-Abelian gauge potentials

    NASA Astrophysics Data System (ADS)

    Lepori, L.; Fulga, I. C.; Trombettoni, A.; Burrello, M.

    2016-11-01

    We study the effect of a non-Abelian SU(2) gauge potential mimicking spin-orbit coupling on the topological semimetal induced by a magnetic field having π flux per plaquette and acting on fermions in a three-dimensional (3D) cubic lattice. The Abelian π -flux term gives rise to a spectrum characterized by Weyl points. The non-Abelian term is chosen to be gauge equivalent to both a 2D Rashba and a Dresselhaus spin-orbit coupling. As a result of the anisotropic nature of the coupling between spin and momentum and of the presence of a C4 rotation symmetry, when the non-Abelian part is turned on, the Weyl points assume a quadratic dispersion along two directions and constitute double monopoles for the Berry curvature. We examine the main features of this system both analytically and numerically, focusing on its gapless surface modes, the so-called Fermi arcs. We discuss the stability of the system under confining hard-wall and harmonic potentials, relevant for the implementation in ultracold atom settings, and the effect of rotation symmetry breaking.

  16. Abelian and non-Abelian bosonization: The operator solution of the WZW. sigma. model

    SciTech Connect

    do Amaral, R.L.P.G. ); Stephany Ruiz, J.E. )

    1991-03-15

    The complete equivalence between the Abelian and the non-Abelian bosonization formalisms for the treatment of SU({ital N}) fermions in two dimensions is analyzed and the operator solution of the Wess-Zumino-Witten nonlinear {sigma} model, written in terms of the scalar fields of the non-Abelian construction, is obtained. The importance of the order and disorder operators is stressed. In particular, they are used to show that an adequate reinterpretation of Mandelstam's formula gives the fermion representation in the non-Abelian bosonization formalism.

  17. Conformal field theory approach to Abelian and non-Abelian quantum Hall quasielectrons.

    PubMed

    Hansson, T H; Hermanns, M; Regnault, N; Viefers, S

    2009-04-24

    The quasiparticles in quantum Hall liquids carry fractional charge and obey fractional quantum statistics. Of particular recent interest are those with non-Abelian statistics, since their braiding properties could, in principle, be used for robust coding of quantum information. There is already a good theoretical understanding of quasiholes in both Abelian and non-Abelian quantum Hall states. Here we develop conformal field theory methods that allow for an equally precise description of quasielectrons and explicitly construct two- and four-quasielectron excitations of the non-Abelian Moore-Read state.

  18. On S-Duality in Abelian Gauge Theory

    NASA Astrophysics Data System (ADS)

    Witten, Edward

    1995-09-01

    U(1) gauge theory on R4 is known to possess an electric-magnetic duality symmetry that inverts the coupling constant and extends to an action of SL(2,Z). In this paper, the duality is studied on a general four-manifold and it is shown that the partition function is not a modular-invariant function but transforms as a modular form. This result plays an essential role in determining a new low-energy interaction that arises when N=2 supersymmetric Yang-Mills theory is formulated on a four-manifold; the determination of this interaction gives a new test of the solution of the model and would enter in computations of the Donaldson invariants of four-manifolds with b+2≤1. Certain other aspects of abelian duality, relevant to matters such as the dependence of Donaldson invariants on the second Stieffel-Whitney class, are also analyzed.

  19. Non-Abelian gauge field theory in scale relativity

    SciTech Connect

    Nottale, Laurent; Celerier, Marie-Noeelle; Lehner, Thierry

    2006-03-15

    Gauge field theory is developed in the framework of scale relativity. In this theory, space-time is described as a nondifferentiable continuum, which implies it is fractal, i.e., explicitly dependent on internal scale variables. Owing to the principle of relativity that has been extended to scales, these scale variables can themselves become functions of the space-time coordinates. Therefore, a coupling is expected between displacements in the fractal space-time and the transformations of these scale variables. In previous works, an Abelian gauge theory (electromagnetism) has been derived as a consequence of this coupling for global dilations and/or contractions. We consider here more general transformations of the scale variables by taking into account separate dilations for each of them, which yield non-Abelian gauge theories. We identify these transformations with the usual gauge transformations. The gauge fields naturally appear as a new geometric contribution to the total variation of the action involving these scale variables, while the gauge charges emerge as the generators of the scale transformation group. A generalized action is identified with the scale-relativistic invariant. The gauge charges are the conservative quantities, conjugates of the scale variables through the action, which find their origin in the symmetries of the ''scale-space.'' We thus found in a geometric way and recover the expression for the covariant derivative of gauge theory. Adding the requirement that under the scale transformations the fermion multiplets and the boson fields transform such that the derived Lagrangian remains invariant, we obtain gauge theories as a consequence of scale symmetries issued from a geometric space-time description.

  20. Non-Abelian Braiding of Light

    NASA Astrophysics Data System (ADS)

    Iadecola, Thomas; Schuster, Thomas; Chamon, Claudio

    2016-08-01

    Many topological phenomena first proposed and observed in the context of electrons in solids have recently found counterparts in photonic and acoustic systems. In this work, we demonstrate that non-Abelian Berry phases can arise when coherent states of light are injected into "topological guided modes" in specially fabricated photonic waveguide arrays. These modes are photonic analogues of topological zero modes in electronic systems. Light traveling inside spatially well-separated topological guided modes can be braided, leading to the accumulation of non-Abelian phases, which depend on the order in which the guided beams are wound around one another. Notably, these effects survive the limit of large photon occupation, and can thus also be understood as wave phenomena arising directly from Maxwell's equations, without resorting to the quantization of light. We propose an optical interference experiment as a direct probe of this non-Abelian braiding of light.

  1. Effective Abelian and non-Abelian gauge potentials in cavity QED.

    PubMed

    Larson, Jonas; Levin, Sergey

    2009-07-03

    Cavity QED models are analyzed in terms of field quadrature operators. We demonstrate that in such representation, the problem can be formulated in terms of effective gauge potentials. In this respect, it presents a completely new system in which gauge fields arise, possessing the advantages of purity, high control of system parameters as well as preparation and detection methods. Studying three well-known models, it is shown that either Abelian or non-Abelian gauge potentials can be constructed. The non-Abelian characteristics are confirmed via numerical simulations utilizing experimental parameters.

  2. Non-Abelian Dual Superconductivity in SU(3) Yang-Mills Theory due to Non-Abelian Magnetic Monopoles

    NASA Astrophysics Data System (ADS)

    Kondo, Kei-Ichi; Shibata, Akihiro; Kato, Seikou; Shinohara, Toru

    We give numerical evidences for the non-Abelian dual superconductivity due to non-Abelian magnetic monopoles in SU(3) Yang-Mills theory as a mechanism for quark confinement, based on our new formulation of lattice gauge theory.

  3. Non-Abelian black hole solutions in supergravity

    SciTech Connect

    Meessen, P.

    2009-05-01

    In this contribution we shall discuss some analytic examples of non-Abelian black holes in a specific N = 2 d = 4 supergravity theory. Some remarks will be made on a possible non-Abelian version of the attractor mechanism, that works in the Abelian theories.

  4. Unconventional Superconductivity in La(7)Ir(3) Revealed by Muon Spin Relaxation: Introducing a New Family of Noncentrosymmetric Superconductor That Breaks Time-Reversal Symmetry.

    PubMed

    Barker, J A T; Singh, D; Thamizhavel, A; Hillier, A D; Lees, M R; Balakrishnan, G; Paul, D McK; Singh, R P

    2015-12-31

    The superconductivity of the noncentrosymmetric compound La(7)Ir(3) is investigated using muon spin rotation and relaxation. Zero-field measurements reveal the presence of spontaneous static or quasistatic magnetic fields below the superconducting transition temperature T(c)=2.25  K-a clear indication that the superconducting state breaks time-reversal symmetry. Furthermore, transverse-field rotation measurements suggest that the superconducting gap is isotropic and that the pairing symmetry of the superconducting electrons is predominantly s wave with an enhanced binding strength. The results indicate that the superconductivity in La(7)Ir(3) may be unconventional and paves the way for further studies of this family of materials.

  5. Directed Abelian algebras and their application to stochastic models

    NASA Astrophysics Data System (ADS)

    Alcaraz, F. C.; Rittenberg, V.

    2008-10-01

    With each directed acyclic graph (this includes some D -dimensional lattices) one can associate some Abelian algebras that we call directed Abelian algebras (DAAs). On each site of the graph one attaches a generator of the algebra. These algebras depend on several parameters and are semisimple. Using any DAA, one can define a family of Hamiltonians which give the continuous time evolution of a stochastic process. The calculation of the spectra and ground-state wave functions (stationary state probability distributions) is an easy algebraic exercise. If one considers D -dimensional lattices and chooses Hamiltonians linear in the generators, in finite-size scaling the Hamiltonian spectrum is gapless with a critical dynamic exponent z=D . One possible application of the DAA is to sandpile models. In the paper we present this application, considering one- and two-dimensional lattices. In the one-dimensional case, when the DAA conserves the number of particles, the avalanches belong to the random walker universality class (critical exponent στ=3/2 ). We study the local density of particles inside large avalanches, showing a depletion of particles at the source of the avalanche and an enrichment at its end. In two dimensions we did extensive Monte-Carlo simulations and found στ=1.780±0.005 .

  6. Dragging Maintaining Symmetry: Can It Generate the Concept of Inclusivity as well as a Family of Shapes?

    ERIC Educational Resources Information Center

    Forsythe, Susan K.

    2015-01-01

    This article describes a project using Design Based Research methodology to ascertain whether a pedagogical task based on a dynamic figure designed in a Dynamic Geometry Software (DGS) program could be instrumental in developing students' geometrical reasoning. A dragging strategy which I have named "Dragging Maintaining Symmetry" (DMS)…

  7. Symmetry-induced anyon breeding in fractional quantum Hall states

    NASA Astrophysics Data System (ADS)

    Lu, Yuan-Ming; Fidkowski, Lukasz

    2014-03-01

    An exotic feature of the fractional quantum Hall effect is the emergence of anyons, which are quasiparticle excitations with fractional statistics. In the presence of a symmetry, such as U (1) charge conservation, it is well known that anyons can carry fractional symmetry quantum numbers. In this paper we reveal a different class of symmetry realizations, i.e., anyons can "breed" in multiples under symmetry operation. We focus on the global Ising (Z2) symmetry and show examples of these unconventional symmetry realizations in Laughlin-type fractional quantum Hall states. One remarkable consequence of such an Ising symmetry is the emergence of anyons on the Ising symmetry domain walls. We also provide a mathematical framework which generalizes this phenomenon to any Abelian topological orders.

  8. Symmetry impedes symmetry discrimination.

    PubMed

    Tjan, Bosco S; Liu, Zili

    2005-12-16

    Objects in the world, natural and artificial alike, are often bilaterally symmetric. The visual system is likely to take advantage of this regularity to encode shapes for efficient object recognition. The nature of encoding a symmetric shape, and of encoding any departure from it, is therefore an important matter in visual perception. We addressed this issue of shape encoding empirically, noting that a particular encoding scheme necessarily leads to a specific profile of sensitivity in perceptual discriminations. We studied symmetry discrimination using human faces and random dots. Each face stimulus was a frontal view of a three-dimensional (3-D) face model. The 3-D face model was a linearly weighted average (a morph) between the model of an original face and that of the corresponding mirror face. Using this morphing technique to vary the degree of asymmetry, we found that, for faces and analogously generated random-dot patterns alike, symmetry discrimination was worst when the stimuli were nearly symmetric, in apparent opposition to almost all studies in the literature. We analyzed the previous work and reconciled the old and new results using a generic model with a simple nonlinearity. By defining asymmetry as the minimal difference between the left and right halves of an object, we found that the visual system was disproportionately more sensitive to larger departures from symmetry than to smaller ones. We further demonstrated that our empirical and modeling results were consistent with Weber-Fechner's and Stevens's laws.

  9. Electric-magnetic duality of Abelian gauge theory on the four-torus, from the fivebrane on T 2 × T 4, via their partition functions

    NASA Astrophysics Data System (ADS)

    Dolan, Louise; Sun, Yang

    2015-06-01

    We compute the partition function of four-dimensional abelian gauge theory on a general four-torus T 4 with flat metric using Dirac quantization. In addition to an symmetry, it possesses symmetry that is electromagnetic S-duality. We show explicitly how this S-duality of the 4 d abelian gauge theory has its origin in symmetries of the 6 d (2 , 0) tensor theory, by computing the partition function of a single fivebrane compactified on T 2 times T 4, which has symmetry. If we identify the couplings of the abelian gauge theory with the complex modulus of the T 2 torus , then in the small T 2 limit, the partition function of the fivebrane tensor field can be factorized, and contains the partition function of the 4 d gauge theory. In this way the symmetry of the 6d tensor partition function is identified with the S-duality symmetry of the 4d gauge partition function. Each partition function is the product of zero mode and oscillator contributions, where the acts suitably. For the 4d gauge theory, which has a Lagrangian, this product redistributes when using path integral quantization.

  10. Asymptotically free scaling solutions in non-Abelian Higgs models

    NASA Astrophysics Data System (ADS)

    Gies, Holger; Zambelli, Luca

    2015-07-01

    We construct asymptotically free renormalization group trajectories for the generic non-Abelian Higgs model in four-dimensional spacetime. These ultraviolet-complete trajectories become visible by generalizing the renormalization/boundary conditions in the definition of the correlation functions of the theory. Though they are accessible in a controlled weak-coupling analysis, these trajectories originate from threshold phenomena which are missed in a conventional perturbative analysis relying on the deep Euclidean region. We identify a candidate three-parameter family of renormalization group trajectories interconnecting the asymptotically free ultraviolet regime with a Higgs phase in the low-energy limit. We provide estimates of their low-energy properties in the light of a possible application to the standard model Higgs sector. Finally, we find a two-parameter subclass of asymptotically free Coleman-Weinberg-type trajectories that do not suffer from a naturalness problem.

  11. Aspects of quantum corrections in a Lorentz-violating extension of the Abelian Higgs model

    NASA Astrophysics Data System (ADS)

    Brito, L. C. T.; Fargnoli, H. G.; Baêta Scarpelli, A. P.

    2013-06-01

    We investigate new aspects related to the Abelian gauge-Higgs model with the addition of the Carroll-Field-Jackiw term. We focus on one-loop quantum corrections to the photon and Higgs sectors due to spontaneous breaking of gauge symmetry and show that new finite and definite Lorentz-breaking terms are induced. Specifically in the gauge sector, a CPT-even aether term is induced. Besides, aspects of the one-loop renormalization of the background vector-dependent terms are discussed.

  12. Abelian and non-Abelian states in ν = 2 / 3 bilayer fractional quantum Hall systems

    NASA Astrophysics Data System (ADS)

    Peterson, Michael; Wu, Yang-Le; Cheng, Meng; Barkeshli, Maissam; Wang, Zhenghan

    There are several possible theoretically allowed non-Abelian fractional quantum Hall (FQH) states that could potentially be realized in one- and two-component FQH systems at total filling fraction ν = n + 2 / 3 , for integer n. Some of these states even possess quasiparticles with non-Abelian statistics that are powerful enough for universal topological quantum computation, and are thus of particular interest. Here we initiate a systematic numerical study, using both exact diagonalization and variational Monte Carlo, to investigate the phase diagram of FQH systems at total filling fraction ν = n + 2 / 3 , including in particular the possibility of the non-Abelian Z4 parafermion state. In ν = 2 / 3 bilayers we determine the phase diagram as a function of interlayer tunneling and repulsion, finding only three competing Abelian states, without the Z4 state. On the other hand, in single-component systems at ν = 8 / 3 , we find that the Z4 parafermion state has significantly higher overlap with the exact ground state than the Laughlin state, together with a larger gap, suggesting that the experimentally observed ν = 8 / 3 state may be non-Abelian. Our results from the two complementary numerical techniques agree well with each other qualitatively. We acknowledge the Office of Research and Sponsored Programs at California State University Long Beach and Microsoft Station Q.

  13. Abelian Duality on Globally Hyperbolic Spacetimes

    NASA Astrophysics Data System (ADS)

    Becker, Christian; Benini, Marco; Schenkel, Alexander; Szabo, Richard J.

    2017-01-01

    We study generalized electric/magnetic duality in Abelian gauge theory by combining techniques from locally covariant quantum field theory and Cheeger-Simons differential cohomology on the category of globally hyperbolic Lorentzian manifolds. Our approach generalizes previous treatments using the Hamiltonian formalism in a manifestly covariant way and without the assumption of compact Cauchy surfaces. We construct semi-classical configuration spaces and corresponding presymplectic Abelian groups of observables, which are quantized by the CCR-functor to the category of C*-algebras. We demonstrate explicitly how duality is implemented as a natural isomorphism between quantum field theories. We apply this formalism to develop a fully covariant quantum theory of self-dual fields.

  14. Special issue on non-Abelian gauge fields Special issue on non-Abelian gauge fields

    NASA Astrophysics Data System (ADS)

    Gerbier, Fabrice; Goldman, Nathan; Lewenstein, Maciej; Sengstock, Klaus

    2012-09-01

    Building a universal quantum computer is a central goal of emerging quantum technologies and it is expected to revolutionize science and technology. Unfortunately, this future does not seem very close, however, quantum computers built for a special purpose, i.e., quantum simulators, are currently being developed in many leading laboratories. Numerous schemes for quantum simulation have been proposed and realized using, e.g., ultracold atoms in optical lattices, ultracold trapped ions, atoms in arrays of cavities, atoms/ions in arrays of traps, quantum dots or superconducting circuits. The progress in experimental implementations is more than spectacular. Particularly interesting are those systems that simulate quantum matter evolving in artificial, or synthetic, Abelian or even non-Abelian gauge fields. Abelian gauge fields are analogues to the standard magnetic field and lead to fascinating effects such as the integer or fractional quantum Hall effects (IQHE, FQHE) and vortex lattices. Non-Abelian gauge fields couple the motional states of the particles to their internal degrees of freedom (such as hyperfine states for atoms or ions, electronic spins for electrons, etc). In this sense, external non-Abelian fields extend the concept of spin-orbit coupling, which is familiar from AMO and condensed matter physics. They lead to yet another variety of fascinating novel phenomena such as the quantum spin Hall effect (QSHE), 3D topological insulators, topological superconductors and superfluids of various kinds. Even more fascinating is the possibility of generating synthetic gauge fields that are dynamical, i.e., that evolve in time according to the corresponding lattice gauge theory (LGT). These dynamical gauge fields can also couple to matter fields, allowing the quantum simulation of such complex systems (notoriously hard to simulate using 'traditional' computers), which are particularly relevant for modern high-energy physics. So far there are only theoretical

  15. Non-Abelian statistics in the fractional quantum Hall states

    NASA Astrophysics Data System (ADS)

    Wen, X. G.

    1991-02-01

    The fractional quantum Hall states with non-Abelian statistics are studied. Those states are shown to be characterized by non-Abelian topological orders and are identified with some of the Jain states. The gapless edge states are found to be described by non-Abelian Kac-Moody algebras. It is argued that the topological orders and the associated properties are robust against any kinds of small perturbations.

  16. Anisotropic inflation with non-abelian gauge kinetic function

    SciTech Connect

    Murata, Keiju; Soda, Jiro E-mail: jiro@tap.scphys.kyoto-u.ac.jp

    2011-06-01

    We study an anisotropic inflation model with a gauge kinetic function for a non-abelian gauge field. We find that, in contrast to abelian models, the anisotropy can be either a prolate or an oblate type, which could lead to a different prediction from abelian models for the statistical anisotropy in the power spectrum of cosmological fluctuations. During a reheating phase, we find chaotic behaviour of the non-abelian gauge field which is caused by the nonlinear self-coupling of the gauge field. We compute a Lyapunov exponent of the chaos which turns out to be uncorrelated with the anisotropy.

  17. Ubiquitous symmetries

    NASA Astrophysics Data System (ADS)

    Nucci, M. C.

    2016-09-01

    We review some of our recent work devoted to the problem of quantization with preservation of Noether symmetries, finding hidden linearity in superintegrable systems, and showing that nonlocal symmetries are in fact local. In particular, we derive the Schrödinger equation for the isochronous Calogero goldfish model using its relation to Darwin equation. We prove the linearity of a classical superintegrable system on a plane of nonconstant curvature. We find the Lie point symmetries that correspond to the nonlocal symmetries (also reinterpreted as λ-symmetries) of the Riccati chain.

  18. Supersymmetry, grand unification and flavor symmetry

    NASA Astrophysics Data System (ADS)

    Enkhbat, Tsedenbaljir

    In this thesis I have presented the findings of my research pursued during my Ph.D. study. The purpose of this thesis was to study different theoretical ideas in high energy physics model building addressed primarily towards understanding the fermion mass problem and the gauge hierarchy problem. These include: Anomalous flavor U(1) symmetry and its experimental implications, finite GUT models with discrete family symmetry, and a product GUT model in a 2D deconstructed theory space. The second and third chapters of the thesis describe our study of lepton flavor violation (LFV) and electric dipole moments (EDM) induced by a flavor-dependent anomalous U(1) gauge symmetry of string origin. The models considered also address the fermion mass hierarchy problem successfully. We have shown that the U(1) sector induces significant LFV and EDMs through the SUSY breaking parameters. These effects arise via renormalization group evolution of the parameters in the momentum regime between the string and the anomalous U(1) breaking scale. The fourth chapter of the thesis contains our work on a concrete realization of SUSY breaking using interference between the anomalous U(1) flavor gauge symmetry and a strongly coupled SU(N c), leading to the so called Split SUSY spectrum where the sfermions and the gravitino acquire masses of order 105 ÷ 108 GeV while the gauginos and the Higgsinos have masses of order 102 ÷ 103 GeV. We have calculated the leading order supergravity corrections and have presented a class of explicit models of Split SUSY which are phenomenologically consistent. In the fifth chapter I have presented models for realistic quark masses and mixings in the context of finite SU(5) GUT wherein the beta functions for the gauge and the Yukawa couplings vanish to all orders in perturbation theory. The models presented are based on non-Abelian discrete symmetries. In the case of (Z4)3 x P and A4 symmetries we have found models finite to all order of perturbation theory

  19. Gluon mass generation and infrared Abelian dominance in Yang-Mills theory

    NASA Astrophysics Data System (ADS)

    Shibata, Akihiro

    2006-12-01

    Dual superconductivity is believed to be a promising mechanism for quark confinement. Indeed, that this picture is true has been confirmed in the maximal Abelian (MA) gauge. However, it is not yet confirmed in any other gauge, and the MA gauge explicitly breaks color symmetry. To remedy this defect, we propose to use our compact formulation of a non-linear change of variables (NLCV), called once by the Cho-Faddeev-Niemi (CFN) decomposition, on a lattice. This formulation has succeeded to extract the magnetic monopole with integer-valued magnetic charge in the gauge-invariant way. We present measurements of various correlation functions for the operators constructed from the NLCV in SU(2) Yang-Mills theory. Some of our results reproduce previous results obtained in MA gauge, e.g., DeGrand-Toussaint monopole, infrared Abelian dominance and off-diagonal gluon mass generation. These studies preserve color symmetry, which is sharp contrast to the conventional MA gauge. We argue the gauge fixing independence of these results and the implications for quark confinement

  20. Symmetry-protected topological entanglement

    NASA Astrophysics Data System (ADS)

    Marvian, Iman

    2017-01-01

    We propose an order parameter for the symmetry-protected topological (SPT) phases which are protected by Abelian on-site symmetries. This order parameter, called the SPT entanglement, is defined as the entanglement between A and B , two distant regions of the system, given that the total charge (associated with the symmetry) in a third region C is measured and known, where C is a connected region surrounded by A , B , and the boundaries of the system. In the case of one-dimensional systems we prove that in the limit where A and B are large and far from each other compared to the correlation length, the SPT entanglement remains constant throughout a SPT phase, and furthermore, it is zero for the trivial phase while it is nonzero for all the nontrivial phases. Moreover, we show that the SPT entanglement is invariant under the low-depth quantum circuits which respect the symmetry, and hence it remains constant throughout a SPT phase in the higher dimensions as well. Also, we show that there is an intriguing connection between SPT entanglement and the Fourier transform of the string order parameters, which are the traditional tool for detecting SPT phases. This leads to an algorithm for extracting the relevant information about the SPT phase of the system from the string order parameters. Finally, we discuss implications of our results in the context of measurement-based quantum computation.

  1. Correlations between Abelian monopoles and center vortices

    NASA Astrophysics Data System (ADS)

    Hosseini Nejad, Seyed Mohsen; Deldar, Sedigheh

    2017-04-01

    We study the correlations between center vortices and Abelian monopoles for SU(3) gauge group. Combining fractional fluxes of monopoles, center vortex fluxes are constructed in the thick center vortex model. Calculating the potentials induced by fractional fluxes constructing the center vortex flux in a thick center vortex-like model and comparing with the potential induced by center vortices, we observe an attraction between fractional fluxes of monopoles constructing the center vortex flux. We conclude that the center vortex flux is stable, as expected. In addition, we show that adding a contribution of the monopole-antimonopole pairs in the potentials induced by center vortices ruins the Casimir scaling at intermediate regime.

  2. Non abelian hydrodynamics and heavy ion collisions

    SciTech Connect

    Calzetta, E.

    2014-01-14

    The goal of the relativistic heavy ion collisions (RHIC) program is to create a state of matter where color degrees of freedom are deconfined. The dynamics of matter in this state, in spite of the complexities of quantum chromodynamics, is largely determined by the conservation laws of energy momentum and color currents. Therefore it is possible to describe its main features in hydrodynamic terms, the very short color neutralization time notwithstanding. In this lecture we shall give a simple derivation of the hydrodynamics of a color charged fluid, by generalizing the usual derivation of hydrodynamics from kinetic theory to the non abelian case.

  3. A heterotic standard model with B - L symmetry and a stable proton

    NASA Astrophysics Data System (ADS)

    Buchbinder, Evgeny I.; Constantin, Andrei; Lukas, Andre

    2014-06-01

    We consider heterotic Calabi-Yau compactifications with S(U(4) × U(1)) background gauge fields. These models lead to gauge groups with an additional U(1) factor which, under certain conditions, can combine with hypercharge to a B - L symmetry. The associated gauge boson is automatically super-massive and, hence, does not constitute a phenomenological problem. We illustrate this class of compactifications with a model based on the monad construction, which leads to a supersymmetric standard model with three families of quarks and leptons, one pair of Higgs doublets, three right-handed neutrinos and no exotics charged under the standard model group. The presence of the B - L symmetry means that the model is safe from proton decay induced by dimension four operators. Due to the presence of a special locus in moduli space where the bundle structure group is Abelian and the low-energy symmetry enhances we can also show the absence of dimension five proton-decay inducing operators.

  4. Non-Abelian Dual Superconductivity in SU(3) Yang-Mills Theory Due to Non-Abelian Magnetic Monopoles

    NASA Astrophysics Data System (ADS)

    Shibata, Akihiro; Kondo, Kei-Ichi; Kato, Seikou; Shinohara, Toru

    The dual superconductivity is the promising mechanism for quark confinement. We have proposed the non-Abelian dual superconductivity picture in the SU(3) Yang-Mills theory, and already presented numerical evidences for the restricted field dominance and the non-Abelian magnetic monopole dominance in the string tension, by applying our new formulation of Yang-Mills theory to a lattice. In this talk, we focus on the non-Abelian dual Meissner effect and the type of dual superconductivity. We find that the measured chromo-electric flux tube between a quark and antiquark pair strongly supports the non-Abelian dual Meissner effect due to non-Abelian magnetic monopoles. Moreover, we give a remarkable result that the type of the resulting dual superconductor is the type I in SU(3) Yang-Mills, rather than the border between the type I and II, in marked contrast to the SU(2) case.

  5. Phenomenological analysis of heterotic strings: Non-abelian constructions and landscape studies

    NASA Astrophysics Data System (ADS)

    Wasnik, Vaibhav Hemant

    String theory offers the unique promise of unifying all the known forces in nature. However, the internal consistency of the theory requires that spacetime have more than four dimensions. As a result, the extra dimensions must be compactified in some manner and how this compactification takes place is critical for determining the low-energy physical predictions of the theory. In this thesis we examine two distinct consequences of this fact. First, almost all of the prior research in string model-building has examined the consequences of compactifying on so-called "abelian" orbifolds. However, the most general class of compactifications, namely those on non-abelian orbifolds, remains almost completely unexplored. This thesis focuses on the low-energy phenomenological consequences of compactifying strings on non-abelian orbifolds. One of the main interests in pursuing these theories is that they can, in principle, naturally give rise to low-energy models which simultaneously have N=1 supersymmetry along with scalar particles transforming in the adjoint of the gauge group. These features, which are exceedingly difficult to achieve through abelian orbifolds, are exciting because they are the key ingredients in understanding how grand unification can emerge from string theory. Second, the need to compactify gives rise to a huge "landscape" of possible resulting low-energy phenomenologies. One of the goals of the landscape program in string theory is then to extract information about the space of string vacua in the form of statistical correlations between phenomenological features that are otherwise uncorrelated in field theory. Such correlations would thus represent features of string theory that hold independently of a vacuum-selection principle. In this thesis, we study statistical correlations between two features which are likely to be central to any potential description of nature at high-energy scales: gauge symmetries and spacetime supersymmetry. We analyze

  6. Symmetry matters.

    PubMed

    Moubayidin, Laila; Østergaard, Lars

    2015-09-01

    985 I. 985 II. 986 III. 987 IV. 988 V. 989 989 References 989 SUMMARY: The development of multicellular organisms depends on correct establishment of symmetry both at the whole-body scale and within individual tissues and organs. Setting up planes of symmetry must rely on communication between cells that are located at a distance from each other within the organism, presumably via mobile morphogenic signals. Although symmetry in nature has fascinated scientists for centuries, it is only now that molecular data to unravel mechanisms of symmetry establishment are beginning to emerge. As an example we describe the genetic and hormonal interactions leading to an unusual bilateral-to-radial symmetry transition of an organ in order to promote reproduction.

  7. More on the Abrikosov strings with non-Abelian moduli

    NASA Astrophysics Data System (ADS)

    Shifman, M.; Tallarita, Gianni; Yung, Alexei

    2014-04-01

    We continue explorations of deformed Abrikosov-Nielsen-Olesen (ANO) strings, with non-Abelian moduli on the worldsheet. In a simple model with an extra field, we find classically stable ANO and non-Abelian strings. The tension of the latter is a few percent lower than the tension of the ANO string. Then, we calculate the interpolating field configuration. Once the kink mass Mk and the difference of tensions ΔT are found, we calculate the decay rate of the ANO string with a higher tension ("false vacuum") into the non-Abelian string with the lower tension ("genuine vacuum") through the "bubble" formation in the quasiclassical approximation.

  8. Mesons from (non) Abelian T-dual backgrounds

    NASA Astrophysics Data System (ADS)

    Itsios, Georgios; Núñez, Carlos; Zoakos, Dimitrios

    2017-01-01

    In this work we study mesonic excitations in a Quantum Field Theory dual to the non Abelian T-dual of AdS 5 × S 5, using a D6 brane probe on the Sfetsos-Thompson background. Before and after the duality, we observe interesting differences between the spectra and interpret them. The spectrum of masses and the interactions between mesonic excitations teach valuable lessons about the character of non-Abelian T-duality and its implications for Holography. The case of Abelian T-duality is also studied.

  9. Fractional Fermions with Non-Abelian Statistics

    NASA Astrophysics Data System (ADS)

    Klinovaja, Jelena; Loss, Daniel

    2013-03-01

    We introduce a novel class of low-dimensional topological tight-binding models that allow for bound states that are fractionally charged fermions and exhibit non-Abelian braiding statistics. The proposed model consists of a double (single) ladder of spinless (spinful) fermions in the presence of magnetic fields. We study the system analytically in the continuum limit as well as numerically in the tight-binding representation. We find a topological phase transition with a topological gap that closes and reopens as a function of system parameters and chemical potential. The topological phase is of the type BDI and carries two degenerate midgap bound states that are localized at opposite ends of the ladders. We show numerically that these bound states are robust against a wide class of perturbations.

  10. Moduli of linear and abelian categories

    NASA Astrophysics Data System (ADS)

    Anel, Mathieu

    2006-07-01

    Linear categories naturally have several identification relations : isomorphisms, categorical equivalences and Morita equivalences. In this thesis, we construct the classifying stacks for these three relations (\\ukcatiso, \\ukcateq, \\ukcatmor) together with the classifying stack of abelian categories (\\ukab), the originality of the subject being that, apart from the first one, these are higher stacks. The principal result is that, under some finiteness assumptions, these stacks are geometric in the sense of C. Simpson. In particular, one recover the Hochschild cohomology of a category C as the tangent complex, i.e. the object classifying first order deformations of C, of these stacks at the point defined by C. Moreover, there exists a natural sequence of surjective morphisms of stacks : \\ukcatiso tto \\ukcateq tto \\ukcatmor tto \\ukab for which we prove that the middle one is etale, and the right one is an equivalence.

  11. A new approach to non-Abelian hydrodynamics

    NASA Astrophysics Data System (ADS)

    Fernández-Melgarejo, Jose J.; Rey, Soo-Jong; Surówka, Piotr

    2017-02-01

    We present a new approach to describe hydrodynamics carrying non-Abelian macroscopic degrees of freedom. Based on the Kaluza-Klein compactification of a higher-dimensional neutral dissipative fluid on a manifold of non-Abelian isometry, we obtain a four-dimensional colored dissipative fluid coupled to Yang-Mills gauge field. We derive transport coefficients of resulting colored fluid, which feature non-Abelian character of color charges. In particular, we obtain color-specific terms in the gradient expansions and response quantities such as the conductivity matrix and the chemical potentials. We argue that our Kaluza-Klein approach provides a robust description of non-Abelian hydrodynamics, and discuss some links between this system and quark-gluon plasma and fluid/gravity duality.

  12. Non-Abelian Born Infeld action, geometry and supersymmetry

    NASA Astrophysics Data System (ADS)

    Julio Cirilo-Lombardo, Diego

    2005-12-01

    In this work, we propose a new non-Abelian generalization of the Born Infeld Lagrangian. It is based on a geometrical property of the Abelian Born Infeld Lagrangian in its determinantal form. Our goal is to extend the Abelian second-type Born Infeld action to the non-Abelian form preserving this geometrical property, which permits us to compute the generalized volume element as a linear combination of the components of metric and the Yang Mills energy momentum tensors. Under the BPS-like condition, the action proposed reduces to that of the Yang Mills theory, independently of the gauge group. New instanton-wormhole solution and static and spherically symmetric solution in curved spacetime for an SU(2) isotopic ansatz are solved and the N= 1 supersymmetric extension of the model is performed.

  13. Frustrated topological symmetry breaking: Geometrical frustration and anyon condensation

    NASA Astrophysics Data System (ADS)

    Schulz, Marc D.; Burnell, Fiona J.

    2016-10-01

    We study the phase diagram of a topological string-net-type lattice model in the presence of geometrically frustrated interactions. These interactions drive several phase transitions that reduce the topological order, leading to a rich phase diagram including both Abelian (Z2) and non-Abelian (Ising×Ising¯ ) topologically ordered phases, as well as phases with broken translational symmetry. Interestingly, one of these phases simultaneously exhibits (Abelian) topological order and long-ranged order due to translational symmetry breaking, with nontrivial interactions between excitations in the topological order and defects in the long-ranged order. We introduce a variety of effective models, valid along certain lines in the phase diagram, which can be used to characterize both topological and symmetry-breaking order in these phases and in many cases allow us to characterize the phase transitions that separate them. We use exact diagonalization and high-order series expansion to study areas of the phase diagram where these models break down and to approximate the location of the phase boundaries.

  14. Black string first order flow in N = 2, d = 5 abelian gauged supergravity

    NASA Astrophysics Data System (ADS)

    Klemm, Dietmar; Petri, Nicolò; Rabbiosi, Marco

    2017-01-01

    We derive both BPS and non-BPS first-order flow equations for magnetically charged black strings in five-dimensional N = 2 abelian gauged supergravity, using the Hamilton-Jacobi formalism. This is first done for the coupling to vector multiplets only and U(1) Fayet-Iliopoulos (FI) gauging, and then generalized to the case where also hyper-multiplets are present, and abelian symmetries of the quaternionic hyperscalar target space are gauged. We then use these results to derive the attractor equations for near-horizon geometries of extremal black strings, and solve them explicitely for the case where the constants appearing in the Chern-Simons term of the supergravity action satisfy an adjoint identity. This allows to compute in generality the central charge of the two-dimensional conformal field theory that describes the black strings in the infrared, in terms of the magnetic charges, the CY intersection numbers and the FI constants. Finally, we extend the r-map to gauged supergravity and use it to relate our flow equations to those in four dimensions.

  15. Aharonov-Bohm order parameters for non-Abelian gauge theories

    SciTech Connect

    Lo, H.

    1995-12-15

    The Aharonov-Bohm effect has been invoked to probe the phase structure of a gauge theory. Yet in the case of non-Abelian gauge theories, it proves difficult to formulate a general procedure that unambiguously specifies the realization of the gauge symmetry, e.g., the unbroken subgroup. In this paper we propose a set of order parameters that will do the job. We articulate the fact that any useful Aharonov-Bohm experiment necessarily proceeds in two stages: calibration and measurement. World sheets of virtual cosmic string loops can wrap around test charges, thus changing their states relative to other charges in the universe. Consequently, repeated flux measurements with test charges will not necessarily agree. This was the main stumbling block to previous attempts to construct order parameters for non-Abelian gauge theories. In those works, the particles that one uses for calibration and subsequent measurement are stored in {ital separate} ``boxes.`` By storing all test particles in the {ital same} ``box`` we show how quantum fluctuations can be overcome. The importance of gauge fixing is also emphasized. {copyright} 1995 The American Physical Society.

  16. A non-Abelian SO(8) monopole as generalization of Dirac-Yang monopoles for a 9-dimensional space

    SciTech Connect

    Le, Van-Hoang; Nguyen, Thanh-Son

    2011-03-15

    We establish an explicit form of a non-Abelian SO(8) monopole in a 9-dimensional space and show that it is indeed a direct generalization of Dirac and Yang monopoles. Using the generalized Hurwitz transformation, we have found a connection between a 16-dimensional harmonic oscillator and a 9-dimensional hydrogenlike atom in the field of the SO(8) monopole (MICZ-Kepler problem). Using the built connection the group of dynamical symmetry of the 9-dimensional MICZ-Kepler problem is found as SO(10, 2).

  17. Dual Superconductivity in Abelian Higgs Model of QCD

    NASA Astrophysics Data System (ADS)

    Rajput, B. S.

    2017-04-01

    The study of generalized field associated with Abelian dyons has been undertaken and it has been demonstrated that topologically, a non-Abelian gauge theory is equivalent to a set of Abelian gauge theories supplemented by dyons which undergo condensation leading to confinement and consequently to superconducting model of QCD vacuum, where the Higgs field plays the role of a regulator only. Constructing the effective action for dyonic field in Abelian projection of QCD, it has been demonstrated that any charge (electrical or magnetic) of dyon screens its own direct potential to which it minimally couples and anti-screens the dual potential leading to dual superconductivity in accordance with generalized Meissner effect. In this Abelian projection of QCD an Abelian Higgs model (AHM) has been successfully constructed and it has been shown to incorporate dual superconductivity and confinement as the consequence of dyonic condensation. It has been demonstrated that in AHM t' Hooft loop creates the string (AHM-string) around which the monopole current under London limit leads to vanishing coherence length in the chromo-magnetic superconductor. It has also been shown that in London limit the squared density of monopole current around AHM-string has a maximum at the distance of the order of penetration length.

  18. Spontaneous breaking of nilpotent symmetry in boundary BLG theory

    NASA Astrophysics Data System (ADS)

    Upadhyay, Sudhaker

    2015-09-01

    We exploit boundary term to preserve the supersymmetric gauge invariance of Bagger-Lambert-Gustavsson (BLG) theory. The fermionic rigid BRST and anti-BRST symmetries are studied in linear and nonlinear gauges. Remarkably, for Delbourgo-Jarvis-Baulieu-Thierry-Mieg (DJBTM) type gauge the spontaneous breaking of BRST symmetry occurs in the BLG theory. The responsible guy for such spontaneous breaking is ghost-antighost condensation. Further, we discuss the ghost-antighost condensates in the modified maximally Abelian (MMA) gauge in the BLG theory.

  19. Non-abelian gauge fields and topological insulators in shaken optical lattices.

    PubMed

    Hauke, Philipp; Tieleman, Olivier; Celi, Alessio; Olschläger, Christoph; Simonet, Juliette; Struck, Julian; Weinberg, Malte; Windpassinger, Patrick; Sengstock, Klaus; Lewenstein, Maciej; Eckardt, André

    2012-10-05

    Time-periodic driving like lattice shaking offers a low-demanding method to generate artificial gauge fields in optical lattices. We identify the relevant symmetries that have to be broken by the driving function for that purpose and demonstrate the power of this method by making concrete proposals for its application to two-dimensional lattice systems: We show how to tune frustration and how to create and control band touching points like Dirac cones in the shaken kagome lattice. We propose the realization of a topological and a quantum spin Hall insulator in a shaken spin-dependent hexagonal lattice. We describe how strong artificial magnetic fields can be achieved for example in a square lattice by employing superlattice modulation. Finally, exemplified on a shaken spin-dependent square lattice, we develop a method to create strong non-abelian gauge fields.

  20. A general non-Abelian density matrix renormalization group algorithm with application to the C2 dimer

    NASA Astrophysics Data System (ADS)

    Sharma, Sandeep

    2015-01-01

    We extend our previous work [S. Sharma and G. K.-L. Chan, J. Chem. Phys. 136, 124121 (2012)], which described a spin-adapted (SU(2) symmetry) density matrix renormalization group algorithm, to additionally utilize general non-Abelian point group symmetries. A key strength of the present formulation is that the requisite tensor operators are not hard-coded for each symmetry group, but are instead generated on the fly using the appropriate Clebsch-Gordan coefficients. This allows our single implementation to easily enable (or disable) any non-Abelian point group symmetry (including SU(2) spin symmetry). We use our implementation to compute the ground state potential energy curve of the C2 dimer in the cc-pVQZ basis set (with a frozen-core), corresponding to a Hilbert space dimension of 1012 many-body states. While our calculated energy lies within the 0.3 mEh error bound of previous initiator full configuration interaction quantum Monte Carlo and correlation energy extrapolation by intrinsic scaling calculations, our estimated residual error is only 0.01 mEh, much more accurate than these previous estimates. Due to the additional efficiency afforded by the algorithm, the excitation energies (Te) of eight lowest lying excited states: a3Πu, b 3 Σg - , A1Πu, c 3 Σu + , B1Δg, B ' 1 Σg + , d3Πg, and C1Πg are calculated, which agree with experimentally derived values to better than 0.06 eV. In addition, we also compute the potential energy curves of twelve states: the three lowest levels for each of the irreducible representations 1 Σg + , 1 Σu + , 1 Σg - , and 1 Σu - , to an estimated accuracy of 0.1 mEh of the exact result in this basis.

  1. Harada–Tsutsui gauge recovery procedure: From Abelian gauge anomalies to the Stueckelberg mechanism

    SciTech Connect

    Lima, Gabriel Di Lemos Santiago

    2014-02-15

    Revisiting a path-integral procedure developed by Harada and Tsutsui for recovering gauge invariance from anomalous effective actions, it is shown that there are two ways to achieve gauge symmetry: one already presented by the authors, which is shown to preserve the anomaly in the sense of standard current conservation law, and another one which is anomaly-free, preserving current conservation. It is also shown that the application of the Harada–Tsutsui technique to other models which are not anomalous but do not exhibit gauge invariance allows the identification of the gauge invariant formulation of the Proca model, also done by the referred authors, with the Stueckelberg model, leading to the interpretation of the gauge invariant map as a generalization of the Stueckelberg mechanism. -- Highlights: • A gauge restoration technique from Abelian anomalous models is discussed. • It is shown that there is another way that leads to gauge symmetry restoration from such technique. • It is shown that the first gauge restoration preserves the anomaly, while the proposed second one is free from anomalies. • It is shown that the proposed gauge symmetry restoration can be identified with the Stueckelberg mechanism.

  2. Family symmetries and proton decay

    SciTech Connect

    Murayama, Hitoshi |; Kaplan, D.B.

    1994-08-01

    The proton decay modes p {yields} K{sup 0}e{sup +} and p {yields} K{sup 0}{mu}{sup +} may be visible in certain supersymmetric theories, and if seen would provide evidence for new flavor physics at extremely short distances. These decay modes can arise from the dimension five operator (Q{sub 1}Q{sub 1}Q{sub 2}L{sub 1,2}), where Q{sub i} and L{sub i} are i{sup th} generation quark and lepton superfields respectively. Such an operator is not generated at observable levels due to gauge or Higgs boson exchange in a minimal GUT. However in theories that explain the fermion mass hierarchy, it may be generated at the Planck scale with a strength such that the decays p {yields} K{sup 0}{ell}{sup +} are both compatible with the proton lifetime and visible at Super-Kamiokande. Observable proton decay can even occur in theories without unification.

  3. A symmetry principle for topological quantum order

    SciTech Connect

    Nussinov, Zohar Ortiz, Gerardo

    2009-05-15

    We present a unifying framework to study physical systems which exhibit topological quantum order (TQO). The major guiding principle behind our approach is that of symmetries and entanglement. These symmetries may be actual symmetries of the Hamiltonian characterizing the system, or emergent symmetries. To this end, we introduce the concept of low-dimensional Gauge-like symmetries (GLSs), and the physical conservation laws (including topological terms, fractionalization, and the absence of quasi-particle excitations) which emerge from them. We prove then sufficient conditions for TQO at both zero and finite temperatures. The physical engine for TQO are topological defects associated with the restoration of GLSs. These defects propagate freely through the system and enforce TQO. Our results are strongest for gapped systems with continuous GLSs. At zero temperature, selection rules associated with the GLSs enable us to systematically construct general states with TQO; these selection rules do not rely on the existence of a finite gap between the ground states to all other excited states. Indices associated with these symmetries correspond to different topological sectors. All currently known examples of TQO display GLSs. Other systems exhibiting such symmetries include Hamiltonians depicting orbital-dependent spin-exchange and Jahn-Teller effects in transition metal orbital compounds, short-range frustrated Klein spin models, and p+ip superconducting arrays. The symmetry based framework discussed herein allows us to go beyond standard topological field theories and systematically engineer new physical models with finite temperature TQO (both Abelian and non-Abelian). Furthermore, we analyze the insufficiency of entanglement entropy (we introduce SU(N) Klein models on small world networks to make the argument even sharper), spectral structures, maximal string correlators, and fractionalization in establishing TQO. We show that Kitaev's Toric code model and Wen

  4. Inherited Symmetry

    ERIC Educational Resources Information Center

    Attanucci, Frank J.; Losse, John

    2008-01-01

    In a first calculus course, it is not unusual for students to encounter the theorems which state: If f is an even (odd) differentiable function, then its derivative is odd (even). In our paper, we prove some theorems which show how the symmetry of a continuous function f with respect to (i) the vertical line: x = a or (ii) with respect to the…

  5. Abelian non-global logarithms from soft gluon clustering

    NASA Astrophysics Data System (ADS)

    Kelley, Randall; Walsh, Jonathan R.; Zuberi, Saba

    2012-09-01

    Most recombination-style jet algorithms cluster soft gluons in a complex way. This leads to previously identified correlations in the soft gluon phase space and introduces logarithmic corrections to jet cross sections, which are known as clustering logarithms. The leading Abelian clustering logarithms occur at least at next-to leading logarithm (NLL) in the exponent of the distribution. Using the framework of Soft Collinear Effective Theory (SCET), we show that new clustering effects contributing at NLL arise at each order. While numerical resummation of clustering logs is possible, it is unlikely that they can be analytically resummed to NLL. Clustering logarithms make the anti-kT algorithm theoretically preferred, for which they are power suppressed. They can arise in Abelian and non-Abelian terms, and we calculate the Abelian clustering logarithms at O ( {α_s^2} ) for the jet mass distribution using the Cambridge/Aachen and kT algorithms, including jet radius dependence, which extends previous results. We find that clustering logarithms can be naturally thought of as a class of non-global logarithms, which have traditionally been tied to non-Abelian correlations in soft gluon emission.

  6. Core Structure and Non-Abelian Reconnection of Defects in a Biaxial Nematic Spin-2 Bose-Einstein Condensate

    NASA Astrophysics Data System (ADS)

    Borgh, Magnus O.; Ruostekoski, Janne

    2016-12-01

    We calculate the energetic structure of defect cores and propose controlled methods to imprint a nontrivially entangled vortex pair that undergoes non-Abelian vortex reconnection in a biaxial nematic spin-2 condensate. For a singular vortex, we find three superfluid cores in addition to depletion of the condensate density. These exhibit order parameter symmetries that are different from the discrete symmetry of the biaxial nematic phase, forming an interface between the defect and the bulk superfluid. We provide a detailed analysis of phase mixing in the resulting vortex cores and find an instability dependent upon the orientation of the order parameter. We further show that the spin-2 condensate is a promising system for observing spontaneous deformation of a point defect into an "Alice ring" that has so far avoided experimental detection.

  7. Core Structure and Non-Abelian Reconnection of Defects in a Biaxial Nematic Spin-2 Bose-Einstein Condensate.

    PubMed

    Borgh, Magnus O; Ruostekoski, Janne

    2016-12-30

    We calculate the energetic structure of defect cores and propose controlled methods to imprint a nontrivially entangled vortex pair that undergoes non-Abelian vortex reconnection in a biaxial nematic spin-2 condensate. For a singular vortex, we find three superfluid cores in addition to depletion of the condensate density. These exhibit order parameter symmetries that are different from the discrete symmetry of the biaxial nematic phase, forming an interface between the defect and the bulk superfluid. We provide a detailed analysis of phase mixing in the resulting vortex cores and find an instability dependent upon the orientation of the order parameter. We further show that the spin-2 condensate is a promising system for observing spontaneous deformation of a point defect into an "Alice ring" that has so far avoided experimental detection.

  8. Magnetic effects on color-flavor-locked quark matter and non-Abelian vortices via Ginzburg-Landau approach

    NASA Astrophysics Data System (ADS)

    Zhang, Xiao-Bing; Bu, Zhi-Cheng; Peng, Fu-Ping; Zhang, Yi

    2015-06-01

    By using a general Ginzburg-Landau approach, we study the effects of external magnetic background on color-flavor-locked quark color-superconducting matter. The rotated magnetic field B ˜ is introduced, not only accounting for the unbroken symmetry with the rotated electric charge, but also resulting in new effects for the collective excitations such as the Nambu-Goldstone and Higgs modes. In particular, it is found that the masses of Higgs octet are no longer degenerated and part of them acquire the magnetic-induced contribution. To the leading order in the applied field, we construct an effective Ginzburg-Landau formalism through these B ˜ -related masses. As the application, we investigate magnetic responses of the non-Abelian vortices arising from color-flavor-locked symmetry breaking pattern. The B ˜ -field dependence of their spatial configurations and tension energies are calculated for the first time.

  9. Abelian color cycles: A new approach to strong coupling expansion and dual representations for non-abelian lattice gauge theory

    NASA Astrophysics Data System (ADS)

    Gattringer, Christof; Marchis, Carlotta

    2017-03-01

    We propose a new approach to strong coupling series and dual representations for non-abelian lattice gauge theories using the SU(2) case as an example. The Wilson gauge action is written as a sum over ;abelian color cycles; (ACC) which correspond to loops in color space around plaquettes. The ACCs are complex numbers which can be commuted freely such that the strong coupling series and the dual representation can be obtained as in the abelian case. Using a suitable representation of the SU(2) gauge variables we integrate out all original gauge links and identify the constraints for the dual variables in the SU(2) case. We show that the construction can be generalized to the case of SU(2) gauge fields with staggered fermions. The result is a strong coupling series where all gauge integrals are known in closed form and we discuss its applicability for possible dual simulations. The abelian color cycle concept can be generalized to other non-abelian gauge groups such as SU(3).

  10. Non-Abelian quantum holonomy of hydrogenlike atoms

    SciTech Connect

    Mousolou, Vahid Azimi; Canali, Carlo M.; Sjoeqvist, Erik

    2011-09-15

    We study the Uhlmann holonomy [Rep. Math. Phys. 24, 229 (1986)] of quantum states for hydrogenlike atoms where the intrinsic spin and orbital angular momentum are coupled by the spin-orbit interaction and are subject to a slowly varying magnetic field. We show that the holonomy for the orbital angular momentum and spin subsystems is non-Abelian while the holonomy of the whole system is Abelian. Quantum entanglement in the states of the whole system is crucially related to the non-Abelian gauge structure of the subsystems. We analyze the phase of the Wilson loop variable associated with the Uhlmann holonomy and find a relation between the phase of the whole system and corresponding marginal phases. Based on the results for the model system, we provide evidence that the phase of the Wilson loop variable and the mixed-state geometric phase [E. Sjoeqvist et al., Phys. Rev. Lett. 85, 2845 (2000).] are generally inequivalent.

  11. Gauging the twisted Poincare symmetry as a noncommutative theory of gravitation

    SciTech Connect

    Chaichian, M.; Tureanu, A.; Oksanen, M.; Zet, G.

    2009-02-15

    Einstein's theory of general relativity was formulated as a gauge theory of Lorentz symmetry by Utiyama in 1956, while the Einstein-Cartan gravitational theory was formulated by Kibble in 1961 as the gauge theory of Poincare transformations. In this framework, we propose a formulation of the gravitational theory on canonical noncommutative space-time by covariantly gauging the twisted Poincare symmetry, in order to fulfil the requirement of covariance under the general coordinate transformations, an essential ingredient of the theory of general relativity. It appears that the twisted Poincare symmetry cannot be gauged by generalizing the Abelian twist to a covariant non-Abelian twist, nor by introducing a more general covariant twist element. The advantages of such a formulation as well as the related problems are discussed and possible ways out are outlined.

  12. Simulating Dirac fermions with Abelian and non-Abelian gauge fields in optical lattices

    SciTech Connect

    Alba, E.; Fernandez-Gonzalvo, X.; Mur-Petit, J.; Garcia-Ripoll, J.J.; Pachos, J.K.

    2013-01-15

    In this work we present an optical lattice setup to realize a full Dirac Hamiltonian in 2+1 dimensions. We show how all possible external potentials coupled to the Dirac field can arise from perturbations of the existing couplings of the honeycomb lattice pattern. This greatly simplifies the proposed implementations, requiring only spatial modulations of the intensity of the laser beams to induce complex non-Abelian potentials. We finally suggest several experiments to observe the properties of the quantum field theory in the setup. - Highlights: Black-Right-Pointing-Pointer This work provides a very flexible setup for simulating Dirac fermions. Black-Right-Pointing-Pointer The manuscript contains a detailed study of optical lattice deformations. Black-Right-Pointing-Pointer The link between lattice deformations and effective gauge Hamiltonians is studied.

  13. Abelian Yang-Baxter deformations and TsT transformations

    NASA Astrophysics Data System (ADS)

    Osten, David; van Tongeren, Stijn J.

    2017-02-01

    We prove that abelian Yang-Baxter deformations of superstring coset σ models are equivalent to sequences of commuting TsT transformations, meaning T dualities and coordinate shifts. Our results extend also to fermionic deformations and fermionic T duality, and naturally lead to a TsT subgroup of the superduality group OSp (db ,db | 2df). In cases like AdS5 ×S5, fermionic deformations necessarily lead to complex models. As an illustration of inequivalent deformations, we give all six abelian deformations of AdS3. We comment on the possible dual field theory interpretation of these (super-)TsT models.

  14. Non-Abelian anyons: when Ising meets Fibonacci.

    PubMed

    Grosfeld, E; Schoutens, K

    2009-08-14

    We consider an interface between two non-Abelian quantum Hall states: the Moore-Read state, supporting Ising anyons, and the k=2 non-Abelian spin-singlet state, supporting Fibonacci anyons. It is shown that the interface supports neutral excitations described by a (1+1)-dimensional conformal field theory with a central charge c=7/10. We discuss effects of the mismatch of the quantum statistical properties of the quasiholes between the two sides, as reflected by the interface theory.

  15. Boundaries, mirror symmetry, and symplectic duality in 3d N=4 gauge theory

    NASA Astrophysics Data System (ADS)

    Bullimore, Mathew; Dimofte, Tudor; Gaiotto, Davide; Hilburn, Justin

    2016-10-01

    We introduce several families of N=(2, 2) UV boundary conditions in 3d N=4 gaugetheoriesandstudytheirIRimagesinsigma-modelstotheHiggsandCoulomb branches. In the presence of Omega deformations, a UV boundary condition defines a pair of modules for quantized algebras of chiral Higgs- and Coulomb-branch operators, respec-tively, whose structure we derive. In the case of abelian theories, we use the formalism of hyperplane arrangements to make our constructions very explicit, and construct a half-BPS interface that implements the action of 3d mirror symmetry on gauge theories and boundary conditions. Finally, by studying two-dimensional compactifications of 3d N=4 gauge theories and their boundary conditions, we propose a physical origin for symplectic duality — an equivalence of categories of modules associated to families of Higgs and Coulomb branches that has recently appeared in the mathematics literature, and generalizes classic results on Koszul duality in geometric representation theory. We make several predictions about the structure of symplectic duality, and identify Koszul duality as a special case of wall crossing.

  16. Observable T{sub 7} Lepton Flavor Symmetry at the Large Hadron Collider

    SciTech Connect

    Cao Qinghong; Khalil, Shaaban; Ma, Ernest; Okada, Hiroshi

    2011-04-01

    More often than not, models of flavor symmetry rely on the use of nonrenormalizable operators (in the guise of flavons) to accomplish the phenomenologically successful tribimaximal mixing of neutrinos. We show instead how a simple renormalizable two-parameter neutrino mass model of tribimaximal mixing can be constructed with the non-Abelian discrete symmetry T{sub 7} and the gauging of B-L. This is also achieved without the addition of auxiliary symmetries and particles present in almost all other proposals. Most importantly, it is verifiable at the Large Hadron Collider.

  17. Broken Symmetry

    ScienceCinema

    None

    2016-07-12

    - Physics, as we know it, attempts to interpret the diverse natural phenomena as particular manifestations of general laws. This vision of a world ruled by general testable laws is relatively recent in the history of mankind. Basically it was initiated by the Galilean inertial principle. The subsequent rapid development of large-scale physics is certainly tributary to the fact that gravitational and electromagnetic forces are long-range and hence can be perceived directly without the mediation of highly sophisticated technical devices. - The discovery of subatomic structures and of the concomitant weak and strong short-range forces raised the question of how to cope with short-range forces in relativistic quantum field theory. The Fermi theory of weak interactions, formulated in terms of point-like current-current interaction, was well-defined in lowest order perturbation theory and accounted for existing experimental data.However, it was inconsistent in higher orders because of uncontrollable divergent quantum fluctuations. In technical terms, in contradistinction to quantum electrodynamics, the Fermi theorywas not “renormalizable”. This difficulty could not be solved by smoothing the point-like interaction by a massive, and therefore short-range, charged “vector” particle exchange: theories with massive charged vector bosons were not renormalizable either. In the early nineteen sixties, there seemed to be insuperable obstacles to formulating a consistent theory with short-range forces mediated by massive vectors. - The breakthrough came from the notion of spontaneous symmetry breaking which arose in the study of phase transitions and was introduced in field theory by Nambu in 1960. - Ferromagnets illustrate the notion in phase transitions. Although no direction is dynamically preferred, the magnetization selects a global orientation. This is a spontaneous broken symmetry(SBS)of rotational invariance. Such continuous SBS imply the existence of

  18. Broken Symmetry

    SciTech Connect

    2011-02-24

    - Physics, as we know it, attempts to interpret the diverse natural phenomena as particular manifestations of general laws. This vision of a world ruled by general testable laws is relatively recent in the history of mankind. Basically it was initiated by the Galilean inertial principle. The subsequent rapid development of large-scale physics is certainly tributary to the fact that gravitational and electromagnetic forces are long-range and hence can be perceived directly without the mediation of highly sophisticated technical devices. - The discovery of subatomic structures and of the concomitant weak and strong short-range forces raised the question of how to cope with short-range forces in relativistic quantum field theory. The Fermi theory of weak interactions, formulated in terms of point-like current-current interaction, was well-defined in lowest order perturbation theory and accounted for existing experimental data.However, it was inconsistent in higher orders because of uncontrollable divergent quantum fluctuations. In technical terms, in contradistinction to quantum electrodynamics, the Fermi theorywas not “renormalizable”. This difficulty could not be solved by smoothing the point-like interaction by a massive, and therefore short-range, charged “vector” particle exchange: theories with massive charged vector bosons were not renormalizable either. In the early nineteen sixties, there seemed to be insuperable obstacles to formulating a consistent theory with short-range forces mediated by massive vectors. - The breakthrough came from the notion of spontaneous symmetry breaking which arose in the study of phase transitions and was introduced in field theory by Nambu in 1960. - Ferromagnets illustrate the notion in phase transitions. Although no direction is dynamically preferred, the magnetization selects a global orientation. This is a spontaneous broken symmetry(SBS)of rotational invariance. Such continuous SBS imply the existence of

  19. Index theorem and Majorana zero modes along a non-Abelian vortex in a color superconductor

    SciTech Connect

    Fujiwara, Takanori; Fukui, Takahiro; Nitta, Muneto; Yasui, Shigehiro

    2011-10-01

    Color superconductivity in high-density QCD exhibits the color-flavor-locked phase. To explore zero modes in the color-flavor-locked phase in the presence of a non-Abelian vortex with an SU(2) symmetry in the vortex core, we apply the index theorem to the Bogoliubov-de Gennes (BdG) Hamiltonian. From the calculation of the topological index, we find that triplet, doublet and singlet sectors of SU(2) have certain number of chiral Majorana zero modes in the limit of vanishing chemical potential. We also solve the BdG equation by the use of the series expansion to show that the number of zero modes and their chirality match the result of the index theorem. From particle-hole symmetry of the BdG Hamiltonian, we conclude that if and only if the index of a given sector is odd, one zero mode survives generically for a finite chemical potential. We argue that this result should hold nonperturbatively even in the high-density limit.

  20. Perfect Abelian dominance of confinement in mesons and baryons in SU(3) lattice QCD

    NASA Astrophysics Data System (ADS)

    Sakumichi, Naoyuki; Suganuma, Hideo

    2016-11-01

    For a long time, the quark confinement mechanism has been one of the most difficult problems in theoretical physics. In particular, there is no clear correspondence between the confinement and non-Abelian nature of QCD. We study the static interquark potential and its Abelian projection in both mesons and baryons in the maximally Abelian (MA) gauge in SU(3) quenched lattice QCD. Remarkably, we find that the quark confining force in QCD can be perfectly described only with Abelian variables in theMAgauge, which we call "perfect Abelian dominance" of the quark confinement.

  1. Non-Abelian strings in supersymmetric Yang-Mills

    SciTech Connect

    Shifman, M.

    2012-09-26

    I give a broad review of novel phenomena discovered in certain Yang-Mills theories: non-Abelian strings and confined monopoles. Then I explain how these phenomena allow one to study strong dynamics of gauge theories in four dimensions from two-dimensional models emerging on the string world sheet.

  2. Fibonacci anyons from Abelian bilayer quantum Hall states.

    PubMed

    Vaezi, Abolhassan; Barkeshli, Maissam

    2014-12-05

    The possibility of realizing non-Abelian statistics and utilizing it for topological quantum computation (TQC) has generated widespread interest. However, the non-Abelian statistics that can be realized in most accessible proposals is not powerful enough for universal TQC. In this Letter, we consider a simple bilayer fractional quantum Hall system with the 1/3 Laughlin state in each layer. We show that interlayer tunneling can drive a transition to an exotic non-Abelian state that contains the famous "Fibonacci" anyon, whose non-Abelian statistics is powerful enough for universal TQC. Our analysis rests on startling agreements from a variety of distinct methods, including thin torus limits, effective field theories, and coupled wire constructions. We provide evidence that the transition can be continuous, at which point the charge gap remains open while the neutral gap closes. This raises the question of whether these exotic phases may have already been realized at ν=2/3 in bilayers, as past experiments may not have definitively ruled them out.

  3. Abelian anomaly and neutral pion production

    NASA Astrophysics Data System (ADS)

    Roberts, Craig

    2011-04-01

    The process γ* γ -->π0 is fascinating because in order to explain the associated transition form factor within the Standard Model on the full domain of momentum transfer, one must combine, using a single internally-consistent framework, an explanation of the essentially nonperturbative Abelian anomaly with the features of perturbative QCD. The case for attempting this has received a significant boost with the publication of data from the BaBar Collaboration [Phys. Rev. D 80, 052002 (2009)] because, while they agree with earlier experiments on their common domain of squared-momentum-transfer [CELLO - Z. Phys. C 49, 401 (1991); CLEO - Phys. Rev. D 57, 33 (1998)], the BaBar data are unexpectedly far above the prediction of perturbative QCD at larger values of Q2. I will elucidate the sensitivity of the γ* γ -->π0 transition form factor, Gγ* γπ(Q2) , to the pointwise behaviour of the interaction between quarks; and use existing Dyson-Schwinger equation calculations of this and the kindred γ*γ* -->π0 form factor to characterize the Q2-dependence of Gγ* γπ(Q2) . It will become apparent that in fully-self-consistent treatments of pion: static properties; and elastic and transition form factors, the asymptotic limit of the product Q2Gγ* γπ0(Q2) , which is determined a priori by the interaction employed, is not exceeded at any finite value of spacelike momentum transfer: the product is a monotonically-increasing concave function. Studies exist which interpret the BaBar data as an indication that the pion's distribution amplitude, φπ(x) , deviates dramatically from its QCD asymptotic form, indeed, that φπ(x) = constant, or is at least flat and nonvanishing at x = 0 , 1 . I will explain that such a distribution amplitude characterises an essentially-pointlike pion; and show that, when used in a fully-consistent treatment, it produces results for pion elastic and transition form factors that are in striking disagreement with experiment. A bound-state pion

  4. Mu-tau reflection symmetry with a texture-zero

    NASA Astrophysics Data System (ADS)

    Nishi, C. C.; Sánchez-Vega, B. L.

    2017-01-01

    The μτ-reflection symmetry is a simple symmetry capable of predicting all the unknown CP phases of the lepton sector and the atmospheric angle but too simple to predict the absolute neutrino mass scale or the mass ordering. We show that by combining it with a discrete abelian symmetry in a nontrivial way we can additionally enforce a texture-zero and obtain a highly predictive scenario where the lightest neutrino mass is fixed to be in the few meV range for two normal ordering (NO) solutions or in the tens of meV in one inverted ordering (IO) solution. The rate for neutrinoless double beta decay is predicted to be negligible for NO or have effective mass m ββ ≈ 14-29 meV for IO, right in the region to be probed in future experiments.

  5. Continuous symmetry measures for complex symmetry group.

    PubMed

    Dryzun, Chaim

    2014-04-05

    Symmetry is a fundamental property of nature, used extensively in physics, chemistry, and biology. The Continuous symmetry measures (CSM) is a method for estimating the deviation of a given system from having a certain perfect symmetry, which enables us to formulate quantitative relation between symmetry and other physical properties. Analytical procedures for calculating the CSM of all simple cyclic point groups are available for several years. Here, we present a methodology for calculating the CSM of any complex point group, including the dihedral, tetrahedral, octahedral, and icosahedral symmetry groups. We present the method and analyze its performances and errors. We also introduce an analytical method for calculating the CSM of the linear symmetry groups. As an example, we apply these methods for examining the symmetry of water, the symmetry maps of AB4 complexes, and the symmetry of several Lennard-Jones clusters.

  6. Symmetries, weak symmetries, and related solutions of the Grad-Shafranov equation

    SciTech Connect

    Cicogna, G.; Pegoraro, F.; Ceccherini, F.

    2010-10-15

    We discuss a new family of solutions of the Grad-Shafranov (GS) equation that describes D-shaped toroidal plasma equilibria with sharp gradients at the plasma edge. These solutions have been derived by exploiting the continuous Lie symmetry properties of the GS equation and in particular a special type of 'weak' symmetries. In addition, we review the continuous Lie symmetry properties of the GS equation and present a short but exhaustive survey of the possible choices for the arbitrary flux functions that yield GS equations admitting some continuous Lie symmetry. Particular solutions related to these symmetries are also discussed.

  7. Maximal Abelian gauge and a generalized BRST transformation

    NASA Astrophysics Data System (ADS)

    Deguchi, Shinichi; Pandey, Vipul Kumar; Mandal, Bhabani Prasad

    2016-05-01

    We apply a generalized Becchi-Rouet-Stora-Tyutin (BRST) formulation to establish a connection between the gauge-fixed SU (2) Yang-Mills (YM) theories formulated in the Lorenz gauge and in the Maximal Abelian (MA) gauge. It is shown that the generating functional corresponding to the Faddeev-Popov (FP) effective action in the MA gauge can be obtained from that in the Lorenz gauge by carrying out an appropriate finite and field-dependent BRST (FFBRST) transformation. In this procedure, the FP effective action in the MA gauge is found from that in the Lorenz gauge by incorporating the contribution of non-trivial Jacobian due to the FFBRST transformation of the path integral measure. The present FFBRST formulation might be useful to see how Abelian dominance in the MA gauge is realized in the Lorenz gauge.

  8. Non-Abelian Vortex Lattice in Dense QCD

    NASA Astrophysics Data System (ADS)

    Nakano, E.

    2015-11-01

    We show a possible spontaneous color ferromagnetismin the lattice system of non-Abelian vortices in rotating quark matter. The non-Abelian vortex has Nambu-Goldstone (NG) modes and CP(N-1) modes for SU(N) color and SU(N) flavor, which are localized along the vortex core. The CP(N-1) mode on each vortex site represents an orientation of color flux, and interaction among these modes causes the color ferromagnetism. The low energy effective theory in this system is described bya 3+1 dimensional CP(N-1) non-linear sigma model, from which we obtain magnon-like NG modes with an anisotropic dispersion relationω_p^2=apx,y^2+bp_z^2, when the vortex lines extend along z axis.

  9. Topologically stratified energy minimizers in a product Abelian field theory

    NASA Astrophysics Data System (ADS)

    Han, Xiaosen; Yang, Yisong

    2015-09-01

    We study a recently developed product Abelian gauge field theory by Tong and Wong hosting magnetic impurities. We first obtain a necessary and sufficient condition for the existence of a unique solution realizing such impurities in the form of multiple vortices. We next reformulate the theory into an extended model that allows the coexistence of vortices and anti-vortices. The two Abelian gauge fields in the model induce two species of magnetic vortex-lines resulting from Ns vortices and Ps anti-vortices (s = 1, 2) realized as the zeros and poles of two complex-valued Higgs fields, respectively. An existence theorem is established for the governing equations over a compact Riemann surface S which states that a solution with prescribed N1, N2 vortices and P1, P2 anti-vortices of two designated species exists if and only if the inequalities

  10. Non-Abelian gauge theory on q-Quantum spaces

    SciTech Connect

    Schraml, Stefan L.

    2002-08-23

    Gauge theories on q-deformed spaces are constructed using covariant derivatives. For this purpose a ''vielbein'' is introduced, which transforms under gauge transformations. The non-Abelian case is treated by establishing a connection to gauge theories on commutative spaces, i.e. by a Seiberg-Witten map. As an example we consider the Manin plane. Remarks are made concerning the relation between covariant coordinates and covariant derivatives.

  11. Non-Abelian Vortices, Hecke Modifications and Singular Monopoles

    NASA Astrophysics Data System (ADS)

    Baptista, J. M.

    2010-06-01

    In this note, we show that for the group G = U( N) the space of Hecke modifications of a rank N vector bundle over a Riemann surface C coincides with the moduli space of solutions of certain non-Abelian vortex equations over C. Through the recent work of Kapustin and Witten this then leads to an isomorphism between the moduli space of vortices and the moduli space of singular monopoles on the product of C with a closed interval I.

  12. Designer non-Abelian anyon platforms: from Majorana to Fibonacci

    NASA Astrophysics Data System (ADS)

    Alicea, Jason; Stern, Ady

    2015-12-01

    The emergence of non-Abelian anyons from large collections of interacting elementary particles is a conceptually beautiful phenomenon with important ramifications for fault-tolerant quantum computing. Over the last few decades the field has evolved from a highly theoretical subject to an active experimental area, particularly following proposals for trapping non-Abelian anyons in ‘engineered’ structures built from well-understood components. In this short overview we briefly tour the impressive progress that has taken place in the quest for the simplest type of non-Abelian anyon—defects binding Majorana zero modes—and then turn to similar strategies for pursuing more exotic excitations. Specifically, we describe how interfacing simple quantum Hall systems with conventional superconductors yields ‘parafermionic’ generalizations of Majorana modes and even Fibonacci anyons—the latter enabling fully fault tolerant universal quantum computation. We structure our treatment in a manner that unifies these topics in a coherent way. The ideas synthesized here spotlight largely uncharted experimental territory in the field of quantum Hall physics that appears ripe for discovery.

  13. Detecting 3d Non-Abelian Anyons via Adiabatic Cooling

    NASA Astrophysics Data System (ADS)

    Yamamoto, Seiji; Freedman, Michael; Yang, Kun

    2011-03-01

    Majorana fermions lie at the heart of a number of recent developments in condensed matter physics. One important application is the realization of non-abelian statistics and consequently a foundation for topological quantum computation. Theoretical propositions for Majorana systems abound, but experimental detection has proven challenging. Most attempts involve interferometry, but the degeneracy of the anyon state can be leveraged to produce a cooling effect, as previously shown in 2d. We apply this method of anyon detection to the 3d anyon model of Teo and Kane. Like the Fu-Kane model, this involves a hybrid system of topological insulator (TI) and superconductor (SC). The Majorana modes are localized to anisotropic hedgehogs in the order parameter which appear at the TI-SC interface. The effective model bears some resemblance to the non-Abelian Higgs model with scalar coupling as studied, for example, by Jackiw and Rebbi. In order to make concrete estimates relevant to experiments, we use parameters appropriate to Ca doped Bi 2 Se 3 as the topological insulator and Cu doped Bi 2 Se 3 as the superconductor. We find a temperature window in the milli-Kelvin regime where the presence of 3d non-abelian anyons will lead to an observable cooling effect.

  14. Quantisation of monopoles with non-abelian magnetic charge

    NASA Astrophysics Data System (ADS)

    Bais, F. A.; Schroers, B. J.

    1998-02-01

    Magnetic monopoles in Yang-Mills-Higgs theory with a non-abelian unbroken gauge group are classified by holomorphic charges in addition to the topological charges familiar from the abelian case. As a result the moduli spaces of monopoles of given topological charge are stratified according to the holomorphic charges. Here the physical consequences of the stratification are explored in the case where the gauge group SU(3) is broken to U(2). The description due to Dancer of the moduli space of charge-two monopoles is reviewed and interpreted physically in terms of non-abelian magnetic dipole moments. Semi-classical quantisation leads to dyonic states which are labelled by a magnetic charge and a representation of the subgroup of U(2) which leaves the magnetic charge invariant (centraliser subgroup). A key result of this paper is that these states fall into representations of the semi-direct product U(2) ⋉ R4. The combination rules (Clebsch-Gordan coefficients) of dyonic states can thus be deduced. Electric-magnetic duality properties of the theory are discussed in the light of our results, and supersymmetric dyonic BPS states which fill the SL(2, Z) orbit of the basic massive W-bosons are found.

  15. Discrete symmetries and de Sitter spacetime

    SciTech Connect

    Cotăescu, Ion I. Pascu, Gabriel

    2014-11-24

    Aspects of the ambiguity in defining quantum modes on de Sitter spacetime using a commuting system composed only of differential operators are discussed. Discrete symmetries and their actions on the wavefunction in commonly used coordinate charts are reviewed. It is argued that the system of commuting operators can be supplemented by requiring the invariance of the wavefunction to combined discrete symmetries- a criterion which selects a single state out of the α-vacuum family. Two such members of this family are singled out by particular combined discrete symmetries- states between which exists a well-known thermality relation.

  16. Quark confinement due to non-Abelian magnetic monopoles in SU(3) Yang-Mills theory

    SciTech Connect

    Kondo, Kei-Ichi; Shibata, Akihiro; Shinohara, Toru; Kato, Seikou

    2012-10-23

    We present recent results on quark confinement: in SU(3) Yang-Mills theory, confinement of fundamental quarks is obtained due to the dual Meissner effect originated from non-Abelian magnetic monopoles defined in a gauge-invariant way, which is distinct from the well-known Abelian projection scenario. This is achieved by using a non-Abelian Stokes theorem for the Wilson loop operator and a new reformulation of the Yang-Mills theory.

  17. Faddeev–Jackiw quantization of an Abelian and non-Abelian exotic action for gravity in three dimensions

    SciTech Connect

    Escalante, Alberto Manuel-Cabrera, J.

    2015-10-15

    A detailed Faddeev–Jackiw quantization of an Abelian and non-Abelian exotic action for gravity in three dimensions is performed. We obtain for the theories under study the constraints, the gauge transformations, the generalized Faddeev–Jackiw brackets and we perform the counting of physical degrees of freedom. In addition, we compare our results with those found in the literature where the canonical analysis is developed, in particular, we show that both the generalized Faddeev–Jackiw brackets and Dirac’s brackets coincide to each other. Finally we discuss some remarks and prospects. - Highlights: • A detailed Faddeev–Jackiw analysis for exotic action of gravity is performed. • We show that Dirac’s brackets and Generalized [FJ] brackets are equivalent. • Without fixing the gauge exotic action is a non-commutative theory. • The fundamental gauge transformations of the theory are found. • Dirac and Faddeev–Jackiw approaches are compared.

  18. Tri-bimaximal mixing from twisted Friedberg-Lee symmetry

    NASA Astrophysics Data System (ADS)

    Araki, Takeshi; Takahashi, Ryo

    2009-10-01

    We investigate the Friedberg-Lee (FL) symmetry and its promotion to include the μ- τ symmetry, and call this the twisted FL symmetry. Based on the twisted FL symmetry, two possible schemes are presented toward the realistic neutrino mass spectrum and the tri-bimaximal mixing. In the first scheme, we suggest the semi-uniform translation of the FL symmetry. The second one is based on the S 3 permutation family symmetry. The breaking terms, which are twisted FL symmetric, are introduced. Some viable models in each scheme are also presented.

  19. Galactic center γ-ray excess in hidden sector DM models with dark gauge symmetries: local Z{sub 3} symmetry as an example

    SciTech Connect

    Ko, P.; Tang, Yong

    2015-01-16

    We show that hidden sector dark matter (DM) models with local dark gauge symmetries make a natural playground for the possible γ-ray excess from the galactic center (GC). We first discuss in detail the GC γ-ray excess in a scalar dark matter (DM) model with local Z{sub 3} symmetry which was recently proposed by the present authors. Within this model, scalar DM with mass 30–70 GeV is allowed due to the newly-opened (semi-)annihilation channels of a DM pair into dark Higgs ϕ and/or dark photon Z′ pair, and the γ-ray spectrum from the GC can be fit within this model. Then we argue that the GC gamma ray excess can be easily accommodated within hidden sector dark matter models where DM is stabilized by local gauge symmetries, due to the presence of dark Higgs (and also dark photon for Abelian dark gauge symmetry)

  20. Galactic center γ-ray excess in hidden sector DM models with dark gauge symmetries: local Z{sub 3} symmetry as an example

    SciTech Connect

    Ko, P.; Tang, Yong E-mail: ytang@kias.re.kr

    2015-01-01

    We show that hidden sector dark matter (DM) models with local dark gauge symmetries make a natural playground for the possible γ-ray excess from the galactic center (GC). We first discuss in detail the GC γ-ray excess in a scalar dark matter (DM) model with local Z{sub 3} symmetry which was recently proposed by the present authors. Within this model, scalar DM with mass 30–70 GeV is allowed due to the newly-opened (semi-)annihilation channels of a DM pair into dark Higgs φ and/or dark photon Z' pair, and the γ-ray spectrum from the GC can be fit within this model. Then we argue that the GC gamma ray excess can be easily accommodated within hidden sector dark matter models where DM is stabilized by local gauge symmetries, due to the presence of dark Higgs (and also dark photon for Abelian dark gauge symmetry)

  1. Gauge-invariant implementation of the Abelian-Higgs model on optical lattices

    NASA Astrophysics Data System (ADS)

    Bazavov, A.; Meurice, Y.; Tsai, S.-W.; Unmuth-Yockey, J.; Zhang, Jin

    2015-10-01

    We present a gauge-invariant effective action for the Abelian-Higgs model (scalar electrodynamics) with a chemical potential μ on a (1 +1 )-dimensional lattice. This formulation provides an expansion in the hopping parameter κ which we test with Monte Carlo simulations for a broad range of the inverse gauge coupling βp l=1 /g2 and small values of the scalar self-coupling λ . In the opposite limit of infinitely large λ , the partition function can be written as a traced product of local tensors which allows us to write exact blocking formulas. Gauss's law is automatically satisfied and the introduction of μ has consequences only if we have an external electric field, g2=0 or an explicit gauge symmetry breaking. The time-continuum limit of the blocked transfer matrix can be obtained numerically and, for g2=0 and a spin-1 truncation, the small volume energy spectrum is identical to the low energy spectrum of a two-species Bose-Hubbard model in the limit of large on-site repulsion. We extend this procedure for finite βp l and derive a spin-1 approximation of the Hamiltonian. It involves new terms corresponding to transitions among the two species in the Bose-Hubbard model. We propose an optical lattice implementation involving a ladder structure.

  2. Relativistic Pseudospin Symmetry

    SciTech Connect

    Ginocchio, Joseph N.

    2011-05-06

    We show that the pseudospin symmetry that Akito Arima discovered many years ago (with collaborators) is a symmetry of the the Dirac Hamiltonian for which the sum of the scalar and vector potentials are a constant. In this paper we discuss some of the implications of this relativistic symmetry and the experimental data that support these predictions. In his original paper Akito also discussed pseudo-U(3) symmetry. We show that pseudo-U(3) symmetry is a symmetry of the Dirac Hamiltonian for which the sum of harmonic oscillator vector and scalar potentials are equal to a constant, and we give the generators of pseudo-U(3) symmetry. Going beyond the mean field we summarize new results on non relativistic shell model Hamiltonians that have pseudospin symmetry and pseudo-orbital angular momentum symmetry as a dynamical symmetries.

  3. Global symmetries and renormalizability of Lee-Wick theories

    SciTech Connect

    Chivukula, R. Sekhar; Farzinnia, Arsham; Foadi, Roshan; Simmons, Elizabeth H.

    2010-08-01

    In this paper we discuss the global symmetries and the renormalizability of Lee-Wick (LW) scalar QED. In particular, in the ''auxiliary-field'' formalism we identify softly broken SO(1,1) global symmetries of the theory. We introduce SO(1,1) invariant gauge-fixing conditions that allow us to show in the auxiliary-field formalism directly that the number of superficially divergent amplitudes in a LW Abelian gauge theory is finite. To illustrate the renormalizability of the theory, we explicitly carry out the one-loop renormalization program in LW scalar QED and demonstrate how the counterterms required are constrained by the joint conditions of gauge and SO(1,1) invariance. We also compute the one-loop beta functions in LW scalar QED and contrast them with those of ordinary scalar QED.

  4. The near-symmetry of proteins.

    PubMed

    Bonjack-Shterengartz, Maayan; Avnir, David

    2015-04-01

    The majority of protein oligomers form clusters which are nearly symmetric. Understanding of that imperfection, its origins, and perhaps also its advantages requires the conversion of the currently used vague qualitative descriptive language of the near-symmetry into an accurate quantitative measure that will allow to answer questions such as: "What is the degree of symmetry deviation of the protein?," "how do these deviations compare within a family of proteins?," and so on. We developed quantitative methods to answer this type of questions, which are capable of analyzing the whole protein, its backbone or selected portions of it, down to comparison of symmetry-related specific amino-acids, and which are capable of visualizing the various levels of symmetry deviations in the form of symmetry maps. We have applied these methods on an extensive list of homomers and heteromers and found that apparently all proteins never reach perfect symmetry. Strikingly, even homomeric protein clusters are never ideally symmetric. We also found that the main burden of symmetry distortion is on the amino-acids near the symmetry axis; that it is mainly the more hydrophilic amino-acids that take place in symmetry-distortive interactions; and more. The remarkable ability of heteromers to preserve near-symmetry, despite the different sequences, was also shown and analyzed. The comprehensive literature on the suggested advantages symmetric oligomerizations raises a yet-unsolved key question: If symmetry is so advantageous, why do proteins stop shy of perfect symmetry? Some tentative answers to be tested in further studies are suggested in a concluding outlook.

  5. Rotating black holes with non-Abelian hair

    NASA Astrophysics Data System (ADS)

    Kleihaus, Burkhard; Kunz, Jutta; Navarro-Lérida, Francisco

    2016-12-01

    We here review asymptotically flat rotating black holes in the presence of non-Abelian gauge fields. Like their static counterparts these black holes are no longer uniquely determined by their global charges. In the case of pure SU(2) Yang-Mills fields, the rotation generically induces an electric charge, while the black holes do not carry a magnetic charge. When a Higgs field is coupled, rotating black holes with monopole hair arise in the case of a Higgs triplet, while in the presence of a complex Higgs doublet the black holes carry sphaleron hair. The inclusion of a dilaton allows for Smarr type mass formulae.

  6. Abelian tensor hierarchy in 4D N = 1 conformal supergravity

    NASA Astrophysics Data System (ADS)

    Aoki, Shuntaro; Higaki, Tetsutaro; Yamada, Yusuke; Yokokura, Ryo

    2016-09-01

    We consider Abelian tensor hierarchy in four-dimensional N = 1 supergravity in the conformal superspace formalism, where the so-called covariant approach is used to antisymmetric tensor fields. We introduce p-form gauge superfields as superforms in the conformal superspace. We solve the Bianchi identities under the constraints for the super-forms. As a result, each of form fields is expressed by a single gauge invariant superfield. We also show the relation between the superspace formalism and the superconformal tensor calculus.

  7. Abelian tensor hierarchy in 4D, N = 1 superspace

    NASA Astrophysics Data System (ADS)

    Becker, Katrin; Becker, Melanie; Linch, William D.; Robbins, Daniel

    2016-03-01

    With the goal of constructing the supersymmetric action for all fields, massless and massive, obtained by Kaluza-Klein compactification from type II theory or M-theory in a closed form, we embed the (Abelian) tensor hierarchy of p-forms in four-dimensional, N =1superspaceandconstructitsChern-Simons-likeinvariants. Whenspecializedtothe case in which the tensors arise from a higher-dimensional theory, the invariants may be interpreted as higher-dimensional Chern-Simons forms reduced to four dimensions. As an application of the formalism, we construct the eleven-dimensional Chern-Simons form in terms of four-dimensional, N = 1 superfields.

  8. On spectral synthesis on zero-dimensional Abelian groups

    SciTech Connect

    Platonov, S S

    2013-09-30

    Let G be a zero-dimensional locally compact Abelian group all of whose elements are compact, and let C(G) be the space of all complex-valued continuous functions on G. A closed linear subspace H⊆C(G) is said to be an invariant subspace if it is invariant with respect to the translations τ{sub y}:f(x)↦f(x+y), y∈G. In the paper, it is proved that any invariant subspace H admits spectral synthesis, that is, H coincides with the closed linear span of the characters of G belonging to H. Bibliography: 25 titles.

  9. On flavor symmetry in lattice quantum chromodynamics

    NASA Astrophysics Data System (ADS)

    Saidi, El Hassan

    2012-02-01

    Using a well established method to engineer non-abelian symmetries in superstring compactifications, we study the link between the point splitting method of Creutz et al. [PoS: Lattice 2010, 078 (2010) and Creutz et al. JHEP 041, 1012 (2010)] for implementing flavor symmetry in lattice QCD; and singularity theory in complex algebraic geometry. We show amongst others that Creutz flavors for naive fermions are intimately related with toric singularities of a class of complex Kahler manifolds that are explicitly built here. In the case of naive fermions of QCD2N, Creutz flavors are shown to live at the poles of real 2-spheres and carry quantum charges of the fundamental of [SU(2)]2N. We show moreover that the two Creutz flavors in Karsten-Wilczek model, with Dirac operator in reciprocal space of the form i{γ }1F1+i{γ }2F2+ i{γ }3F3+ i/sin α {γ }_{4}F4, are related with the small resolution of conifold singularity that live at sin α = 0. Other related features are also studied.

  10. Flavor symmetry breaking and meson masses.

    SciTech Connect

    Bhagwat, M. S.; Chang, L.; Liu, Y.-X.; Roberts, C. D.; Tandy, P. C.; Physics; Peking Univ.; National Lab. of Heavy Ion Accelerator; The Key Lab. of Heavy Ion Physics; Kent State Univ.

    2007-10-01

    The axial-vector Ward-Takahashi identity is used to derive mass formulas for neutral pseudoscalar mesons. Flavor symmetry breaking entails nonideal flavor content for these states. Adding that the {eta} is not a Goldstone mode, exact chiral-limit relations are developed from the identity. They connect the dressed-quark propagator to the topological susceptibility. It is confirmed that in the chiral limit the {eta} mass is proportional to the matrix element which connects this state to the vacuum via the topological susceptibility. The implications of the mass formulas are illustrated using an elementary dynamical model, which includes an Ansatz for that part of the Bethe-Salpeter kernel related to the non-Abelian anomaly. In addition to the current-quark masses, the model involves two parameters, one of which is a mass-scale. It is employed in an analysis of pseudoscalar- and vector-meson bound-states. While the effects of SU(N{sub f}=2) and SU(N{sub f}=3) flavor symmetry breaking are emphasized, the five-flavor spectra are described. Despite its simplicity, the model is elucidative and phenomenologically efficacious; e.g., it predicts {eta}-{eta} mixing angles of {approx} -15{sup o} and {pi}{sup 0}-{eta} angles of {approx}1{sup o}.

  11. Entanglement entropy and nonabelian gauge symmetry

    NASA Astrophysics Data System (ADS)

    Donnelly, William

    2014-11-01

    Entanglement entropy has proven to be an extremely useful concept in quantum field theory. Gauge theories are of particular interest, but for these systems the entanglement entropy is not clearly defined because the physical Hilbert space does not factor as a tensor product according to regions of space. Here we review a definition of entanglement entropy that applies to abelian and nonabelian lattice gauge theories. This entanglement entropy is obtained by embedding the physical Hilbert space into a product of Hilbert spaces associated to regions with boundary. The latter Hilbert spaces include degrees of freedom on the entangling surface that transform like surface charges under the gauge symmetry. These degrees of freedom are shown to contribute to the entanglement entropy, and the form of this contribution is determined by the gauge symmetry. We test our definition using the example of two-dimensional Yang-Mills theory, and find that it agrees with the thermal entropy in de Sitter space, and with the results of the Euclidean replica trick. We discuss the possible implications of this result for more complicated gauge theories, including quantum gravity.

  12. Non-Abelian dynamics in the resonant decay of the Higgs after inflation

    SciTech Connect

    Enqvist, Kari; Nurmi, Sami; Rusak, Stanislav E-mail: sami.nurmi@helsinki.fi

    2014-10-01

    We study the resonant decay of the Higgs condensate into weak gauge bosons after inflation and estimate the corrections arising from the non-Abelian self-interactions of the gauge fields. We find that non-Abelian interaction terms induce an effective mass which tends to shut down the resonance. For the broad resonance relevant for the Standard Model Higgs the produced gauge particles backreact on the dynamics of the Higgs condensate before the non-Abelian terms grow large. The non-Abelian terms can however significantly affect the final stages of the resonance after the backreaction. In the narrow resonance regime, which may be important for extensions of the Standard Model, the non-Abelian terms affect already the linear stage and terminate the resonance before the Higgs condensate is affected by the backreaction of decay products.

  13. Symmetries in Physics

    NASA Astrophysics Data System (ADS)

    Brading, Katherine; Castellani, Elena

    2010-01-01

    Preface; Copyright acknowledgements; List of contributors; 1. Introduction; Part I. Continuous Symmetries: 2. Classic texts: extracts from Weyl and Wigner; 3. Review paper: On the significance of continuous symmetry to the foundations of physics C. Martin; 4. The philosophical roots of the gauge principle: Weyl and transcendental phenomenological idealism T. Ryckman; 5. Symmetries and Noether's theorems K. A. Brading and H. R. Brown; 6. General covariance, gauge theories, and the Kretschmann objection J. Norton; 7. The interpretation of gauge symmetry M. Redhead; 8. Tracking down gauge: an ode to the constrained Hamiltonian formalism J. Earman; 9. Time-dependent symmetries: the link between gauge symmetries and indeterminism D. Wallace; 10. A fourth way to the Aharanov-Bohm effect A. Nounou; Part II. Discrete Symmetries: 11. Classic texts: extracts from Lebniz, Kant and Black; 12. Review paper: Understanding permutation symmetry S. French and D. Rickles; 13. Quarticles and the identity of discernibles N. Hugget; 14. Review paper: Handedness, parity violation, and the reality of space O. Pooley; 15. Mirror symmetry: what is it for a relational space to be orientable? N. Huggett; 16. Physics and Leibniz's principles S. Saunders; Part III. Symmetry Breaking: 17: Classic texts: extracts from Curie and Weyl; 18. Extract from G. Jona-Lasinio: Cross-fertilization in theoretical physics: the case of condensed matter and particle physics G. Jona-Lasinio; 19. Review paper: On the meaning of symmetry breaking E. Castellani; 20. Rough guide to spontaneous symmetry breaking J. Earman; 21. Spontaneous symmetry breaking: theoretical arguments and philosophical problems M. Morrison; Part IV. General Interpretative Issues: 22. Classic texts: extracts from Wigner; 23. Symmetry as a guide to superfluous theoretical structure J. Ismael and B. van Fraassen; 24. Notes on symmetries G. Belot; 25. Symmetry, objectivity, and design P. Kosso; 26. Symmetry and equivalence E. Castellani.

  14. Generalized CP symmetries and special regions of parameter space in the two-Higgs-doublet model

    SciTech Connect

    Ferreira, P. M.; Haber, Howard E.; Silva, Joao P.

    2009-06-01

    We consider the impact of imposing generalized CP symmetries on the Higgs sector of the two-Higgs-doublet model, and identify three classes of symmetries. Two of these classes constrain the scalar potential parameters to an exceptional region of parameter space, which respects either a Z{sub 2} discrete flavor symmetry or a U(1) symmetry. We exhibit a basis-invariant quantity that distinguishes between these two possible symmetries. We also show that the consequences of imposing these two classes of CP symmetry can be achieved by combining Higgs family symmetries, and that this is not possible for the usual CP symmetry. We comment on the vacuum structure and on renormalization in the presence of these symmetries. Finally, we demonstrate that the standard CP symmetry can be used to build all the models we identify, including those based on Higgs family symmetries.

  15. Approximate flavor symmetries

    SciTech Connect

    Rasin, A.

    1994-04-01

    We discuss the idea of approximate flavor symmetries. Relations between approximate flavor symmetries and natural flavor conservation and democracy models is explored. Implications for neutrino physics are also discussed.

  16. Magnetohydrodynamic equilibria with incompressible flows: Symmetry approach

    SciTech Connect

    Cicogna, G.; Pegoraro, F.

    2015-02-15

    We identify and discuss a family of azimuthally symmetric, incompressible, magnetohydrodynamic plasma equilibria with poloidal and toroidal flows in terms of solutions of the Generalized Grad Shafranov (GGS) equation. These solutions are derived by exploiting the incompressibility assumption, in order to rewrite the GGS equation in terms of a different dependent variable, and the continuous Lie symmetry properties of the resulting equation and, in particular, a special type of “weak” symmetries.

  17. Matrix product states and the non-Abelian rotor model

    NASA Astrophysics Data System (ADS)

    Milsted, Ashley

    2016-04-01

    We use uniform matrix product states to study the (1 +1 )D O (2 ) and O (4 ) rotor models, which are equivalent to the Kogut-Susskind formulation of matter-free non-Abelian lattice gauge theory on a "Hawaiian earring" graph for U (1 ) and S U (2 ), respectively. Applying tangent space methods to obtain ground states and determine the mass gap and the β function, we find excellent agreement with known results, locating the Berezinskii-Kosterlitz-Thouless transition for O (2 ) and successfully entering the asymptotic weak-coupling regime for O (4 ). To obtain a finite local Hilbert space, we truncate in the space of generalized Fourier modes of the gauge group, comparing the effects of different cutoff values. We find that higher modes become important in the crossover and weak-coupling regimes of the non-Abelian theory, where entanglement also suddenly increases. This could have important consequences for tensor network state studies of Yang-Mills on higher-dimensional graphs.

  18. Topology, and (in)stability of non-Abelian monopoles

    NASA Astrophysics Data System (ADS)

    Zhang, Peng-Ming; Horvathy, Peter A.; Rawnsley, John

    2012-01-01

    The stability problem of non-Abelian monopoles with respect to "Brandt-Neri-Coleman type" variations reduces to that of a pure gauge theory on the two-sphere. Each topological sector admits exactly one stable monopole charge, and each unstable monopole admits 2∑(2|q|-1) negative modes, where the sum goes over the negative eigenvalues q of an operator related to the non-Abelian charge Q of Goddard, Nuyts and Olive. An explicit construction for the [up-to-conjugation] unique stable charge, as well as the negative modes of the Hessian at any other charge is given. The relation to loops in the residual group is explained. From the global point of view, the instability is associated with energy-reducing two-spheres, which, consistently with the Morse theory, generate the homology of the configuration space. Our spheres are tangent to the negative modes at the considered critical point, and may indicate possible decay routes of an unstable monopole as a cascade into lower lying critical points.

  19. Adiabatic limit in Abelian Higgs model with application to Seiberg-Witten equations

    NASA Astrophysics Data System (ADS)

    Sergeev, A.

    2017-03-01

    In this paper we deal with the (2 + 1)-dimensional Higgs model governed by the Ginzburg-Landau Lagrangian. The static solutions of this model, called otherwise vortices, are described by the theorem of Taubes. This theorem gives, in particular, an explicit description of the moduli space of vortices (with respect to gauge transforms). However, much less is known about the moduli space of dynamical solutions. A description of slowly moving solutions may be given in terms of the adiabatic limit. In this limit the dynamical Ginzburg-Landau equations reduce to the adiabatic equation coinciding with the Euler equation for geodesics on the moduli space of vortices with respect to the Riemannian metric (called T-metric) determined by the kinetic energy of the model. A similar adiabatic limit procedure can be used to describe approximately solutions of the Seiberg-Witten equations on 4-dimensional symplectic manifolds. In this case the geodesics of T-metric are replaced by the pseudoholomorphic curves while the solutions of Seiberg-Witten equations reduce to the families of vortices defined in the normal planes to the limiting pseudoholomorphic curve. Such families should satisfy a nonlinear ∂-equation which can be considered as a complex analogue of the adiabatic equation. Respectively, the arising pseudoholomorphic curves may be considered as complex analogues of adiabatic geodesics in (2 + 1)-dimensional case. In this sense the Seiberg-Witten model may be treated as a (2 + 1)-dimensional analogue of the (2 + 1)-dimensional Abelian Higgs model2.

  20. Polynomial Graphs and Symmetry

    ERIC Educational Resources Information Center

    Goehle, Geoff; Kobayashi, Mitsuo

    2013-01-01

    Most quadratic functions are not even, but every parabola has symmetry with respect to some vertical line. Similarly, every cubic has rotational symmetry with respect to some point, though most cubics are not odd. We show that every polynomial has at most one point of symmetry and give conditions under which the polynomial has rotational or…

  1. Chiral symmetry and chiral-symmetry breaking

    SciTech Connect

    Peskin, M.E.

    1982-12-01

    These lectures concern the dynamics of fermions in strong interaction with gauge fields. Systems of fermions coupled by gauge forces have a very rich structure of global symmetries, which are called chiral symmetries. These lectures will focus on the realization of chiral symmetries and the causes and consequences of thier spontaneous breaking. A brief introduction to the basic formalism and concepts of chiral symmetry breaking is given, then some explicit calculations of chiral symmetry breaking in gauge theories are given, treating first parity-invariant and then chiral models. These calculations are meant to be illustrative rather than accurate; they make use of unjustified mathematical approximations which serve to make the physics more clear. Some formal constraints on chiral symmetry breaking are discussed which illuminate and extend the results of our more explicit analysis. Finally, a brief review of the phenomenological theory of chiral symmetry breaking is presented, and some applications of this theory to problems in weak-interaction physics are discussed. (WHK)

  2. Symmetry operation measures.

    PubMed

    Pinsky, Mark; Casanova, David; Alemany, Pere; Alvarez, Santiago; Avnir, David; Dryzun, Chaim; Kizner, Ziv; Sterkin, Alexander

    2008-01-30

    We introduce a new mathematical tool for quantifying the symmetry contents of molecular structures: the Symmetry Operation Measures. In this approach, we measure the minimal distance between a given structure and the structure which is obtained after applying a selected symmetry operation on it. If the given operation is a true symmetry operation for the structure, this distance is zero; otherwise it gives an indication of how different the transformed structure is from the original one. Specifically, we provide analytical solutions for measures of all the improper rotations, S n p, including mirror symmetry and inversion, as well as for all pure rotations, C n p. These measures provide information complementary to the Continuous Symmetry Measures (CSM) that evaluate the distance between a given structure and the nearest structure which belongs to a selected symmetry point-group.

  3. Josephson instantons and Josephson monopoles in a non-Abelian Josephson junction

    NASA Astrophysics Data System (ADS)

    Nitta, Muneto

    2015-08-01

    The non-Abelian Josephson junction is a junction of non-Abelian color superconductors sandwiching an insulator, or a non-Abelian domain wall if flexible, whose low-energy dynamics is described by a U (N ) principal chiral model with the conventional pion mass. A non-Abelian Josephson vortex is a non-Abelian vortex (color magnetic flux tube) residing inside the junction, that is described as a non-Abelian sine-Gordon soliton. In this paper, we propose Josephson instantons and Josephson monopoles, that is, Yang-Mills instantons and monopoles inside a non-Abelian Josephson junction, respectively, and show that they are described as S U (N ) Skyrmions and U (1 )N -1 vortices in the U (N ) principal chiral model without and with a twisted-mass term, respectively. Instantons with a twisted boundary condition are reduced (or T-dual) to monopoles, implying that C PN -1 lumps are T-dual to C PN -1 kinks inside a vortex. Here we find S U (N ) Skyrmions are T-dual to U (1 )N-1 vortices inside a wall. Our configurations suggest a yet another duality between C PN -1 lumps and S U (N ) Skyrmions as well as that between C PN -1 kinks and U (1 )N-1 vortices, viewed from different host solitons. They also suggest a duality between fractional instantons and bions in the C PN -1 model and those in the S U (N ) principal chiral model.

  4. CP symmetry in optical systems

    NASA Astrophysics Data System (ADS)

    Dana, Brenda; Bahabad, Alon; Malomed, Boris A.

    2015-04-01

    We introduce a model of a dual-core optical waveguide with opposite signs of the group-velocity dispersion in the two cores, and a phase-velocity mismatch between them. The coupler is embedded into an active host medium, which provides for the linear coupling of a gain-loss type between the two cores. The same system can be derived, without phenomenological assumptions, by considering the three-wave propagation in a medium with the quadratic nonlinearity, provided that the depletion of the second-harmonic pump is negligible. This linear system offers an optical realization of the charge-parity symmetry, while the addition of the intracore cubic nonlinearity breaks the symmetry. By means of direct simulations and analytical approximations, it is demonstrated that the linear system generates expanding Gaussian states, while the nonlinear one gives rise to broad oscillating solitons, as well as a general family of stable stationary gap solitons.

  5. Detecting non-Abelian geometric phases with three-level Λ systems

    NASA Astrophysics Data System (ADS)

    Du, Yan-Xiong; Xue, Zheng-Yuan; Zhang, Xin-Ding; Yan, Hui

    2011-09-01

    We show that a non-Abelian gauge potential in two nearly degenerated dressed states may be induced by two laser beams interacting with a three-level Λ atomic system. We demonstrate that the populations of the atomic states at the end of a composed path formed by two closed loops are dependent on the order of those two loops, showing an unambiguous signature of the non-Abelian geometric phase. Through numerical calculations, we show that the non-Abelian feature of the geometric phases can be tested under realistic conditions.

  6. Detecting non-Abelian geometric phases with three-level {Lambda} systems

    SciTech Connect

    Du Yanxiong; Xue Zhengyuan; Zhang Xinding; Yan Hui

    2011-09-15

    We show that a non-Abelian gauge potential in two nearly degenerated dressed states may be induced by two laser beams interacting with a three-level {Lambda} atomic system. We demonstrate that the populations of the atomic states at the end of a composed path formed by two closed loops are dependent on the order of those two loops, showing an unambiguous signature of the non-Abelian geometric phase. Through numerical calculations, we show that the non-Abelian feature of the geometric phases can be tested under realistic conditions.

  7. Contraction of broken symmetries via Kac-Moody formalism

    NASA Astrophysics Data System (ADS)

    Daboul, Jamil

    2006-08-01

    I investigate contractions via Kac-Moody formalism. In particular, I show how the symmetry algebra of the standard two-dimensional Kepler system, which was identified by Daboul and Slodowy as an infinite-dimensional Kac-Moody loop algebra, and was denoted by H2, gets reduced by the symmetry breaking term, defined by the Hamiltonian H(β )=(1/2m)(p12+p22)-α/r-βr-1/2cos((φ-γ)/2). For this H(β ) I define two symmetry loop algebras Li(β), i =1,2, by choosing the "basic generators" differently. These Li(β) can be mapped isomorphically onto subalgebras of H2, of codimension two or three, revealing the reduction of symmetry. Both factor algebras Li(β)/Ii(E,β), relative to the corresponding energy-dependent ideals Ii(E,β), are isomorphic to so(3) and so(2,1) for E <0 and E >0, respectively, just as for the pure Kepler case. However, they yield two different nonstandard contractions as E →0, namely to the Heisenberg-Weyl algebra h3=w1 or to an Abelian Lie algebra, instead of the Euclidean algebra e(2) for the pure Kepler case. The above-noted example suggests a general procedure for defining generalized contractions, and also illustrates the "deformation contraction hysteresis," where contraction which involves two contraction parameters can yield different contracted algebras, if the limits are carried out in different order.

  8. Symplectic analysis of three-dimensional Abelian topological gravity

    NASA Astrophysics Data System (ADS)

    Cartas-Fuentevilla, R.; Escalante, Alberto; Herrera-Aguilar, Alfredo

    2017-02-01

    A detailed Faddeev-Jackiw quantization of an Abelian topological gravity is performed; we show that this formalism is equivalent and more economical than Dirac's method. In particular, we identify the complete set of constraints of the theory, from which the number of physical degrees of freedom is explicitly computed. We prove that the generalized Faddeev-Jackiw brackets and the Dirac ones coincide with each other. Moreover, we perform the Faddeev-Jackiw analysis of the theory at the chiral point, and the full set of constraints and the generalized Faddeev-Jackiw brackets are constructed. Finally we compare our results with those found in the literature and we discuss some remarks and prospects.

  9. Abelian gauge theories on compact manifolds and the Gribov ambiguity

    SciTech Connect

    Kelnhofer, Gerald

    2008-05-15

    We study the quantization of Abelian gauge theories of principal torus bundles over compact manifolds with and without boundary. It is shown that these gauge theories suffer from a Gribov ambiguity originating in the nontriviality of the bundle of connections whose geometrical structure will be analyzed in detail. Motivated by the stochastic quantization approach, we propose a modified functional integral measure on the space of connections that takes the Gribov problem into account. This functional integral measure is used to calculate the partition function, Green's functions, and the field strength correlating functions in any dimension by using the fact that the space of inequivalent connections itself admits the structure of a bundle over a finite dimensional torus. Green's functions are shown to be affected by the nontrivial topology, giving rise to nonvanishing vacuum expectation values for the gauge fields.

  10. Matrix model for non-Abelian quantum Hall states

    NASA Astrophysics Data System (ADS)

    Dorey, Nick; Tong, David; Turner, Carl

    2016-08-01

    We propose a matrix quantum mechanics for a class of non-Abelian quantum Hall states. The model describes electrons which carry an internal SU(p ) spin. The ground states of the matrix model include spin-singlet generalizations of the Moore-Read and Read-Rezayi states and, in general, lie in a class previously introduced by Blok and Wen. The effective action for these states is a U(p ) Chern-Simons theory. We show how the matrix model can be derived from quantization of the vortices in this Chern-Simons theory and how the matrix model ground states can be reconstructed as correlation functions in the boundary WZW model.

  11. Three-loop calculations in non-abelian gauge theories

    NASA Astrophysics Data System (ADS)

    Tarasov, O. V.; Vladimirov, A. A.

    2013-09-01

    A detailed description of the method for analytical evaluation of the three-loop contributions to renormalization group functions is presented. This method is employed to calculate the charge renormalization function and anomalous dimensions for non-Abelian gauge theories with fermions in the three-loop approximation. A three-loop expression for the effective charge of QCD is given. Charge renormalization effects in the SU(4)-supersymmetric gauge model is shown to vanish at this level. A complete list of required formulas is given in Appendix. The above-mentioned results of three-loop calculations were published by the present authors (with A.Yu. Zharkov and L.V. Avdeev) in 1980 in Physics Letters B. The present text, which treats the subject in more details and contains a lot of calculational techniques, was also published in 1980 as the JINR Communication E2-80-483.

  12. Topological degeneracy of non-Abelian states for dummies

    NASA Astrophysics Data System (ADS)

    Oshikawa, Masaki; Kim, Yong Baek; Shtengel, Kirill; Nayak, Chetan; Tewari, Sumanta

    2007-06-01

    We present a physical construction of degenerate groundstates of the Moore-Read Pfaffian states, which exhibits non-Abelian statistics, on general Riemann surface with genus g. The construction is given by a generalization of the recent argument [M.O., T. Senthil, Phys. Rev. Lett. 96 (2006) 060601] which relates fractionalization and topological order. The nontrivial groundstate degeneracy obtained by Read and Green [Phys. Rev. B 61 (2000) 10267] based on differential geometry is reproduced exactly. Some restrictions on the statistics, due to the fractional charge of the quasiparticle are also discussed. Furthermore, the groundstate degeneracy of the p + i p superconductor in two dimensions, which is closely related to the Pfaffian states, is discussed with a similar construction.

  13. Classification and properties of symmetry-enriched topological phases: Chern-Simons approach with applications to Z2 spin liquids

    NASA Astrophysics Data System (ADS)

    Lu, Yuan-Ming; Vishwanath, Ashvin

    2016-04-01

    We study (2+1)-dimensional phases with topological order, such as fractional quantum Hall states and gapped spin liquids, in the presence of global symmetries. Phases that share the same topological order can then differ depending on the action of symmetry, leading to symmetry-enriched topological (SET) phases. Here, we present a K -matrix Chern-Simons approach to identify distinct phases with Abelian topological order, in the presence of unitary or antiunitary global symmetries. A key step is the identification of a smooth edge sewing condition that is used to check if two putative phases are indeed distinct. We illustrate this method by classifying Z2 topological order (Z2 spin liquids) in the presence of an internal Z2 global symmetry for which we find six distinct phases. These include two phases with an unconventional action of symmetry that permutes anyons leading to symmetry-protected Majorana edge modes. Other routes to realizing protected edge states in SET phases are identified. Symmetry-enriched Laughlin states and double-semion theories are also discussed. Somewhat surprisingly, we observe that (i) gauging the global symmetry of distinct SET phases leads to topological orders with the same total quantum dimension, and (ii) a pair of distinct SET phases can yield the same topological order on gauging the symmetry.

  14. Non-abelian black holes and black strings in higher dimensions

    NASA Astrophysics Data System (ADS)

    Hartmann, Betti

    2009-05-01

    We review the properties of static, higher dimensional black hole solutions in theories where non-abelian gauge fields are minimally coupled to gravity. It is shown that black holes with hyperspherically symmetric horizon topology do not exist in d>4, but that hyperspherically symmetric black holes can be constructed numerically in generalized Einstein-Yang-Mills models. 5-dimensional black strings with horizon topology S2xS1 are also discussed. These are so-called undeformed and deformed non-abelian black strings, which are translationally invariant and correspond to 4-dimensional non-abelian black holes trivially extended into one extra dimensions. The fact that black strings can be deformed, i.e. axially symmetric for constant values of the extra coordinate is a new feature as compared to black string solutions of Einstein (-Maxwell) theory. It is argued that these non-abelian black strings are thermodynamically unstable.

  15. Free energy for a damped cold atom in SU(2) non-Abelian gauge potentials

    NASA Astrophysics Data System (ADS)

    Guingarey, Issoufou; Avossevou, Gabriel Y. H.

    2017-03-01

    Our main aim in this work is to find out the exact formula of the equilibrium free energy for a cold atom subjected to a harmonic potential in the background of an artificial non-Abelian uniform magnetic field and linearly coupled to a heat bath. The heat bath consists of a collection of independent quantum harmonic oscillators, while its interaction with the cold atom is modeled in terms of bilinear coupling between the coordinate variables of the cold atom and the oscillators. The main thermodynamic properties of such a system are modified in comparison with the Abelian case. For a non-Abelian magnetic field generated from the laser methods employing degenerate dark states, we evaluate the effect of the non-Abelian dynamics on the magnetic moment of the cold atom.

  16. Field theory aspects of non-Abelian T-duality and {N} =2 linear quivers

    NASA Astrophysics Data System (ADS)

    Lozano, Yolanda; Núñez, Carlos

    2016-05-01

    In this paper we propose a linear quiver with gauge groups of increasing rank as field theory dual to the AdS 5 background constructed by Sfetsos and Thompson through non-Abelian T-duality. The formalism to study 4d {N} = 2 SUSY CFTs developed by Gaiotto and Maldacena is essential for our proposal. We point out an interesting relation between (Hopf) Abelian and non-Abelian T-dual backgrounds that allows to see both backgrounds as different limits of a solution constructed by Maldacena and Núñez. This suggests different completions of the long quiver describing the CFT dual to the nonAbelian T-dual background that match different observables.

  17. On algebraic cycles on complex Abelian schemes over smooth projective curves

    NASA Astrophysics Data System (ADS)

    Tankeev, S. G.

    2008-08-01

    If the Hodge conjecture holds for some generic (in the sense of Weil) geometric fibre X_s of an Abelian scheme \\pi\\colon X\\to C over a smooth projective curve C, then numerical equivalence of algebraic cycles on X coincides with homological equivalence. The Hodge conjecture for all complex Abelian varieties is equivalent to the standard conjecture B(X) of Lefschetz type on the algebraicity of the Hodge operator \\ast for all Abelian schemes \\pi\\colon X\\to C over smooth projective curves. We investigate some properties of the Gauss-Manin connection and Hodge bundles associated with Abelian schemes over smooth projective curves, with applications to the conjectures of Hodge and Tate.

  18. Renormalizability of a generalized gauge fixing interpolating among the Coulomb, Landau and maximal Abelian gauges

    SciTech Connect

    Capri, M.A.L. . E-mail: marcio@dft.if.uerj.br; Sobreiro, R.F. . E-mail: sobreiro@uerj.br; Sorella, S.P. . E-mail: sorella@uerj.br; Thibes, R. . E-mail: thibes@dft.if.uerj.br

    2007-08-15

    A detailed discussion of the renormalization properties of a class of gauges which interpolates among the Landau, Coulomb and maximal Abelian gauges is provided in the framework of the algebraic renormalization in Euclidean Yang-Mills theories in four dimensions.

  19. Internal symmetry in protein structures: prevalence, functional relevance and evolution.

    PubMed

    Balaji, Santhanam

    2015-06-01

    Symmetry has been found at various levels of biological organization in the protein structural universe. Numerous evolutionary studies have proposed connections between internal symmetry within protein tertiary structures, quaternary associations and protein functions. Recent computational methods, such as SymD and CE-Symm, facilitate a large-scale detection of internal symmetry in protein structures. Based on the results from these methods, about 20% of SCOP folds, superfamilies and families are estimated to have structures with internal symmetry (Figure 1d). All-β and membrane proteins fold classes contain a relatively high number of unique instances of internal symmetry. In addition to the axis of symmetry, anecdotal evidence suggests that, the region of connection or contact between symmetric units could coincide with functionally relevant sites within a fold. General principles that underlie protein internal symmetry and their connections to protein structural integrity and functions remain to be elucidated.

  20. Magnetic monopoles and Abelian gauge fixing in SU(4) gauge group

    NASA Astrophysics Data System (ADS)

    Rafibakhsh, Shahnoosh; Eshraghi, Mojtaba; Kahnemuii, Mohammad Javad

    2016-01-01

    Abelian gauge fixing procedure is used to create the SU (4) magnetic monopoles in the vicinity of the points where the gluon field becomes singular. The matrix of the scalar field is considered as almost diagonal in the SU (2) and SU (3) subspaces. The gauge transformation which diagonalizes the hedgehog filed, transforms the gluon field into two regular and singular parts. The abelian magnetic monopoles which appear in the latter part obey the quantization condition.

  1. Dual Meissner Effect and Non-Abelian Magnetic Monopole in SU(3) Yang-Mills Theory

    NASA Astrophysics Data System (ADS)

    Shibata, Akihiro; Kondo, Kei-Ichi; Shinohara, Toru

    2013-03-01

    We measure the color flux produced by a pair of quark and antiquark and examine whether or not the non-Abelian dual superconductivity claimed by us is indeed a mechanism of quark confinement. We present a preliminary result of the direct evidence for the non-abelian dual Meissner effect, that is to say, restricted U(2)-field part of the flux tube plays the dominant role in the quarkantiquark potential.

  2. Marginal and non-commutative deformations via non-abelian T-duality

    NASA Astrophysics Data System (ADS)

    Hoare, Ben; Thompson, Daniel C.

    2017-02-01

    In this short article we develop recent proposals to relate Yang-Baxter sigmamodels and non-abelian T-duality. We demonstrate explicitly that the holographic spacetimes associated to both (multi-parameter)- β-deformations and non-commutative deformations of N = 4 super Yang-Mills gauge theory including the RR fluxes can be obtained via the machinery of non-abelian T-duality in Type II supergravity.

  3. Cost of seven-brane gauge symmetry in a quadrillion F-theory compactifications

    NASA Astrophysics Data System (ADS)

    Halverson, James; Tian, Jiahua

    2017-01-01

    We study seven-branes in O (1 015) four-dimensional F-theory compactifications where seven-brane moduli must be tuned in order to achieve non-Abelian gauge symmetry. The associated compact spaces B are the set of all smooth weak Fano toric threefolds. By a study of fine-star-regular triangulations of three-dimensional reflexive polytopes, the number of such spaces is estimated to be 5.8 ×1 014≲Nbases≲1.8 ×1 017 . Typically hundreds or thousands of moduli must be tuned to achieve symmetry for h11(B )<10 , but the average number drops sharply into the range O (25 )- O (200 ) as h11(B ) increases. For some low-rank groups, such as S U (2 ) and S U (3 ), there exist examples where only a few moduli must be tuned in order to achieve seven-brane gauge symmetry.

  4. Neutrino mass and mixing with discrete symmetry.

    PubMed

    King, Stephen F; Luhn, Christoph

    2013-05-01

    This is a review paper about neutrino mass and mixing and flavour model building strategies based on discrete family symmetry. After a pedagogical introduction and overview of the whole of neutrino physics, we focus on the PMNS mixing matrix and the latest global fits following the Daya Bay and RENO experiments which measure the reactor angle. We then describe the simple bimaximal, tri-bimaximal and golden ratio patterns of lepton mixing and the deviations required for a non-zero reactor angle, with solar or atmospheric mixing sum rules resulting from charged lepton corrections or residual trimaximal mixing. The different types of see-saw mechanism are then reviewed as well as the sequential dominance mechanism. We then give a mini-review of finite group theory, which may be used as a discrete family symmetry broken by flavons either completely, or with different subgroups preserved in the neutrino and charged lepton sectors. These two approaches are then reviewed in detail in separate chapters including mechanisms for flavon vacuum alignment and different model building strategies that have been proposed to generate the reactor angle. We then briefly review grand unified theories (GUTs) and how they may be combined with discrete family symmetry to describe all quark and lepton masses and mixing. Finally, we discuss three model examples which combine an SU(5) GUT with the discrete family symmetries A₄, S₄ and Δ(96).

  5. Symmetries in Lagrangian Dynamics

    ERIC Educational Resources Information Center

    Ferrario, Carlo; Passerini, Arianna

    2007-01-01

    In the framework of Noether's theorem, a distinction between Lagrangian and dynamical symmetries is made, in order to clarify some aspects neglected by textbooks. An intuitive setting of the concept of invariance of differential equations is presented. The analysis is completed by deriving the symmetry properties in the motion of a charged…

  6. Symmetry and Interculturality

    ERIC Educational Resources Information Center

    Marchis, Iuliana

    2009-01-01

    Symmetry is one of the fundamental concepts in Geometry. It is a Mathematical concept, which can be very well connected with Art and Ethnography. The aim of the article is to show how to link the geometrical concept symmetry with interculturality. For this mosaics from different countries are used.

  7. Symmetry-respecting topologically ordered surface phase of three-dimensional electron topological insulators

    NASA Astrophysics Data System (ADS)

    Metlitski, Max A.; Kane, C. L.; Fisher, Matthew P. A.

    2015-09-01

    A three-dimensional electron topological insulator (ETI) is a phase of matter protected by particle-number conservation and time-reversal symmetry. It was previously believed that the surface of an ETI must be gapless unless one of these symmetries is broken. A well-known symmetry-preserving, gapless surface termination of an ETI supports an odd number of Dirac cones. In this paper, we deduce a symmetry-respecting, gapped surface termination of an ETI, which carries an intrinsic two-dimensional (2d) topological order, Moore-Read×U (1) -2 . The Moore-Read sector supports non-Abelian charge 1 /4 anyons, while the Abelian, U (1) -2 , (antisemion) sector is electrically neutral. Time-reversal symmetry is implemented in this surface phase in a highly nontrivial way. Moreover, it is impossible to realize this phase strictly in 2d, simultaneously preserving its implementation of both the particle-number and time-reversal symmetries. A one-dimensional (1d) edge on the ETI surface between the topologically ordered phase and the topologically trivial time-reversal-broken phase with a Hall conductivity σx y=1 /2 carries a right-moving neutral Majorana mode, a right-moving bosonic charge mode, and a left-moving bosonic neutral mode. The topologically ordered phase is separated from the surface superconductor by a direct second-order phase transition in the X Y* universality class, which is driven by the condensation of a charge 1 /2 boson, when approached from the topologically ordered side, and proliferation of a flux 4 π (2 h c /e ) vortex, when approached from the superconducting side. In addition, we prove that time-reversal invariant (interacting) electron insulators with no intrinsic topological order and electromagnetic response characterized by a θ angle, θ =π , do not exist if the electrons transform as Kramers singlets under time reversal.

  8. Domain wall network as QCD vacuum: confinement, chiral symmetry, hadronization

    NASA Astrophysics Data System (ADS)

    Nedelko, Sergei N.; Voronin, Vladimir V.

    2017-03-01

    An approach to QCD vacuum as a medium describable in terms of statistical ensemble of almost everywhere homogeneous Abelian (anti-)self-dual gluon fields is reviewed. These fields play the role of the confining medium for color charged fields as well as underline the mechanism of realization of chiral SUL(Nf) × SUR(Nf) and UA(1) symmetries. Hadronization formalism based on this ensemble leads to manifestly defined quantum effective meson action. Strong, electromagnetic and weak interactions of mesons are represented in the action in terms of nonlocal n-point interaction vertices given by the quark-gluon loops averaged over the background ensemble. Systematic results for the mass spectrum and decay constants of radially excited light, heavy-light mesons and heavy quarkonia are presented. Relationship of this approach to the results of functional renormalization group and Dyson-Schwinger equations, and the picture of harmonic confinement is briefly outlined.

  9. Preserving spherical symmetry in axisymmetric coordinates for diffusion problems

    SciTech Connect

    Brunner, T. A.; Kolev, T. V.; Bailey, T. S.; Till, A. T.

    2013-07-01

    Persevering symmetric solutions, even in the under-converged limit, is important to the robustness of production simulation codes. We explore the symmetry preservation in both a continuous nodal and a mixed finite element method. In their standard formulation, neither method preserves spherical solution symmetry in axisymmetric (RZ) coordinates. We propose two methods, one for each family of finite elements, that recover spherical symmetry for low-order finite elements on linear or curvilinear meshes. This is a first step toward understanding achieving symmetry for higher-order elements. (authors)

  10. AGT relations for abelian quiver gauge theories on ALE spaces

    NASA Astrophysics Data System (ADS)

    Pedrini, Mattia; Sala, Francesco; Szabo, Richard J.

    2016-05-01

    We construct level one dominant representations of the affine Kac-Moody algebra gl̂k on the equivariant cohomology groups of moduli spaces of rank one framed sheaves on the orbifold compactification of the minimal resolution Xk of the Ak-1 toric singularity C2 /Zk. We show that the direct sum of the fundamental classes of these moduli spaces is a Whittaker vector for gl̂k, which proves the AGT correspondence for pure N = 2 U(1) gauge theory on Xk. We consider Carlsson-Okounkov type Ext-bundles over products of the moduli spaces and use their Euler classes to define vertex operators. Under the decomposition gl̂k ≃ h ⊕sl̂k, these vertex operators decompose as products of bosonic exponentials associated to the Heisenberg algebra h and primary fields of sl̂k. We use these operators to prove the AGT correspondence for N = 2 superconformal abelian quiver gauge theories on Xk.

  11. Non-abelian higher gauge theory and categorical bundle

    NASA Astrophysics Data System (ADS)

    Viennot, David

    2016-12-01

    A gauge theory is associated with a principal bundle endowed with a connection permitting to define horizontal lifts of paths. The horizontal lifts of surfaces cannot be defined into a principal bundle structure. An higher gauge theory is an attempt to generalize the bundle structure in order to describe horizontal lifts of surfaces. A such attempt is particularly difficult for the non-abelian case. Some structures have been proposed to realize this goal (twisted bundle, gerbes with connection, bundle gerbe, 2-bundle). Each of them uses a category in place of the total space manifold of the usual principal bundle structure. Some of them replace also the structure group by a category (more precisely a Lie crossed module viewed as a category). But the base space remains still a simple manifold (possibly viewed as a trivial category with only identity arrows). We propose a new principal categorical bundle structure, with a Lie crossed module as structure groupoid, but with a base space belonging to a bigger class of categories (which includes non-trivial categories), that we called affine 2-spaces. We study the geometric structure of the categorical bundles built on these categories (which are a more complicated structure than the 2-bundles) and the connective structures on these bundles. Finally we treat an example interesting for quantum dynamics which is associated with the Bloch wave operator theory.

  12. Fast non-Abelian geometric gates via transitionless quantum driving.

    PubMed

    Zhang, J; Kyaw, Thi Ha; Tong, D M; Sjöqvist, Erik; Kwek, Leong-Chuan

    2015-12-21

    A practical quantum computer must be capable of performing high fidelity quantum gates on a set of quantum bits (qubits). In the presence of noise, the realization of such gates poses daunting challenges. Geometric phases, which possess intrinsic noise-tolerant features, hold the promise for performing robust quantum computation. In particular, quantum holonomies, i.e., non-Abelian geometric phases, naturally lead to universal quantum computation due to their non-commutativity. Although quantum gates based on adiabatic holonomies have already been proposed, the slow evolution eventually compromises qubit coherence and computational power. Here, we propose a general approach to speed up an implementation of adiabatic holonomic gates by using transitionless driving techniques and show how such a universal set of fast geometric quantum gates in a superconducting circuit architecture can be obtained in an all-geometric approach. Compared with standard non-adiabatic holonomic quantum computation, the holonomies obtained in our approach tends asymptotically to those of the adiabatic approach in the long run-time limit and thus might open up a new horizon for realizing a practical quantum computer.

  13. Non-Abelian dark matter and dark radiation

    NASA Astrophysics Data System (ADS)

    Buen-Abad, Manuel A.; Marques-Tavares, Gustavo; Schmaltz, Martin

    2015-07-01

    We propose a new class of dark matter models with unusual phenomenology. What is ordinary about our models is that dark matter particles are weakly interacting massive particles; they are weakly coupled to the standard model and have weak scale masses. What is unusual is that they come in multiplets of a new dark non-Abelian gauge group with milliweak coupling. The massless dark gluons of this dark gauge group contribute to the energy density of the Universe as a form of weakly self-interacting dark radiation. In this paper we explore the consequences of having (i) dark matter in multiplets, (ii) self-interacting dark radiation, and (iii) dark matter which is weakly coupled to dark radiation. We find that (i) dark matter cross sections are modified by multiplicity factors which have significant consequences for collider searches and indirect detection, and (ii) dark gluons have thermal abundances which affect the cosmic microwave background (CMB) as dark radiation. Unlike additional massless neutrino species the dark gluons are interacting and have vanishing viscosity and (iii) the coupling of dark radiation to dark matter represents a new mechanism for damping the large scale structure power spectrum. A combination of additional radiation and slightly damped structure is interesting because it can remove tensions between global Λ CDM fits from the CMB and direct measurements of the Hubble expansion rate (H0) and large scale structure (σ8).

  14. Aspects of finite field-dependent symmetry in SU(2) Cho-Faddeev-Niemi decomposition

    NASA Astrophysics Data System (ADS)

    Upadhyay, Sudhaker

    2013-11-01

    In this Letter we consider SU(2) Yang-Mills theory analyzed in Cho-Faddeev-Niemi variables which remains invariant under local gauge transformations. The BRST symmetries of this theory are generalized by making the infinitesimal parameter finite and field-dependent. Further, we show that under appropriate choices of finite and field-dependent parameter, the gauge-fixing and ghost terms corresponding to Landau as well as maximal Abelian gauge for such Cho-Faddeev-Niemi decomposed theory appear naturally within functional integral through Jacobian calculation.

  15. (Super)symmetries of semiclassical models in theoretical and condensed matter physics

    NASA Astrophysics Data System (ADS)

    Ngome, J.-P.

    2011-03-01

    Van Holten's covariant algorithm for deriving conserved quantities is presented, with particular attention paid to Runge-Lenz-type vectors. The classical dynamics of isospin-carrying particles is reviewed. Physical applications including non-Abelian monopole-type systems in diatoms, introduced by Moody, Shapere and Wilczek, are considered. Applied to curved space, the formalism of van Holten allows us to describe the dynamical symmetries of generalized Kaluza-Klein monopoles. The framework is extended to supersymmetry and applied to the SUSY of the monopoles. Yet another application concerns the three-dimensional non-commutative oscillator.

  16. Mixed Symmetry-Tipe (k,1) Massless Tensor Fields. Consistent Interactions Of Dual Linearized Gravity

    NASA Astrophysics Data System (ADS)

    Bizdadea, C.; Saliu, S. O.; Toma, M.

    2012-12-01

    A particular case of interactions of a single massless tensor field with the mixed symmetry corresponding to a two-column Young diagram (k,1) with k=4, dual to linearized gravity in D=7, is considered in the context of: self-couplings, cross-interactions with a Pauli-Fierz field, cross-couplings to purely matter theories, and interactions with an Abelian 1-form. The general approach relies on the deformation of the solution to the master equation from the antifield-BRST formalism by means of the local cohomology of the BRST differential.

  17. A universal symmetry detection algorithm.

    PubMed

    Maurer, Peter M

    2015-01-01

    Research on symmetry detection focuses on identifying and detecting new types of symmetry. The paper presents an algorithm that is capable of detecting any type of permutation-based symmetry, including many types for which there are no existing algorithms. General symmetry detection is library-based, but symmetries that can be parameterized, (i.e. total, partial, rotational, and dihedral symmetry), can be detected without using libraries. In many cases it is faster than existing techniques. Furthermore, it is simpler than most existing techniques, and can easily be incorporated into existing software. The algorithm can also be used with virtually any type of matrix-based symmetry, including conjugate symmetry.

  18. Coupled oscillators with parity-time symmetry

    NASA Astrophysics Data System (ADS)

    Tsoy, Eduard N.

    2017-02-01

    Different models of coupled oscillators with parity-time (PT) symmetry are studied. Hamiltonian functions for two and three linear oscillators coupled via coordinates and accelerations are derived. Regions of stable dynamics for two coupled oscillators are obtained. It is found that in some cases, an increase of the gain-loss parameter can stabilize the system. A family of Hamiltonians for two coupled nonlinear oscillators with PT-symmetry is obtained. An extension to high-dimensional PT-symmetric systems is discussed.

  19. Dynamical symmetries for fermions

    SciTech Connect

    Guidry, M.

    1989-01-01

    An introduction is given to the Fermion Dynamical Symmetry Model (FDSM). The analytical symmetry limits of the model are then applied to the calculation of physical quantities such as ground-state masses and B(E{sub 2}) values in heavy nuclei. These comparisons with data provide strong support for a new principle of collective motion, the Dynamical Pauli Effect, and suggest that dynamical symmetries which properly account for the pauli principle are much more persistent in nuclear structure than the corresponding boson symmetries. Finally, we present an assessment of criticisms which have been voiced concerning the FDSM, and a discussion of new phenomena and exotic spectroscopy'' which may be suggested by the model. 14 refs., 8 figs., 4 tabs.

  20. Dynamical spacetime symmetry

    NASA Astrophysics Data System (ADS)

    Lovelady, Benjamin C.; Wheeler, James T.

    2016-04-01

    According to the Coleman-Mandula theorem, any gauge theory of gravity combined with an internal symmetry based on a Lie group must take the form of a direct product in order to be consistent with basic assumptions of quantum field theory. However, we show that an alternative gauging of a simple group can lead dynamically to a spacetime with compact internal symmetry. The biconformal gauging of the conformal symmetry of n-dimensional Euclidean space doubles the dimension to give a symplectic manifold. Examining one of the Lagrangian submanifolds in the flat case, we find that in addition to the expected S O (n ) connection and curvature, the solder form necessarily becomes Lorentzian. General coordinate invariance gives rise to an S O (n -1 ,1 ) connection on the spacetime. The principal fiber bundle character of the original S O (n ) guarantees that the two symmetries enter as a direct product, in agreement with the Coleman-Mandula theorem.

  1. Gauge symmetry from decoupling

    NASA Astrophysics Data System (ADS)

    Wetterich, C.

    2017-02-01

    Gauge symmetries emerge from a redundant description of the effective action for light degrees of freedom after the decoupling of heavy modes. This redundant description avoids the use of explicit constraints in configuration space. For non-linear constraints the gauge symmetries are non-linear. In a quantum field theory setting the gauge symmetries are local and can describe Yang-Mills theories or quantum gravity. We formulate gauge invariant fields that correspond to the non-linear light degrees of freedom. In the context of functional renormalization gauge symmetries can emerge if the flow generates or preserves large mass-like terms for the heavy degrees of freedom. They correspond to a particular form of gauge fixing terms in quantum field theories.

  2. The Symmetries of QCD

    ScienceCinema

    Sekhar Chivukula

    2016-07-12

    The symmetries of a quantum field theory can be realized in a variety of ways. Symmetries can be realized explicitly, approximately, through spontaneous symmetry breaking or, via an anomaly, quantum effects can dynamically eliminate a symmetry of the theory that was present at the classical level.  Quantum Chromodynamics (QCD), the modern theory of the strong interactions, exemplify each of these possibilities. The interplay of these effects determine the spectrum of particles that we observe and, ultimately, account for 99% of the mass of ordinary matter. 

  3. Animal Gaits and Symmetry

    NASA Astrophysics Data System (ADS)

    Golubitsky, Martin

    2012-04-01

    Many gaits of four-legged animals are described by symmetry. For example, when a horse paces it moves both left legs in unison and then both right legs and so on. The motion is described by two symmetries: Interchange front and back legs, and swap left and right legs with a half-period phase shift. Biologists postulate the existence of a central pattern generator (CPG) in the neuronal system that sends periodic signals to the legs. CPGs can be thought of as electrical circuits that produce periodic signals and can be modeled by systems with symmetry. In this lecture we discuss animal gaits; use gait symmetries to construct a simplest CPG architecture that naturally produces quadrupedal gait rhythms; and make several testable predictions about gaits.

  4. Nonzero {theta}{sub 13} for neutrino mixing in a supersymmetric B-L gauge model with T{sub 7} lepton flavor symmetry

    SciTech Connect

    Cao Qinghong; Khalil, Shaaban; Ma, Ernest; Okada, Hiroshi

    2011-10-01

    We discuss how {theta}{sub 13}{ne}0 is accommodated in a recently proposed renormalizable model of neutrino mixing using the non-Abelian discrete symmetry T{sub 7} in the context of a supersymmetric extension of the standard model with gauged U(1){sub B-L}. We predict a correlation between {theta}{sub 13} and {theta}{sub 23}, as well as the effective neutrino mass m{sub ee} in neutrinoless double beta decay.

  5. Non-Abelian hydrodynamics and the flow of spin in spin orbit coupled substances

    NASA Astrophysics Data System (ADS)

    Leurs, B. W. A.; Nazario, Z.; Santiago, D. I.; Zaanen, J.

    2008-04-01

    Motivated by the heavy ion collision experiments there is much activity in studying the hydrodynamical properties of non-Abelian (quark-gluon) plasmas. A major question is how to deal with color currents. Although not widely appreciated, quite similar issues arise in condensed matter physics in the context of the transport of spins in the presence of spin-orbit coupling. The key insight is that the Pauli Hamiltonian governing the leading relativistic corrections in condensed matter systems can be rewritten in a language of SU(2) covariant derivatives where the role of the non-Abelian gauge fields is taken by the physical electromagnetic fields: the Pauli system can be viewed as Yang-Mills quantum-mechanics in a 'fixed frame', and it can be viewed as an 'analogous system' for non-Abelian transport in the same spirit as Volovik's identification of the He superfluids as analogies for quantum fields in curved space time. We take a similar perspective as Jackiw and coworkers in their recent study of non-Abelian hydrodynamics, twisting the interpretation into the 'fixed frame' context, to find out what this means for spin transport in condensed matter systems. We present an extension of Jackiw's scheme: non-Abelian hydrodynamical currents can be factored in a 'non-coherent' classical part, and a coherent part requiring macroscopic non-Abelian quantum entanglement. Hereby it becomes particularly manifest that non-Abelian fluid flow is a much richer affair than familiar hydrodynamics, and this permits us to classify the various spin transport phenomena in condensed matter physics in an unifying framework. The "particle based hydrodynamics" of Jackiw et al. is recognized as the high temperature spin transport associated with semiconductor spintronics. In this context the absence of faithful hydrodynamics is well known, but in our formulation it is directly associated with the fact that the covariant conservation of non-Abelian currents turns into a disastrous non

  6. Quantum Spectral Symmetries

    NASA Astrophysics Data System (ADS)

    Hamhalter, Jan; Turilova, Ekaterina

    2017-02-01

    Quantum symmetries of spectral lattices are studied. Basic properties of spectral order on A W ∗-algebras are summarized. Connection between projection and spectral automorphisms is clarified by showing that, under mild conditions, any spectral automorphism is a composition of function calculus and Jordan ∗-automorphism. Complete description of quantum spectral symmetries on Type I and Type II A W ∗-factors are completely described.

  7. Fractional quantum Hall bilayers at half filling: Tunneling-driven non-Abelian phase

    NASA Astrophysics Data System (ADS)

    Zhu, W.; Liu, Zhao; Haldane, F. D. M.; Sheng, D. N.

    2016-12-01

    Multicomponent quantum Hall systems with internal degrees of freedom provide a fertile ground for the emergence of exotic quantum liquids. Here, we investigate the possibility of non-Abelian topological order in the half-filled fractional quantum Hall (FQH) bilayer system driven by the tunneling effect between two layers. By means of the state-of-the-art density-matrix renormalization group, we unveil "fingerprint" evidence of the non-Abelian Moore-Read Pfaffian state emerging in the intermediate-tunneling regime, including the ground-state degeneracy on the torus geometry and the topological entanglement spectroscopy (entanglement spectrum and topological entanglement entropy) on the spherical geometry, respectively. Remarkably, the phase transition from the previously identified Abelian (331) Halperin state to the non-Abelian Moore-Read Pfaffian state is determined to be continuous, which is signaled by the continuous evolution of the universal part of the entanglement spectrum, and discontinuities in the excitation gap and the derivative of the ground-state energy. Our results not only provide a "proof-of-principle" demonstration of realizing a non-Abelian state through coupling different degrees of freedom, but also open up a possibility in FQH bilayer systems for detecting different chiral p -wave pairing states.

  8. The nuclear symmetry energy

    NASA Astrophysics Data System (ADS)

    Baldo, M.; Burgio, G. F.

    2016-11-01

    The nuclear symmetry energy characterizes the variation of the binding energy as the neutron to proton ratio of a nuclear system is varied. This is one of the most important features of nuclear physics in general, since it is just related to the two component nature of the nuclear systems. As such it is one of the most relevant physical parameters that affect the physics of many phenomena and nuclear processes. This review paper presents a survey of the role and relevance of the nuclear symmetry energy in different fields of research and of the accuracy of its determination from the phenomenology and from the microscopic many-body theory. In recent years, a great interest was devoted not only to the Nuclear Matter symmetry energy at saturation density but also to its whole density dependence, which is an essential ingredient for our understanding of many phenomena. We analyze the nuclear symmetry energy in different realms of nuclear physics and astrophysics. In particular we consider the nuclear symmetry energy in relation to nuclear structure, astrophysics of Neutron Stars and supernovae, and heavy ion collision experiments, trying to elucidate the connections of these different fields on the basis of the symmetry energy peculiarities. The interplay between experimental and observational data and theoretical developments is stressed. The expected future developments and improvements are schematically addressed, together with most demanded experimental and theoretical advances for the next few years.

  9. Alternative schemes of predicting lepton mixing parameters from discrete flavor and C P symmetry

    NASA Astrophysics Data System (ADS)

    Lu, Jun-Nan; Ding, Gui-Jun

    2017-01-01

    We suggest two alternative schemes to predict lepton mixing angles as well as C P violating phases from a discrete flavor symmetry group combined with C P symmetry. In the first scenario, the flavor and C P symmetry is broken to the residual groups of the structure Z2×C P in the neutrino and charged lepton sectors. The resulting lepton mixing matrix depends on two free parameters θν and θl. This type of breaking pattern is extended to the quark sector. In the second scenario, an Abelian subgroup of the flavor group is preserved by the charged lepton mass matrix and the neutrino mass matrix is invariant under a single remnant C P transformation, all lepton mixing parameters are determined in terms of three free parameters θ1 ,2 ,3. We derive the most general criterion to determine whether two distinct residual symmetries lead to the same mixing pattern if the redefinition of the free parameters θν ,l and θ1 ,2 ,3 is taken into account. We have studied the lepton mixing patterns arising from the flavor group S4 and C P symmetry which are subsequently broken to all of the possible residual symmetries discussed in this work.

  10. Pauli-Villars Regularization of Non-Abelian Gauge Theories

    NASA Astrophysics Data System (ADS)

    Hiller, J. R.

    2016-07-01

    As an extension of earlier work on QED, we construct a BRST-invariant Lagrangian for SU(N) Yang-Mills theory with fundamental matter, regulated by the inclusion of massive Pauli-Villars (PV) gluons and PV quarks. The underlying gauge symmetry for massless PV gluons is generalized to accommodate the PV-index-changing currents that are required by the regularization. Auxiliary adjoint scalars are used, in a mechanism due to Stueckelberg, to attribute mass to the PV gluons and the PV quarks. The addition of Faddeev-Popov ghosts then establishes a residual BRST symmetry. Although there are drawbacks to the approach, in particular the computational load of a large number of PV fields and a nonlocal interaction of the ghost fields, this formulation could provide a foundation for renormalizable nonperturbative solutions of light-front QCD in an arbitrary covariant gauge.

  11. Perfect Abelian dominance of confinement in quark-antiquark potential in SU(3) lattice QCD

    NASA Astrophysics Data System (ADS)

    Suganuma, Hideo; Sakumichi, Naoyuki

    2016-01-01

    In the context of the dual superconductor picture for the confinement mechanism, we study maximally Abelian (MA) projection of quark confinement in SU(3) quenched lattice QCD with 324 at β=6.4 (i.e., a ≃ 0.058 fm). We investigate the static quark-antiquark potential V(r), its Abelian part VAbel(r) and its off-diagonal part Voff(r), respectively, from the on-axis lattice data. As a remarkable fact, we find almost perfect Abelian dominance for quark confinement, i.e., σAbel ≃ σ for the string tension, on the fine and large-volume lattice. We find also a nontrivial summation relation of V (r) ≃ VAbel(r)+Voff(r).

  12. Perfect Abelian dominance of confinement in quark-antiquark potential in SU(3) lattice QCD

    SciTech Connect

    Suganuma, Hideo; Sakumichi, Naoyuki

    2016-01-22

    In the context of the dual superconductor picture for the confinement mechanism, we study maximally Abelian (MA) projection of quark confinement in SU(3) quenched lattice QCD with 32{sup 4} at β=6.4 (i.e., a ≃ 0.058 fm). We investigate the static quark-antiquark potential V(r), its Abelian part V{sub Abel}(r) and its off-diagonal part V{sub off}(r), respectively, from the on-axis lattice data. As a remarkable fact, we find almost perfect Abelian dominance for quark confinement, i.e., σ{sub Abel} ≃ σ for the string tension, on the fine and large-volume lattice. We find also a nontrivial summation relation of V (r) ≃ V{sub Abel}(r)+V{sub off}(r)

  13. Abelian projections of the mass-deformed ABJM theory and weakly curved dual geometry

    NASA Astrophysics Data System (ADS)

    Hyun, Young-Hwan; Kim, Yoonbai; Kwon, O.-Kab; Tolla, D. D.

    2013-04-01

    We construct N=2, 4 supersymmetric Abelian projections of the N=6 mass-deformed Aharony-Bergman-Jafferis-Maldacena (ABJM) theory. There are well-defined dual background geometries for the N=2 Abelian theory, while those geometries are unclear for the N=4 Abelian theory. The N=2 theory is built on the supersymmetric vacua of the mass-deformed ABJM theory, which are proven to have a one-to-one correspondence with the Zk quotient of Lin-Lunin-Maldacena geometries. We select one special vacuum of the mass-deformed ABJM theory and show that the corresponding geometry is weakly curved at every point of the entire space transverse to the M2-branes in the large-N limit.

  14. Controlling and probing non-abelian emergent gauge potentials in spinor Bose-Fermi mixtures

    PubMed Central

    Phuc, Nguyen Thanh; Tatara, Gen; Kawaguchi, Yuki; Ueda, Masahito

    2015-01-01

    Gauge fields, typified by the electromagnetic field, often appear as emergent phenomena due to geometrical properties of a curved Hilbert subspace, and provide a key mechanism for understanding such exotic phenomena as the anomalous and topological Hall effects. Non-abelian gauge potentials serve as a source of non-singular magnetic monopoles. Here we show that unlike conventional solid materials, the non-abelianness of emergent gauge potentials in spinor Bose-Fermi atomic mixtures can be continuously varied by changing the relative particle-number densities of bosons and fermions. The non-abelian feature is captured by an explicit dependence of the measurable spin current density of fermions in the mixture on the variable coupling constant. Spinor mixtures also provide us with a method to coherently and spontaneously generate a pure spin current without relying on the spin Hall effect. Such a spin current is expected to have potential applications in the new generation of atomtronic devices. PMID:26330292

  15. Topological quantum phase transition in synthetic non-Abelian gauge potential: gauge invariance and experimental detections.

    PubMed

    Sun, Fadi; Yu, Xiao-Lu; Ye, Jinwu; Fan, Heng; Liu, Wu-Ming

    2013-01-01

    The method of synthetic gauge potentials opens up a new avenue for our understanding and discovering novel quantum states of matter. We investigate the topological quantum phase transition of Fermi gases trapped in a honeycomb lattice in the presence of a synthetic non-Abelian gauge potential. We develop a systematic fermionic effective field theory to describe a topological quantum phase transition tuned by the non-Abelian gauge potential and explore its various important experimental consequences. Numerical calculations on lattice scales are performed to compare with the results achieved by the fermionic effective field theory. Several possible experimental detection methods of topological quantum phase transition are proposed. In contrast to condensed matter experiments where only gauge invariant quantities can be measured, both gauge invariant and non-gauge invariant quantities can be measured by experimentally generating various non-Abelian gauges corresponding to the same set of Wilson loops.

  16. Topological Quantum Phase Transition in Synthetic Non-Abelian Gauge Potential: Gauge Invariance and Experimental Detections

    PubMed Central

    Sun, Fadi; Yu, Xiao-Lu; Ye, Jinwu; Fan, Heng; Liu, Wu-Ming

    2013-01-01

    The method of synthetic gauge potentials opens up a new avenue for our understanding and discovering novel quantum states of matter. We investigate the topological quantum phase transition of Fermi gases trapped in a honeycomb lattice in the presence of a synthetic non-Abelian gauge potential. We develop a systematic fermionic effective field theory to describe a topological quantum phase transition tuned by the non-Abelian gauge potential and explore its various important experimental consequences. Numerical calculations on lattice scales are performed to compare with the results achieved by the fermionic effective field theory. Several possible experimental detection methods of topological quantum phase transition are proposed. In contrast to condensed matter experiments where only gauge invariant quantities can be measured, both gauge invariant and non-gauge invariant quantities can be measured by experimentally generating various non-Abelian gauges corresponding to the same set of Wilson loops. PMID:23846153

  17. Lectures on Yangian symmetry

    NASA Astrophysics Data System (ADS)

    Loebbert, Florian

    2016-08-01

    In these introductory lectures we discuss the topic of Yangian symmetry from various perspectives. Forming the classical counterpart of the Yangian and an extension of ordinary Noether symmetries, first the concept of nonlocal charges in classical, two-dimensional field theory is reviewed. We then define the Yangian algebra following Drinfel’d's original motivation to construct solutions to the quantum Yang-Baxter equation. Different realizations of the Yangian and its mathematical role as a Hopf algebra and quantum group are discussed. We demonstrate how the Yangian algebra is implemented in quantum, two-dimensional field theories and how its generators are renormalized. Implications of Yangian symmetry on the two-dimensional scattering matrix are investigated. We furthermore consider the important case of discrete Yangian symmetry realized on integrable spin chains. Finally we give a brief introduction to Yangian symmetry in planar, four-dimensional super Yang-Mills theory and indicate its impact on the dilatation operator and tree-level scattering amplitudes. These lectures are illustrated by several examples, in particular the two-dimensional chiral Gross-Neveu model, the Heisenberg spin chain and { N }=4 superconformal Yang-Mills theory in four dimensions.

  18. Symmetry of priapulids (Priapulida). 2. Symmetry of larvae.

    PubMed

    Adrianov, A V; Malakhov, V V

    2001-02-01

    Larvae of priapulids are characterized by radial symmetry evident from both external and internal characters of the introvert and lorica. The bilaterality appears as a result of a combination of several radial symmetries: pentaradial symmetry of the teeth, octaradial symmetry of the primary scalids, 25-radial symmetry of scalids, biradial symmetry of the neck, and biradial and decaradial symmetry of the trunk. Internal radiality is exhibited by musculature and the circumpharyngeal nerve ring. Internal bilaterality is evident from the position of the ventral nerve cord and excretory elements. Externally, the bilaterality is determined by the position of the anal tubulus and two shortened midventral rows of scalids bordering the ventral nerve cord. The lorical elements define the biradial symmetry that is missing in adult priapulids. The radial symmetry of larvae is a secondary appearance considered an evolutionary adaptation to a lifestyle within the three-dimensional environment of the benthic sediment.

  19. Cold Atoms in Non-Abelian Gauge Potentials: From the Hofstadter Moth to Lattice Gauge Theory

    SciTech Connect

    Osterloh, K.; Baig, M.; Santos, L.; Zoller, P.; Lewenstein, M.

    2005-07-01

    We demonstrate how to create artificial external non-Abelian gauge potentials acting on cold atoms in optical lattices. The method employs atoms with k internal states, and laser assisted state sensitive tunneling, described by unitary kxk matrices. The single-particle dynamics in the case of intense U(2) vector potentials lead to a generalized Hofstadter butterfly spectrum which shows a complex mothlike structure. We discuss the possibility to realize non-Abelian interferometry (Aharonov-Bohm effect) and to study many-body dynamics of ultracold matter in external lattice gauge fields.

  20. Non-Abelian monopole in the parameter space of point-like interactions

    SciTech Connect

    Ohya, Satoshi

    2014-12-15

    We study non-Abelian geometric phase in N=2 supersymmetric quantum mechanics for a free particle on a circle with two point-like interactions at antipodal points. We show that non-Abelian Berry’s connection is that of SU(2) magnetic monopole discovered by Moody, Shapere and Wilczek in the context of adiabatic decoupling limit of diatomic molecule. - Highlights: • Supersymmetric quantum mechanics is an ideal playground for studying geometric phase. • We determine the parameter space of supersymmetric point-like interactions. • Berry’s connection is given by a Wu–Yang-like magnetic monopole in SU(2) Yang–Mills.

  1. Non-Abelian geometric phase and long-range atomic forces

    NASA Technical Reports Server (NTRS)

    Zygelman, B.

    1990-01-01

    It is shown how gauge fields, or geometric phases, manifest as observable effects in both bound and free diatom systems. It is shown that, in addition to altering energy splittings in bound systems, geometric phases induce transitions in levels separated by a finite-energy gap. An example is given where the non-Abelian gauge field couples nondegenerate electronic levels in a diatom. This gauge-field coupling gives rise to an observable effect. It is shown that when the diatom is 'pulled apart', the non-Abelian geometric phase manifests as a long-range atomic force.

  2. CP(N-1) model on a disk and decay of a non-Abelian string

    NASA Astrophysics Data System (ADS)

    Gorsky, A.; Milekhin, A.

    2013-10-01

    We consider the role of quantum effects in the nonperturbative decay of the non-Abelian string with orientational moduli in nonsupersymmetric D=4 gauge theory. To this aim the effective action in the CP(N-1) model on a disk at large N has been calculated. It exhibits a phase transition at some radius, the “wrong sign” Luscher term, and a large boundary boojumlike negative contribution. The effect of the θ term and the possibility of the spontaneous creation of the non-Abelian string are briefly discussed.

  3. Symmetry in context: salience of mirror symmetry in natural patterns.

    PubMed

    Cohen, Elias H; Zaidi, Qasim

    2013-05-31

    Symmetry is a biologically relevant, mathematically involving, and aesthetically compelling visual phenomenon. Mirror symmetry detection is considered particularly rapid and efficient, based on experiments with random noise. Symmetry detection in natural settings, however, is often accomplished against structured backgrounds. To measure salience of symmetry in diverse contexts, we assembled mirror symmetric patterns from 101 natural textures. Temporal thresholds for detecting the symmetry axis ranged from 28 to 568 ms indicating a wide range of salience (1/Threshold). We built a model for estimating symmetry-energy by connecting pairs of mirror-symmetric filters that simulated cortical receptive fields. The model easily identified the axis of symmetry for all patterns. However, symmetry-energy quantified at this axis correlated weakly with salience. To examine context effects on symmetry detection, we used the same model to estimate approximate symmetry resulting from the underlying texture throughout the image. Magnitudes of approximate symmetry at flanking and orthogonal axes showed strong negative correlations with salience, revealing context interference with symmetry detection. A regression model that included the context-based measures explained the salience results, and revealed why perceptual symmetry can differ from mathematical characterizations. Using natural patterns thus produces new insights into symmetry perception and its possible neural circuits.

  4. Symmetry in context: Salience of mirror symmetry in natural patterns

    PubMed Central

    Cohen, Elias H.; Zaidi, Qasim

    2013-01-01

    Symmetry is a biologically relevant, mathematically involving, and aesthetically compelling visual phenomenon. Mirror symmetry detection is considered particularly rapid and efficient, based on experiments with random noise. Symmetry detection in natural settings, however, is often accomplished against structured backgrounds. To measure salience of symmetry in diverse contexts, we assembled mirror symmetric patterns from 101 natural textures. Temporal thresholds for detecting the symmetry axis ranged from 28 to 568 ms indicating a wide range of salience (1/Threshold). We built a model for estimating symmetry-energy by connecting pairs of mirror-symmetric filters that simulated cortical receptive fields. The model easily identified the axis of symmetry for all patterns. However, symmetry-energy quantified at this axis correlated weakly with salience. To examine context effects on symmetry detection, we used the same model to estimate approximate symmetry resulting from the underlying texture throughout the image. Magnitudes of approximate symmetry at flanking and orthogonal axes showed strong negative correlations with salience, revealing context interference with symmetry detection. A regression model that included the context-based measures explained the salience results, and revealed why perceptual symmetry can differ from mathematical characterizations. Using natural patterns thus produces new insights into symmetry perception and its possible neural circuits. PMID:23729773

  5. Weakly broken galileon symmetry

    SciTech Connect

    Pirtskhalava, David; Santoni, Luca; Trincherini, Enrico; Vernizzi, Filippo

    2015-09-01

    Effective theories of a scalar ϕ invariant under the internal galileon symmetryϕ→ϕ+b{sub μ}x{sup μ} have been extensively studied due to their special theoretical and phenomenological properties. In this paper, we introduce the notion of weakly broken galileon invariance, which characterizes the unique class of couplings of such theories to gravity that maximally retain their defining symmetry. The curved-space remnant of the galileon’s quantum properties allows to construct (quasi) de Sitter backgrounds largely insensitive to loop corrections. We exploit this fact to build novel cosmological models with interesting phenomenology, relevant for both inflation and late-time acceleration of the universe.

  6. Baryons and chiral symmetry

    NASA Astrophysics Data System (ADS)

    Liu, Keh-Fei

    The relevance of chiral symmetry in baryons is highlighted in three examples in the nucleon spectroscopy and structure. The first one is the importance of chiral dynamics in understanding the Roper resonance. The second one is the role of chiral symmetry in the lattice calculation of πNσ term and strangeness. The third one is the role of chiral U(1) anomaly in the anomalous Ward identity in evaluating the quark spin and the quark orbital angular momentum. Finally, the chiral effective theory for baryons is discussed.

  7. BOOK REVIEW: Symmetry Breaking

    NASA Astrophysics Data System (ADS)

    Ryder, L. H.

    2005-11-01

    One of the most fruitful and enduring advances in theoretical physics during the last half century has been the development of the role played by symmetries. One needs only to consider SU(3) and the classification of elementary particles, the Yang Mills enlargement of Maxwell's electrodynamics to the symmetry group SU(2), and indeed the tremendous activity surrounding the discovery of parity violation in the weak interactions in the late 1950s. This last example is one of a broken symmetry, though the symmetry in question is a discrete one. It was clear to Gell-Mann, who first clarified the role of SU(3) in particle physics, that this symmetry was not exact. If it had been, it would have been much easier to discover; for example, the proton, neutron, Σ, Λ and Ξ particles would all have had the same mass. For many years the SU(3) symmetry breaking was assigned a mathematical form, but the importance of this formulation fell away when the quark model began to be taken seriously; the reason the SU(3) symmetry was not exact was simply that the (three, in those days) quarks had different masses. At the same time, and in a different context, symmetry breaking of a different type was being investigated. This went by the name of `spontaneous symmetry breaking' and its characteristic was that the ground state of a given system was not invariant under the symmetry transformation, though the interactions (the Hamiltonian, in effect) was. A classic example is ferromagnetism. In a ferromagnet the atomic spins are aligned in one direction only—this is the ground state of the system. It is clearly not invariant under a rotation, for that would change the ground state into a (similar but) different one, with the spins aligned in a different direction; this is the phenomenon of a degenerate vacuum. The contribution of the spin interaction, s1.s2, to the Hamiltonian, however, is actually invariant under rotations. As Coleman remarked, a little man living in a ferromagnet would

  8. Symmetry constraint for foreground extraction.

    PubMed

    Fu, Huazhu; Cao, Xiaochun; Tu, Zhuowen; Lin, Dongdai

    2014-05-01

    Symmetry as an intrinsic shape property is often observed in natural objects. In this paper, we discuss how explicitly taking into account the symmetry constraint can enhance the quality of foreground object extraction. In our method, a symmetry foreground map is used to represent the symmetry structure of the image, which includes the symmetry matching magnitude and the foreground location prior. Then, the symmetry constraint model is built by introducing this symmetry structure into the graph-based segmentation function. Finally, the segmentation result is obtained via graph cuts. Our method encourages objects with symmetric parts to be consistently extracted. Moreover, our symmetry constraint model is applicable to weak symmetric objects under the part-based framework. Quantitative and qualitative experimental results on benchmark datasets demonstrate the advantages of our approach in extracting the foreground. Our method also shows improved results in segmenting objects with weak, complex symmetry properties.

  9. Superfield Approach to Nilpotent Symmetries of the Freedman-Townsend Model: Novel Features

    NASA Astrophysics Data System (ADS)

    Malik, R. P.

    2012-09-01

    We perform the Becchi-Rouet-Stora-Tyutin (BRST) analysis of the Freedman-Townsend (FT) model of topologically massive non-Abelian theory by exploiting its (1-form) Yang-Mills (YM) gauge transformations to show the existence of some novel features that are totally different from the results obtained in such a kind of consideration carried out for the dynamical non-Abelian 2-form theory. We tap here the potential and power of the augmented version of Bonora-Tonin's superfield approach to BRST formalism to derive the full set of off-shell nilpotent and absolutely anticommuting (anti-)BRST symmetry transformations where, in addition to the horizontality condition (HC), we are theoretically compelled to exploit the appropriate gauge-invariant restrictions (GIRs) on the (super)fields for the derivation of the appropriate symmetry transformations for all the relevant fields. We compare our key results with that of the other such attempt for the discussion of the present model within the framework of BRST formalism.

  10. New approach to flavor symmetry and an extended naturalness principle

    NASA Astrophysics Data System (ADS)

    Barr, S. M.

    2010-09-01

    A class of nonsupersymmetric extensions of the standard model is proposed in which there is a multiplicity of light scalar doublets in a multiplet of a nonabelian family group with the standard model Higgs doublet. Anthropic tuning makes the latter light, and consequently the other scalar doublets remain light because of the family symmetry. The family symmetry greatly constrains the pattern of flavor-changing neutral-current interactions (FCNC) and p decay operators coming from scalar-exchange. Such models show that useful constraints on model-building can come from an extended naturalness principle when the electroweak scale is anthropically tuned.

  11. From non-Abelian anyons to quantum computation to coin-flipping by telephone

    NASA Astrophysics Data System (ADS)

    Mochon, Carlos

    Following their divorce, Alice and Bob would like to split some of their possessions by flipping a coin. Unwilling to meet in person, and without a trusted third party, they must figure out a scheme to flip the coin over a telephone that guarantees that neither party can cheat. The preceding scenario is the traditional definition of two-party coin-flipping. In a classical setting, without limits on the available computational power, one player can always guarantee a coin-flipping victory by cheating. However, by employing quantum communication it is possible to guarantee, with only information-theoretic assumptions, that neither party can win by cheating, with a probability greater than two thirds. Along with the description of such a protocol, this thesis derives a tight lower bound on the bias for a large family of quantum weak coin-flipping protocols, proving such a protocol optimal within the family. The protocol described herein is an improvement and generalization of one examined by Spekkens and Rudolph. The key steps of the analysis involve Kitaev's description of quantum coin-flipping as a semidefinite program whose dual problem provides a certificate that upper bounds the amount of cheating for each party. In order for such quantum protocols to be viable, though, a number of practical obstacles involving the communication and processing of quantum information must be resolved. In the second half of this thesis, a scheme for processing quantum information is presented, which uses non-abelian anyons that are the magnetic and electric excitations of a discrete-group quantum gauge theory. In particular, the connections between group structure and computational power are examined, generalizing previous work by Kitaev, Ogburn and Preskill. Anyon based computation has the advantage of being topological, which exponentially suppresses the rate of decoherence and the errors associated with the elementary quantum gates. Though no physical systems with such

  12. Nilpotent and absolutely anticommuting symmetries in the Freedman-Townsend model: Augmented superfield formalism

    NASA Astrophysics Data System (ADS)

    Shukla, A.; Krishna, S.; Malik, R. P.

    2014-12-01

    We derive the off-shell nilpotent and absolutely anticommuting Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations, corresponding to the (1-form) Yang-Mills (YM) and (2-form) tensorial gauge symmetries of the four (3+1)-dimensional (4D) Freedman-Townsend (FT) model, by exploiting the augmented version of Bonora-Tonin's (BT) superfield approach to BRST formalism where the 4D flat Minkowskian theory is generalized onto the (4, 2)-dimensional supermanifold. One of the novel observations is the fact that we are theoretically compelled to go beyond the horizontality condition (HC) to invoke an additional set of gauge-invariant restrictions (GIRs) for the derivation of the full set of proper (anti-)BRST symmetries. To obtain the (anti-)BRST symmetry transformations, corresponding to the tensorial (2-form) gauge symmetries within the framework of augmented version of BT-superfield approach, we are logically forced to modify the FT-model to incorporate an auxiliary 1-form field and the kinetic term for the antisymmetric (2-form) gauge field. This is also a new observation in our present investigation. We point out some of the key differences between the modified FT-model and Lahiri-model (LM) of the dynamical non-Abelian 2-form gauge theories. We also briefly mention a few similarities.

  13. Enhanced symmetries of gauge theory and resolving the spectrum of local operators

    NASA Astrophysics Data System (ADS)

    Kimura, Yusuke; Ramgoolam, Sanjaye

    2008-12-01

    Enhanced global non-Abelian symmetries at zero coupling in Yang Mills theory play an important role in diagonalizing the two-point functions of multimatrix operators. Generalized Casimirs constructed from the iterated commutator action of these enhanced symmetries resolve all the multiplicity labels of the bases of matrix operators which diagonalize the two-point function. For the case of U(N) gauge theory with a single complex matrix in the adjoint of the gauge group we have a U(N)×4 global symmetry of the scaling operator at zero coupling. Different choices of commuting sets of Casimirs, for the case of a complex matrix, lead to the restricted Schur basis previously studied in connection with string excitations of giant gravitons and the Brauer basis studied in connection with brane-antibrane systems. More generally these remarks can be extended to the diagonalization for any global symmetry group G. Schur-Weyl duality plays a central role in connecting the enhanced symmetries and the diagonal bases.

  14. Theory of (2+1)-dimensional fermionic topological orders and fermionic/bosonic topological orders with symmetries

    NASA Astrophysics Data System (ADS)

    Lan, Tian; Kong, Liang; Wen, Xiao-Gang

    2016-10-01

    We propose a systematic framework to classify (2+1)-dimensional (2+1D) fermionic topological orders without symmetry and 2+1D fermionic/bosonic topological orders with symmetry G . The key is to use the so-called symmetric fusion category E to describe the symmetry. Here, E =sRep (Z2f) describing particles in a fermionic product state without symmetry, or E =sRep (Gf) [E =Rep (G )] describing particles in a fermionic (bosonic) product state with symmetry G . Then, topological orders with symmetry E are classified by nondegenerate unitary braided fusion categories over E , plus their modular extensions and total chiral central charges. This allows us to obtain a list that contains all 2+1D fermionic topological orders without symmetry. For example, we find that, up to p +i p fermionic topological orders, there are only four fermionic topological orders with one nontrivial topological excitation: (1) the K =( -1 0 0 2) fractional quantum Hall state, (2) a Fibonacci bosonic topological order stacking with a fermionic product state, (3) the time-reversal conjugate of the previous one, and (4) a fermionic topological order with chiral central charge c =1/4 , whose only topological excitation has non-Abelian statistics with spin s =1/4 and quantum dimension d =1 +√{2 } .

  15. Symmetry in Season.

    ERIC Educational Resources Information Center

    Seidel, Judith Day

    1998-01-01

    Presents activities that demonstrate how technology can help students discover the mathematics in nature. Claims that these experiences can clarify students' vision of the symmetry of beauty that fills the world beyond the computer. Concludes that the use of flexible software tools helps students explore how a shape is affected when they change…

  16. Horror Vacui Symmetry.

    ERIC Educational Resources Information Center

    Crumpecker, Cheryl

    2003-01-01

    Describes an art lesson used with children in the third grade to help them learn about symmetry, as well as encouraging them to draw larger than usual. Explains that students learn about the belief called "Horror Vacui" of the Northwest American Indian tribes and create their interpretation of this belief. (CMK)

  17. Stationary axisymmetric SU(2) Einstein-Yang-Mills fields with restricted circularity conditions are Abelian

    NASA Astrophysics Data System (ADS)

    Chinea, F. J.; Navarro-Lérida, F.

    2002-03-01

    In this paper we prove that in a stationary axisymmetric SU(2) Einstein-Yang-Mills theory the most reasonable circularity conditions that can be considered for the Yang-Mills fields imply in fact that the field is of embedded Abelian type, or else that the metric is not asymptotically flat.

  18. Dual computations of non-Abelian Yang-Mills theories on the lattice

    NASA Astrophysics Data System (ADS)

    Cherrington, J. Wade; Christensen, J. Daniel; Khavkine, Igor

    2007-11-01

    In the past several decades there have been a number of proposals for computing with dual forms of non-Abelian Yang-Mills theories on the lattice. Motivated by the gauge-invariant, geometric picture offered by dual models and successful applications of duality in the U(1) case, we revisit the question of whether it is practical to perform numerical computation using non-Abelian dual models. Specifically, we consider three-dimensional SU(2) pure Yang-Mills as an accessible yet nontrivial case in which the gauge group is non-Abelian. Using methods developed recently in the context of spin foam quantum gravity, we derive an algorithm for efficiently computing the dual amplitude and describe Metropolis moves for sampling the dual ensemble. We relate our algorithms to prior work in non-Abelian dual computations of Hari Dass and his collaborators, addressing several problems that have been left open. We report results of spin expectation value computations over a range of lattice sizes and couplings that are in agreement with our conventional lattice computations. We conclude with an outlook on further development of dual methods and their application to problems of current interest.

  19. A Lindemann-Weierstrass theorem for semi-abelian varieties over function fields

    NASA Astrophysics Data System (ADS)

    Bertrand, Daniel; Pillay, Anand

    2010-04-01

    We prove an analogue of the Lindemann-Weierstrass theorem (that the exponentials of a {Q} -linearly independent set of algebraic numbers are algebraically independent), replacing {Q}^{alg} by {C}(t)^{alg} and {G}_{m}^{n} by a semi-abelian variety over {C}(t)^{alg} . Both the formulations of our results and the methods are differential algebraic in nature.

  20. Improved HDRG decoders for qudit and non-Abelian quantum error correction

    NASA Astrophysics Data System (ADS)

    Hutter, Adrian; Loss, Daniel; Wootton, James R.

    2015-03-01

    Hard-decision renormalization group (HDRG) decoders are an important class of decoding algorithms for topological quantum error correction. Due to their versatility, they have been used to decode systems with fractal logical operators, color codes, qudit topological codes, and non-Abelian systems. In this work, we develop a method of performing HDRG decoding which combines strengths of existing decoders and further improves upon them. In particular, we increase the minimal number of errors necessary for a logical error in a system of linear size L from \\Theta ({{L}2/3}) to Ω ({{L}1-ε }) for any ε \\gt 0. We apply our algorithm to decoding D({{{Z}}d}) quantum double models and a non-Abelian anyon model with Fibonacci-like fusion rules, and show that it indeed significantly outperforms previous HDRG decoders. Furthermore, we provide the first study of continuous error correction with imperfect syndrome measurements for the D({{{Z}}d}) quantum double models. The parallelized runtime of our algorithm is poly(log L) for the perfect measurement case. In the continuous case with imperfect syndrome measurements, the averaged runtime is O(1) for Abelian systems, while continuous error correction for non-Abelian anyons stays an open problem.

  1. Generalized type IIB supergravity equations and non-Abelian classical r-matrices

    NASA Astrophysics Data System (ADS)

    Orlando, Domenico; Reffert, Susanne; Sakamoto, Jun-ichi; Yoshida, Kentaroh

    2016-11-01

    We study Yang-Baxter deformations of the {{AdS}}5× {S}5 superstring with non-Abelian classical r-matrices which satisfy the homogeneous classical Yang-Baxter equation. By performing a supercoset construction, we can get deformed {{AdS}}5× {S}5 backgrounds. While this is a new area of research, the current understanding is that Abelian classical r-matrices give rise to solutions of type IIB supergravity, while non-Abelian classical r-matrices lead to solutions of the generalized supergravity equations. We examine here some examples of non-Abelian classical r-matrices and derive the associated backgrounds explicitly. All of the resulting backgrounds satisfy the generalized equations. For some of them, we derive ‘T-dualized’ backgrounds by adding a linear coordinate dependence to the dilaton and show that these satisfy the usual type IIB supergravity equations. Remarkably, some of the ‘T-dualized’ backgrounds are locally identical to undeformed {{AdS}}5× {S}5 after an appropriate coordinate transformation, but this seems not to be generally the case.

  2. Non-Abelian effects in a quadrupole system rotating around two axes

    SciTech Connect

    Zwanziger, J.W.; Koenig, M.; Pines, A. Department of Chemistry, University of California, Berkeley, CA )

    1990-09-01

    The {sup 35}Cl nuclear quadrupole resonance spectrum of a single crystal of sodium chlorate (R. Tycko, Phys. Rev. Lett. 58, 2281 (1987)) rotating about two axes reflects a non-Abelian gauge potential. This gauge potential is an example of Wilczek and Zee's (Phys. Rev. Lett. 52, 2111 (1984)) generalization of Berry's phase to the adiabatic transport of degenerate states.

  3. Quantum non-Abelian hydrodynamics: Anyonic or spin-orbital entangled liquids, nonunitarity of scattering matrix and charge fractionalization

    NASA Astrophysics Data System (ADS)

    Pareek, Tribhuvan Prasad

    2015-09-01

    In this article, we develop an exact (nonadiabatic, nonperturbative) density matrix scattering theory for a two component quantum liquid which interacts or scatters off from a generic spin-dependent quantum potential. The generic spin dependent quantum potential [Eq. (1)] is a matrix potential, hence, adiabaticity criterion is ill-defined. Therefore the full matrix potential should be treated nonadiabatically. We succeed in doing so using the notion of vectorial matrices which allows us to obtain an exact analytical expression for the scattered density matrix (SDM), ϱsc [Eq. (30)]. We find that the number or charge density in scattered fluid, Tr(ϱsc), expressions in Eqs. (32) depends on nontrivial quantum interference coefficients, Qα β 0ijk, which arises due to quantum interference between spin-independent and spin-dependent scattering amplitudes and among spin-dependent scattering amplitudes. Further it is shown that Tr(ϱsc) can be expressed in a compact form [Eq. (39)] where the effect of quantum interference coefficients can be included using a vector Qαβ, which allows us to define a vector order parameterQ. Since the number density is obtained using an exact scattered density matrix, therefore, we do not need to prove that Q is non-zero. However, for sake of completeness, we make detailed mathematical analysis for the conditions under which the vector order parameterQ would be zero or nonzero. We find that in presence of spin-dependent interaction the vector order parameterQ is necessarily nonzero and is related to the commutator and anti-commutator of scattering matrix S with its dagger S† [Eq. (78)]. It is further shown that Q≠0, implies four physically equivalent conditions,i.e., spin-orbital entanglement is nonzero, non-Abelian scattering phase, i.e., matrices, scattering matrix is nonunitary and the broken time reversal symmetry for SDM. This also implies that quasi particle excitation are anyonic in nature, hence, charge fractionalization is a

  4. Dynamical Symmetries in Classical Mechanics

    ERIC Educational Resources Information Center

    Boozer, A. D.

    2012-01-01

    We show how symmetries of a classical dynamical system can be described in terms of operators that act on the state space for the system. We illustrate our results by considering a number of possible symmetries that a classical dynamical system might have, and for each symmetry we give examples of dynamical systems that do and do not possess that…

  5. Reflections on Symmetry and Proof

    ERIC Educational Resources Information Center

    Merrotsy, Peter

    2008-01-01

    The concept of symmetry is fundamental to mathematics. Arguments and proofs based on symmetry are often aesthetically pleasing because they are subtle and succinct and non-standard. This article uses notions of symmetry to approach the solutions to a broad range of mathematical problems. It responds to Krutetskii's criteria for mathematical…

  6. PSEUDOSPIN SYMMETRY IN NUCLEI, SPIN SYMMETRY IN HADRONS

    SciTech Connect

    P. PAGE; T. GOLDMAN; J. GINOCCHIO

    2000-08-01

    Ginocchio argued that chiral symmetry breaking in QCD is responsible for the relativistic pseudospin symmetry in the Dirac equation, explaining the observed approximate pseudospin symmetry in sizable nuclei. On a much smaller scale, it is known that spin-orbit splittings in hadrons are small. Specifically, new experimental data from CLEO indicate small splittings in D-mesons. For heavy-light mesons we identify a cousin of pseudospin symmetry that suppresses these splittings in the Dirac equation, known as spin symmetry. We suggest an experimental test of the implications of spin symmetry for wave functions in electron-positron annihilation. We investigate how QCD can give rise to two different dynamical symmetries on nuclear and hadronic scales.

  7. Local Rotational Symmetries.

    DTIC Science & Technology

    1985-08-01

    spanner wrench and the teaspoon, the pointed jaws of the wrench, and the main axes of the gourd , the pear, the squash, and the bowl of the teaspoon...regions such as the handle of the spanner wrench and the main axes of the gourd , squash, and teaspoon, and also pointed regions such as the end of the...Local Symmetry representation does not provide in- tuitively acceptable analyses for round regions, such as the lemon and the round ends of the gourd

  8. Binary-Symmetry Detection

    NASA Technical Reports Server (NTRS)

    Lopez, Hiram

    1987-01-01

    Transmission errors for zeros and ones tabulated separately. Binary-symmetry detector employs psuedo-random data pattern used as test message coming through channel. Message then modulo-2 added to locally generated and synchronized version of test data pattern in same manner found in manufactured test sets of today. Binary symmetrical channel shows nearly 50-percent ones to 50-percent zeroes correspondence. Degree of asymmetry represents imbalances due to either modulation, transmission, or demodulation processes of system when perturbed by noise.

  9. Chiral symmetry and pentaquarks

    SciTech Connect

    Dmitri Diakonov

    2004-07-01

    Spontaneous chiral symmetry breaking, mesons and baryons are illustrated in the language of the Dirac theory. Various forces acting between quarks inside baryons are discussed. I explain why the naive quark models typically overestimate pentaquark masses by some 500 MeV and why in the fully relativistic approach to baryons pentaquarks turn out to be light. I discuss briefly why it can be easier to produce pentaquarks at low than at high energies.

  10. PREFACE: Symmetries in Science XV

    NASA Astrophysics Data System (ADS)

    Schuch, Dieter; Ramek, Michael

    2012-08-01

    Logo Bregenz, the peaceful monastery of Mehrerau and the Opera on the Floating Stage again provided the setting for the international symposium 'Symmetries in Science'. The series which has been running for more than 30 years brings together leading theoreticians whose area of research is, in one way or another, related to symmetry. Since 1992 the meeting took place biannually in Brengez until 2003. In 2009, with the endorsement of the founder, Professor Bruno Gruber, we succeeded in re-establishing the series without external funding. The resounding success of that meeting encouraged us to continue in 2011 and, following on the enthusiasm and positive feedback of the participants, we expect to continue in 2013. Yet again, our meeting in 2011 was very international in flavour and brought together some 30 participants representing 12 nationalities, half of them from countries outside the European Union (from New Zealand to Mexico, Russia to Israel). The broad spectrum, a mixture of experienced experts and highly-motivated newcomers, the intensive exchange of ideas in a harmonious and relaxed atmosphere and the resulting joint projects are probably the secrets of why this meeting is considered to be so special to its participants. At the resumption in 2009 some leading experts and younger scientists from economically weak countries were unable to attend due to the lack of financial resources. This time, with the very worthy and unbureaucratic support of the 'Vereinigung von Freunden und Förderern der J W Goethe-Universität Frankfurt am Main' (in short: 'Friends and Supporters of the Frankfurt University'), it was possible for all candidates to participate. In particular some young, inspired scientists had the chance of presenting their work to a very competent, but also friendly, audience. We wish to thank the 'Freunde und Förderer' for supporting Symmetries in Science XV. Almost all participants contributed to the publication of this Conference Proceedings. There

  11. Symmetry and Condensed Matter Physics

    NASA Astrophysics Data System (ADS)

    El-Batanouny, M.; Wooten, F.

    2008-03-01

    Preface; 1. Symmetry and physics; 2. Symmetry and group theory; 3. Group representations: concepts; 4. Group representations: formalism and methodology; 5. Dixon's method for computing group characters; 6. Group action and symmetry projection operators; 7. Construction of the irreducible representations; 8. Product groups and product representations; 9. Induced representations; 10. Crystallographic symmetry and space-groups; 11. Space groups: Irreps; 12. Time-reversal symmetry: color groups and the Onsager relations; 13. Tensors and tensor fields; 14. Electronic properties of solids; 15. Dynamical properties of molecules, solids and surfaces; 16. Experimental measurements and selection rules; 17. Landau's theory of phase transitions; 18. Incommensurate systems and quasi-crystals; References; Bibliography; Index.

  12. Symmetries in laminated composite plates

    NASA Technical Reports Server (NTRS)

    Noor, A. K.

    1976-01-01

    The different types of symmetry exhibited by laminated anisotropic fibrous composite plates are identified and contrasted with the symmetries of isotropic and homogeneous orthotropic plates. The effects of variations in the fiber orientation and the stacking sequence of the layers on the symmetries exhibited by composite plates are discussed. Both the linear and geometrically nonlinear responses of the plates are considered. A simple procedure is presented for exploiting the symmetries in the finite element analysis. Examples are given of square, skew and polygonal plates where use of symmetry concepts can significantly reduce the scope and cost of analysis.

  13. Invariants of broken discrete symmetries.

    PubMed

    Kalozoumis, P A; Morfonios, C; Diakonos, F K; Schmelcher, P

    2014-08-01

    The parity and Bloch theorems are generalized to the case of broken global symmetry. Local inversion or translation symmetries in one dimension are shown to yield invariant currents that characterize wave propagation. These currents map the wave function from an arbitrary spatial domain to any symmetry-related domain. Our approach addresses any combination of local symmetries, thus applying, in particular, to acoustic, optical, and matter waves. Nonvanishing values of the invariant currents provide a systematic pathway to the breaking of discrete global symmetries.

  14. Invariants of Broken Discrete Symmetries

    NASA Astrophysics Data System (ADS)

    Kalozoumis, P. A.; Morfonios, C.; Diakonos, F. K.; Schmelcher, P.

    2014-08-01

    The parity and Bloch theorems are generalized to the case of broken global symmetry. Local inversion or translation symmetries in one dimension are shown to yield invariant currents that characterize wave propagation. These currents map the wave function from an arbitrary spatial domain to any symmetry-related domain. Our approach addresses any combination of local symmetries, thus applying, in particular, to acoustic, optical, and matter waves. Nonvanishing values of the invariant currents provide a systematic pathway to the breaking of discrete global symmetries.

  15. The double cover of the icosahedral symmetry group and quark mass textures

    NASA Astrophysics Data System (ADS)

    Everett, Lisa L.; Stuart, Alexander J.

    2011-04-01

    We investigate the idea that the double cover of the rotational icosahedral symmetry group is the family symmetry group in the quark sector. The icosahedral (A5) group was previously proposed as a viable family symmetry group for the leptons. To incorporate the quarks, it is highly advantageous to extend the group to its double cover, as in the case of tetrahedral (A4) symmetry. We provide the basic group theoretical tools for flavor model-building based on the binary icosahedral group I‧ and construct a model of the quark masses and mixings that yields many of the successful predictions of the well-known U (2) quark texture models.

  16. Control of tripod-scheme cold-atom wavepackets by manipulating a non-Abelian vector potential

    SciTech Connect

    Zhang Qi; Gong Jiangbin; Oh, C.H.

    2010-06-15

    Tripod-scheme cold atoms interacting with laser beams have attracted considerable interest for their role in synthesizing effective non-Abelian vector potentials. Such effective vector potentials can be exploited to realize an all-optical imprinting of geometric phases onto matter waves. By working on carefully designed extensions of our previous work, we show that coherent lattice structure of cold-atom sub-wavepackets can be formed and that the non-Abelian Aharonov-Bohm effect can be easily manifested via the translational motion of cold atoms. We also show that by changing the frame of reference, effects due to a non-Abelian vector potential may be connected with a simple dynamical phase effect, and that under certain conditions it can be understood as an Abelian geometric phase in a different frame of reference. Results should help design better schemes for the control of cold-atom matter waves.

  17. The existence of self-dual vortices in a non-Abelian {Phi}{sup 2} Chern-Simons theory

    SciTech Connect

    Chen Shouxin; Wang Ying

    2010-09-15

    Applying the dynamic shooting method, we proved the existence of nontopological radially symmetric n-vortex solutions to the self-dual equation in non-Abelian Chern-Simons gauge theory with a {Phi}{sup 2}-type potential. Moreover, we obtained all possible radially symmetric nontopological bare (or 0-vortex) solutions in the non-Abelian Chern-Simons model. Meanwhile, we established the asymptotic behavior for the solutions as |x|{yields}{infinity}.

  18. Non-Abelian dual superconductivity in SU(3) Yang-Mills theory: Dual Meissner effect and type of the vacuum

    NASA Astrophysics Data System (ADS)

    Shibata, Akihiro; Kondo, Kei-Ichi; Kato, Seikou; Shinohara, Toru

    2013-03-01

    We have proposed the non-Abelian dual superconductivity picture for quark confinement in the SU(3) Yang-Mills (YM) theory, and have given numerical evidences for the restricted-field dominance and the non-Abelian magnetic monopole dominance in the string tension by applying a new formulation of the YM theory on a lattice. To establish the non-Abelian dual superconductivity picture for quark confinement, we have observed the non-Abelian dual Meissner effect in the SU(3) Yang-Mills theory by measuring the chromoelectric flux created by the quark-antiquark source, and the non-Abelian magnetic monopole currents induced around the flux. We conclude that the dual superconductivity of the SU(3) Yang-Mills theory is strictly the type I and that this type of dual superconductivity is reproduced by the restricted field and the non-Abelian magnetic monopole part, in sharp contrast to the SU(2) case: the border of type I and type II.

  19. Symmetry and structure of SrTiO3 nanotubes

    NASA Astrophysics Data System (ADS)

    Evarestov, Robert

    2011-06-01

    The full study of perovskite type nanotubes with square morphology is given for the first time. The line symmetry group L = ZP (a product of one axial point group P and one infinite cyclic group Z of generalized translations) of single-walled (SW) and double-walled (DW) SrTiO3 nanotubes (NT) is considered. The nanotube is defined by the square lattice translation vector L = l1a + l2b and chiral vector R = n1a + n2b, (l1, l2, n1 and n2 are integers). The nanotube of the chirality (n1,n2) is obtained by folding the (001) slabs of two- layers (with the layer group P4mm) and of three layers (with the layer group P4/mmm) in a way that the chiral vector R becomes circumference of the nanotube. Due to the orthogonality relation (RL) = 0, l1/l2 = -n2/n1 i.e. SW nanotubes with square morphology are commensurate for any rolling vector R(n1,n2). For SW (n,0) NTs the line symmetry groups belong to family 11 (T^Dnh) and are n/mmm or for even and odd n, respectively. For SW (n,n) NTs the line symmetry groups (2n)n/mcm belong to family 13 (T2n1 Dnh). The line symmetry group of a double-wall nanotube is found as intersection L2 = Z2P2 = (L ∩ L') of the symmetry groups L and L' of its single-wall constituents as earlier considered for DW CNTs. The symmetry group of DWNT (n,0)@M(n,0) belongs to the same family 11 (T^Dnh) as its SW constituents. The symmetry group of DWNT (n,n)@M(n,n) depends on the parity of M. For DW NTs with odd M, the line symmetry groups are the same as for their SW constituents and belong to family 13 (T2n1 Dnh). For even M, the rotations about screw axis of order 2n are changed by rotations around pure rotation axis of order n so that DW NT line symmetry groups belong to family 11 (T^Dnh). Commensurate STO DWNTs (n1,0)@(n2,0) and (n1, n1)@(n2, n2) belong to family 11 (T^Dnh) with n equal to the greatest common divisor of n1 and n2.

  20. Symmetry-Breaking Motility

    NASA Astrophysics Data System (ADS)

    Lee, Allen; Lee, Ha Youn; Kardar, Mehran

    2005-09-01

    Locomotion of bacteria by actin polymerization and in vitro motion of spherical beads coated with a protein catalyzing polymerization are examples of active motility. Starting from a simple model of forces locally normal to the surface of a bead, we construct a phenomenological equation for its motion. The singularities at a continuous transition between moving and stationary beads are shown to be related to the symmetries of its shape. Universal features of the phase behavior are calculated analytically and confirmed by simulations. Fluctuations in velocity are shown to be generically non-Maxwellian and correlated to the shape of the bead.

  1. Proposed Aharonov-Casher interferometry of non-Abelian vortices in chiral p-wave superconductors

    NASA Astrophysics Data System (ADS)

    Grosfeld, Eytan; Seradjeh, Babak; Vishveshwara, Smitha

    2011-03-01

    We propose a two-path vortex interferometry experiment based on the Aharonov- Casher effect for detecting the non-Abelian nature of vortices in a chiral p-wave superconductor. The effect is based on observing vortex interference patterns upon enclosing a finite charge of externally controllable magnitude within the interference path. We predict that when the interfering vortices enclose an odd number of identical vortices in their path, the interference pattern disappears only for non-Abelian vortices. When pairing involves two distinct spin species, we derive the mutual statistics between half quantum and full quantum vortices and show that, remarkably, our predictions still hold for the situation of a full quantum vortex enclosing a half quantum vortex in its path. We discuss the experimentally relevant conditions under which these effects can be observed. Work supported by ICMT at UIUC, NSERC of Canada, CAS fellowship at UIUC, and the U.S. Department of Energy.

  2. Particle coupled to a heat bath in non-Abelian gauge potentials.

    PubMed

    Guingarey, Issoufou; Avossevou, Gabriel Y H

    2015-12-01

    We derive the quantum Langevin equation (QLE) for a harmonically single trapped cold atom subjected to artificial non-Abelian gauge potentials and linearly coupled to a heat bath. The independent-oscillator (IO) and the momentum-momenta coupling models are studied. In each case, the non-Abelian effect on the QLE is pointed out for a U(2) gauge transformation. For the IO model, only the generalized Lorentz force is modified by the appearance of an additive term. For the momentum-momenta coupling model, the generalized Lorentz force as well as the friction force are subjected to modifications. The dependence of the system on the magnetic field is explicit even if the gauge potential is uniform in space.

  3. Local Monte Carlo Implementation of the Non-Abelian Landau-Pomeranchuk-Migdal Effect

    SciTech Connect

    Zapp, Korinna; Stachel, Johanna; Wiedemann, Urs Achim

    2009-10-09

    The non-Abelian Landau-Pomeranschuk-Migdal (LPM) effect arises from the quantum interference between spatially separated, inelastic radiation processes in matter. A consistent probabilistic implementation of this LPM effect is a prerequisite for extending the use of Monte Carlo (MC) event generators to the simulation of jetlike multiparticle final states in nuclear collisions. Here, we propose a local MC algorithm, which is based solely on relating the LPM effect to the probabilistic concept of formation time for virtual quanta. This accounts probabilistically for the characteristic L{sup 2} dependence of average parton energy loss and the characteristic 1/sq root(omega) modification of the non-Abelian LPM effect. Additional kinematic constraints are found to modify these L{sup 2} and omega dependencies characteristically in accordance with analytical estimates.

  4. Double and Negative Reflection of Cold Atoms in Non-Abelian Gauge Potentials

    SciTech Connect

    Juzeliunas, Gediminas; Ruseckas, Julius; Jacob, Andreas; Santos, Luis; Oehberg, Patrik

    2008-05-23

    Atom reflection is studied in the presence of a non-Abelian vector potential proportional to a spin-1/2 operator. The potential is produced by a relatively simple laser configuration for atoms with a tripod level scheme. We show that the atomic motion is described by two different dispersion branches with positive or negative chirality. As a consequence, atom reflection shows unusual features, since an incident wave may split into two reflected ones at a barrier, an ordinary specular reflection, and an additional nonspecular one. Remarkably, the latter wave can exhibit negative reflection and may become evanescent if the angle of incidence exceeds a critical value. These reflection properties are crucial for future designs in non-Abelian atom optics.

  5. Non-Abelian vortices on a cylinder: Duality between vortices and walls

    SciTech Connect

    Eto, Minoru; Fujimori, Toshiaki; Isozumi, Youichi; Nitta, Muneto; Ohashi, Keisuke; Sakai, Norisuke; Ohta, Kazutoshi

    2006-04-15

    We investigate vortices on a cylinder in supersymmetric non-Abelian gauge theory with hypermultiplets in the fundamental representation. We identify moduli space of periodic vortices and find that a pair of wall-like objects appears as the vortex moduli is varied. Usual domain walls also can be obtained from the single vortex on the cylinder by introducing a twisted boundary condition. We can understand these phenomena as a T duality among D-brane configurations in type II superstring theories. Using this T-duality picture, we find a one-to-one correspondence between the moduli space of non-Abelian vortices and that of kinky D-brane configurations for domain walls.

  6. Phase structure of an Abelian two-Higgs model and high-temperature superconductors

    SciTech Connect

    Chernodub, M. N.; Ilgenfritz, E.-M.; Schiller, A.

    2006-03-01

    We study the phase structure of a three-dimensional (3D) Abelian Higgs model with singly and doubly charged scalar fields coupled to a compact Abelian gauge field. The model is pretending to describe systems of strongly correlated electrons such as high-T{sub c} superconductivity in overdoped regime and exotic phases supporting excitations with fractionalized quantum numbers. We identify the Fermi liquid, the spin gap, the superconductor, and the strange metallic phases in which densities and properties of holon and spinon vortices and monopoles are explored. The phase diagram in the 3D coupling space is predicted. We show that at sufficiently strong gauge coupling the spinon-pair and holon condensation transitions merge together and become, unexpectedly, first order.

  7. Boundary conformal field theory and tunneling of edge quasiparticles in non-Abelian topological states

    SciTech Connect

    Fendley, Paul; Fisher, Matthew P.A.; Nayak, Chetan

    2009-07-15

    We explain how (perturbed) boundary conformal field theory allows us to understand the tunneling of edge quasiparticles in non-Abelian topological states. The coupling between a bulk non-Abelian quasiparticle and the edge is due to resonant tunneling to a zero mode on the quasiparticle, which causes the zero mode to hybridize with the edge. This can be reformulated as the flow from one conformally invariant boundary condition to another in an associated critical statistical mechanical model. Tunneling from one edge to another at a point contact can split the system in two, either partially or completely. This can be reformulated in the critical statistical mechanical model as the flow from one type of defect line to another. We illustrate these two phenomena in detail in the context of the {nu}=5/2 quantum Hall state and the critical Ising model. We briefly discuss the case of Fibonacci anyons and conclude by explaining the general formulation and its physical interpretation.

  8. Quasinormal modes of non-Abelian hyperscaling violating Lifshitz black holes

    NASA Astrophysics Data System (ADS)

    Bécar, Ramón; González, P. A.; Vásquez, Yerko

    2017-02-01

    We study the quasinormal modes of scalar field perturbations in the background of non-Abelian hyperscaling violating Lifshitz black holes. We find that the quasinormal frequencies have no real part so there is no oscillatory behavior in the perturbations, only exponential decay, that is, the system is always overdamped, which guarantees the mode stability of non-Abelian hyperscaling violating Lifshitz black holes. We determine analytically the quasinormal modes for massless scalar fields for a dynamical exponent z=2 and hyperscaling violating exponent tilde{θ }>-2. Also, we obtain numerically the quasinormal frequencies for different values of the dynamical exponent and the hyperscaling violating exponent by using the improved asymptotic iteration method.

  9. Non-Abelian holonomic transformation in the presence of classical noise

    NASA Astrophysics Data System (ADS)

    Jing, Jun; Lam, Chi-Hang; Wu, Lian-Ao

    2017-01-01

    It is proposed that high-speed universal quantum gates can be realized by using non-Abelian holonomic transformation. A cyclic evolution path which brings the system periodically back to a degenerate qubit subspace is crucial to holonomic quantum computing. The cyclic nature and the resulting gate operations are fully dependent on the precise control of driving parameters, such as the modulated envelop function of Rabi frequency and the control phases. We investigate the effects of fluctuations in these driving parameters on the transformation fidelity of a universal set of single-qubit quantum gates. We compare the damage effects from different noise sources and determine the "sweet spots" in the driving parameter space. The nonadiabatic non-Abelian quantum gate is found to be more susceptible to classical noises on the envelop function than that on the control phases. We also extend our study to a two-qubit quantum gate.

  10. Holographic phase transitions from higgsed, non abelian charged black holes

    NASA Astrophysics Data System (ADS)

    Giordano, Gastón L.; Lugo, Adrián R.

    2015-07-01

    We find solutions of a gravity-Yang-Mills-Higgs theory in four dimensions that represent asymptotic anti-de Sitter charged black holes with partial/full gauge symme-try breaking. We then apply the AdS/CFT correspondence to study the strong coupling regime of a 2 + 1 quantum field theory at temperature T and finite chemical potential, which undergoes transitions to phases exhibiting the condensation of a composite charged vector operator below a critical temperature T c , presumably describing p + ip/p-wave su-perconductors. In the case of p + ip-wave superconductors the transitions are always of second order. But for p-wave superconductors we determine the existence of a critical value αc of the gravitational coupling (for fixed Higgs v.e.v. parameter ) beyond which the transitions become of first order. As a by-product, we show that the p-wave phase is energetically favored over the p + ip one, for any values of the parameters. We also find the ground state solutions corresponding to zero temperature. Such states are described by domain wall geometries that interpolate between AdS 4 spaces with different light veloc-ities, and for a given , they exist below a critical value of the coupling. The behavior of the order parameter as function of the gravitational coupling near the critical coupling suggests the presence of second order quantum phase transitions. We finally study the dependence of the solution on the Higgs coupling, and find the existence of a critical value beyond which no condensed solution is present.

  11. Non-Abelian bremsstrahlung and azimuthal asymmetries in high energy p+A reactions

    NASA Astrophysics Data System (ADS)

    Gyulassy, M.; Levai, P.; Vitev, I.; Biró, T. S.

    2014-09-01

    We apply the GLV reaction operator solution to the Vitev-Gunion-Bertsch (VGB) boundary conditions to compute to all orders in nuclear opacity the non-Abelian gluon bremsstrahlung of event-by-event fluctuating beam jets in nuclear collisions. We evaluate analytically azimuthal Fourier moments of single gluon, vnM{1}, and even numbered 2ℓ gluon distribution, vnM{2ℓ}, inclusive distributions in high-energy p +A reactions as a function of harmonic n, target recoil cluster number, M, and gluon number, 2ℓ, at the RHIC and LHC. Multiple resolved clusters of recoiling target beam jets together with the projectile beam jet form color scintillation antenna (CSA) arrays that lead to characteristic boost-noninvariant trapezoidal rapidity distributions in asymmetric B+A nuclear collisions. The scaling of the intrinsically azimuthally anisotropic and long range in η nature of the non-Abelian bremsstrahlung leads to vn moments that are similar to results from hydrodynamic models, but due entirely to non-Abelian wave interference phenomena sourced by the fluctuating CSA. Our analytic nonflow solutions are similar to recent numerical saturation model predictions but differ by predicting a simple power-law hierarchy of both even and odd vn without invoking kT factorization. A test of the CSA mechanism is the predicted nearly linear η rapidity dependence of the vn(kT,η). Non-Abelian beam jet bremsstrahlung may, thus, provide a simple analytic solution to the beam energy scan puzzle of the near √s independence of vn(pT) moments observed down to 10 AGeV, where large-x valence-quark beam jets dominate inelastic dynamics. Recoil bremsstrahlung from multiple independent CSA clusters could also provide a partial explanation for the unexpected similarity of vn in p(D)+A and noncentral A+A at the same dN/dη multiplicity as observed at the RHIC and LHC.

  12. Maximal Abelian and Curci-Ferrari gauges in momentum subtraction at three loops

    NASA Astrophysics Data System (ADS)

    Bell, J. M.; Gracey, J. A.

    2015-12-01

    The vertex structure of QCD fixed in the maximal Abelian gauge (MAG) and Curci-Ferrari gauge is analyzed at two loops at the fully symmetric point for the 3-point functions corresponding to the three momentum subtraction (MOM) renormalization schemes. Consequently, the three-loop renormalization group functions are determined for each of these three schemes in each gauge using properties of the renormalization group equation.

  13. Exact Solution of the One-Dimensional Non-Abelian Coulomb Gas at Large {ital N}

    SciTech Connect

    Semenoff, G.W.; Tirkkonen, O.; Zarembo, K. |

    1996-09-01

    The problem of computing the thermodynamic properties of a one-dimensional gas of particles which transform in the adjoint representation of the gauge group and interact through non-Abelian electric fields is formulated and solved in the large {ital N} limit. The explicit solution exhibits a first order confinement-deconfinement phase transition with computable properties and describes two-dimensional adjoint QCD in the limit where matter field masses are large. {copyright} {ital 1996 The American Physical Society.}

  14. A reciprocity formula from abelian BF and Turaev-Viro theories

    NASA Astrophysics Data System (ADS)

    Mathieu, P.; Thuillier, F.

    2016-11-01

    In this article we show that the use of Deligne-Beilinson cohomology in the context of the U (1) BF theory on a closed 3-manifold M yields a discrete ZN BF theory whose partition function is an abelian TV invariant of M. By comparing the expectation values of the U (1) and ZN holonomies in both BF theories we obtain a reciprocity formula.

  15. Gauge equivalence of two different IAnsaaumlItze Rfor non-Abelian charged vortices

    SciTech Connect

    Paul, S.K.

    1987-05-15

    Recently the existence of non-Abelian charged vortices has been established by taking two different Ansa$uml: tze in SU(2) gauge theories. We point out that these two Ansa$uml: tze are in two topologically equivalent prescriptions. We show that they are gauge equivalent only at infinity. We also show that this gauge equivalence is not possible for Z/sub N/ vortices in SU(N) gauge theories for Ngreater than or equal to3.

  16. Colorful Horizons with Charge in Anti-de Sitter Space

    SciTech Connect

    Gubser, Steven S.

    2008-11-07

    An Abelian gauge symmetry can be spontaneously broken near a black hole horizon in anti-de Sitter space using a condensate of non-Abelian gauge fields. A second order phase transition is shown to separate Reissner-Nordstroem-anti-de Sitter solutions from a family of symmetry-breaking solutions which preserve a diagonal combination of gauge invariance and spatial rotational invariance.

  17. Galactic oscillator symmetry

    NASA Technical Reports Server (NTRS)

    Rosensteel, George

    1995-01-01

    Riemann ellipsoids model rotating galaxies when the galactic velocity field is a linear function of the Cartesian coordinates of the galactic masses. In nuclear physics, the kinetic energy in the linear velocity field approximation is known as the collective kinetic energy. But, the linear approximation neglects intrinsic degrees of freedom associated with nonlinear velocity fields. To remove this limitation, the theory of symplectic dynamical symmetry is developed for classical systems. A classical phase space for a self-gravitating symplectic system is a co-adjoint orbit of the noncompact group SP(3,R). The degenerate co-adjoint orbit is the 12 dimensional homogeneous space Sp(3,R)/U(3), where the maximal compact subgroup U(3) is the symmetry group of the harmonic oscillator. The Hamiltonian equations of motion on each orbit form a Lax system X = (X,F), where X and F are elements of the symplectic Lie algebra. The elements of the matrix X are the generators of the symplectic Lie algebra, viz., the one-body collective quadratic functions of the positions and momenta of the galactic masses. The matrix F is composed from the self-gravitating potential energy, the angular velocity, and the hydostatic pressure. Solutions to the hamiltonian dynamical system on Sp(3,R)/U(3) are given by symplectic isospectral deformations. The Casimirs of Sp(3,R), equal to the traces of powers of X, are conserved quantities.

  18. Applications of chiral symmetry

    SciTech Connect

    Pisarski, R.D.

    1995-03-01

    The author discusses several topics in the applications of chiral symmetry at nonzero temperature. First, where does the rho go? The answer: up. The restoration of chiral symmetry at a temperature T{sub {chi}} implies that the {rho} and a{sub 1} vector mesons are degenerate in mass. In a gauged linear sigma model the {rho} mass increases with temperature, m{sub {rho}}(T{sub {chi}}) > m{sub {rho}}(0). The author conjectures that at T{sub {chi}} the thermal {rho} - a{sub 1}, peak is relatively high, at about {approximately}1 GeV, with a width approximately that at zero temperature (up to standard kinematic factors). The {omega} meson also increases in mass, nearly degenerate with the {rho}, but its width grows dramatically with temperature, increasing to at least {approximately}100 MeV by T{sub {chi}}. The author also stresses how utterly remarkable the principle of vector meson dominance is, when viewed from the modern perspective of the renormalization group. Secondly, he discusses the possible appearance of disoriented chiral condensates from {open_quotes}quenched{close_quotes} heavy ion collisions. It appears difficult to obtain large domains of disoriented chiral condensates in the standard two flavor model. This leads to the last topic, which is the phase diagram for QCD with three flavors, and its proximity to the chiral critical point. QCD may be very near this chiral critical point, and one might thereby generated large domains of disoriented chiral condensates.

  19. Plasma analogy and non-Abelian statistics for Ising-type quantum Hall states

    SciTech Connect

    Bonderson, Parsa; Gurarie, Victor; Nayak, Chetan

    2011-02-15

    We study the non-Abelian statistics of quasiparticles in the Ising-type quantum Hall states which are likely candidates to explain the observed Hall conductivity plateaus in the second Landau level, most notably the one at filling fraction {nu}=5/2. We complete the program started in V. Gurarie and C. Nayak, [Nucl. Phys. B 506, 685 (1997)]. and show that the degenerate four-quasihole and six-quasihole wave functions of the Moore-Read Pfaffian state are orthogonal with equal constant norms in the basis given by conformal blocks in a c=1+(1/2) conformal field theory. As a consequence, this proves that the non-Abelian statistics of the excitations in this state are given by the explicit analytic continuation of these wave functions. Our proof is based on a plasma analogy derived from the Coulomb gas construction of Ising model correlation functions involving both order and (at most two) disorder operators. We show how this computation also determines the non-Abelian statistics of collections of more than six quasiholes and give an explicit expression for the corresponding conformal block-derived wave functions for an arbitrary number of quasiholes. Our method also applies to the anti-Pfaffian wave function and to Bonderson-Slingerland hierarchy states constructed over the Moore-Read and anti-Pfaffian states.

  20. On entanglement entropy in non-Abelian lattice gauge theory and 3D quantum gravity

    NASA Astrophysics Data System (ADS)

    Delcamp, Clement; Dittrich, Bianca; Riello, Aldo

    2016-11-01

    Entanglement entropy is a valuable tool for characterizing the correlation structure of quantum field theories. When applied to gauge theories, subtleties arise which prevent the factorization of the Hilbert space underlying the notion of entanglement entropy. Borrowing techniques from extended topological field theories, we introduce a new definition of entanglement entropy for both Abelian and non-Abelian gauge theories. Being based on the notion of excitations, it provides a completely relational way of defining regions. Therefore, it naturally applies to background independent theories, e.g. gravity, by circumventing the difficulty of specifying the position of the entangling surface. We relate our construction to earlier proposals and argue that it brings these closer to each other. In particular, it yields the non-Abelian analogue of the `magnetic centre choice', as obtained through an extended-Hilbert-space method, but applied to the recently introduced fusion basis for 3D lattice gauge theories. We point out that the different definitions of entanglement entropy can be related to a choice of (squeezed) vacuum state.

  1. Non-Abelian vortex in four dimensions as a critical superstring

    NASA Astrophysics Data System (ADS)

    Shifman, M.; Yung, A.

    2017-01-01

    We discuss recent progress in describing a certain non-Abelian vortex string as a critical superstring on a conifold and clarify some subtle points. This particular solitonic vortex is supported in four-dimensional N = 2 supersymmetric QCD with the U(2) gauge group, N f = 4 quark flavors and the Fayet-Iliopoulos term. Under certain conditions the non-Abelian vortex can become infinitely thin and can be interpreted as a critical ten-dimensional superstring. In addition to four translational moduli the non-Abelian vortex under consideration carries six orientational and size moduli. The vortex moduli dynamics are described by a twodimensional sigma model with the target space R4 × Y 6 where Y 6 is a non-compact Calabi-Yau conifold. The closed string states which emerge in four dimensions (4D) are identified with hadrons of 4D bulk N = 2 QCD. It turns out that most of the states arising from the ten-dimensional graviton spectrum are non-dynamical in 4D. A single dynamical massless hypermultiplet associated with the deformation of the complex structure of the conifold is found. It is interpreted as a monopole-monopole baryon of the 4D theory (at strong coupling).

  2. Numerical characterization of non-Abelian Moore-Read state in the microscopic lattice boson model

    NASA Astrophysics Data System (ADS)

    Zhu, Wei; Gong, Shoushu; Haldane, F. D. M.; Sheng, D. N.

    2015-03-01

    Identifying the interacting systems that host the non-Abelian (NA) topological phases have attracted intense attention in physics. Theoretically, it is possible to realize the NA Moore-Read (MR) state in bosonic system or double-layer system by coupling two Abelian fractional quantum Hall (FQH) states together. Here, based on the density matrix renormalization group and exact diagonalization calculations, we study two such examples in the microscopic lattice models and investigate their NA nature. In the first example, we provide a thorough characterization of the universal properties of MR state on Haldane honeycomb lattice model, including both the edge spectrum and the bulk anyonic quasiparticle statistics. By inspecting the entanglement spectral response to the U (1) flux, it is found that two of Abelian ground states can be adiabatically connected through a charge unit quasiparticle pumping from one edge to the other. In the second example, we study a double-layer bosonic FQH system built from the π-flux lattice model. Some evidences of NA nature has been identified, including the groundstate degeneracy and finite drag Hall conductance. The numerical methods we developed here provides a useful and practical way for detecting the full information of NA topological order. This research is supported by the U.S. Department of Energy, Office of Basic Energy Sciences under Grant No. DE-FG02-06ER46305.

  3. [Symmetries and homologies of Geomerida].

    PubMed

    Zarenkov, N A

    2005-01-01

    The symmetry of Earths life cover (Geomerida) was described generally by L.A. Zenkevich (1948). It coincides with the symmetry of geographic cover. Its symmetry elements are equatorial plane and three meridonal planes corresponded to oceans and continents. The hypsographic curve with point of inflection (symmetry element) on 3 km depth line should be added to these elements. The plankton and benthos communities as well as fauna of taxons are distributed symmetrically according these symmetry elements. Zenkevich model was successfully extrapolated to plankton by K.V. Beklemishev (1967, 1969) and to abyssal benthos by Sokolova M.N. (1986). The plankton communities inhabiting symmetrically located macrocirculations are considered as homologous. The character of circulation determines the trophic structure of plankton and benthos. In the case of high productivity of plankton, benthic grazing animals feed on sedimented particles have bilateral symmetric mouthpart. Otherwise they have to acquire food from water column and use cyclomeric mouthpart. Thus, the symmetry of macrocirculations determines the symmetry distribution of benthic animals with two major symmetries of mouthparts. The peculiarities of organisms' symmetry are discussed in the context of Pierre Curie principle and the ideas of K.V. Beklemishev concerning evolution of morphological axes.

  4. The abundant symmetry structure of hierarchies of nonlinear equations obtained by reciprocal links

    NASA Astrophysics Data System (ADS)

    Carillo, Sandra; Fuchssteiner, Benno

    1989-07-01

    Explicit computation for a Kawamoto-type equation shows that there is a rich associated symmetry structure for four separate hierarchies of nonlinear integrodifferential equations. Contrary to the general belief that symmetry groups for nonlinear evolution equations in 1+1 dimensions have to be Abelian, it is shown that, in this case, the symmetry group is noncommutative. Its semisimple part is isomorphic to the affine Lie algebra A(1)1 associated to sl(2,C). In two of the additional hierarchies that were found, an explicit dependence of the independent variable occurs. Surprisingly, the generic invariance for the Kawamoto-type equation obtained in Rogers and Carillo [Phys. Scr. 36, 865 (1987)] via a reciprocal link to the Möbius invariance of the singularity equation of the Kaup-Kupershmidt (KK) equation only holds for one of the additional hierarchies of symmetry groups. Thus the generic invariance is not a universal property for the complete symmetry group of equations obtained by reciprocal links. In addition to these results, the bi-Hamiltonian formulation of the hierarchy is given. A direct Bäcklund transformation between the (KK) hierarchy and the hierarchy of singularity equation for the Caudrey-Dodd-Gibbon-Sawada-Kotera equation is exhibited: This shows that the abundant symmetry structure found for the Kawamoto equation must exist for all fifth-order equations, which are known to be completely integrable since these equations are connected either by Bäcklund transformations or reciprocal links. It is shown that similar results must hold for all hierarchies emerging out of singularity hierarchies via reciprocal links. Furthermore, general aspects of the results are discussed.

  5. From Molecular Point Group Symmetry to Space Group Symmetry.

    ERIC Educational Resources Information Center

    Hathaway, Brian

    1979-01-01

    Describes undergraduate chemistry curricula in which the student is asked to either build a model of one asymmetric unit in the unit cell and to indicate the positions of the symmetry-related units by putting in key atoms, or to identify on a prebuild model the asymetric and symmetry-related units. (BB)

  6. Symmetry reduction related with nonlocal symmetry for Gardner equation

    NASA Astrophysics Data System (ADS)

    Ren, Bo

    2017-01-01

    Based on the truncated Painlevé method or the Möbious (conformal) invariant form, the nonlocal symmetry for the (1+1)-dimensional Gardner equation is derived. The nonlocal symmetry can be localized to the Lie point symmetry by introducing one new dependent variable. Thanks to the localization procedure, the finite symmetry transformations are obtained by solving the initial value problem of the prolonged systems. Furthermore, by using the symmetry reduction method to the enlarged systems, many explicit interaction solutions among different types of solutions such as solitary waves, rational solutions, Painlevé II solutions are given. Especially, some special concrete soliton-cnoidal interaction solutions are analyzed both in analytical and graphical ways.

  7. Symmetry and surface symmetry energies in finite nuclei

    SciTech Connect

    Lee, S. J.; Mekjian, A. Z.

    2010-12-15

    A study of the properties of the symmetry energy of nuclei is presented based on density-functional theory. Calculations for finite nuclei are given so that the study includes isospin-dependent surface symmetry considerations as well as isospin-independent surface effects. Calculations are done at both zero and nonzero temperature. It is shown that the surface symmetry energy term is the most sensitive to the temperature while the bulk energy term is the least sensitive. It is also shown that the temperature-dependence terms are insensitive to the force used and even more insensitive to the existence of neutron skin. Results for a symmetry energy with both volume and surface terms are compared with a symmetry energy with only volume terms along the line of {beta} stability. Differences of several MeV are shown over a good fraction of the total mass range in A. Also given are calculations for the bulk, surface and Coulomb terms.

  8. NIF symmetry capsule modeling

    NASA Astrophysics Data System (ADS)

    Weber, S. V.; Casey, D. T.; Pino, J. E.; Rowley, D. P.; Smalyuk, V. A.; Spears, B. K.; Tipton, R. E.

    2013-10-01

    NIF CH ablator symmetry capsules are filled with hydrogen or helium gas. SymCaps have more moderate convergence ratios ~ 15 as opposed to ~ 35 for ignition capsules with DT ice layers, and better agreement has been achieved between simulations and experimental data. We will present modeling of capsules with CD layers and tritium fill, for which we are able to match the dependence of DT yield on recession distance of the CD layer from the gas. We can also match the performance of CH capsules with D3 He fill. The simulations include surface roughness, drive asymmetry, a mock-up of modulation introduced by the tent holding the capsule, and an empirical prescription for ablator-gas atomic mix. This work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.

  9. Quantum walks and non-Abelian discrete gauge theory

    NASA Astrophysics Data System (ADS)

    Arnault, Pablo; Di Molfetta, Giuseppe; Brachet, Marc; Debbasch, Fabrice

    2016-07-01

    A family of discrete-time quantum walks (DTQWs) on the line with an exact discrete U(N ) gauge invariance is introduced. It is shown that the continuous limit of these DTQWs, when it exists, coincides with the dynamics of a Dirac fermion coupled to usual U(N ) gauge fields in two-dimensional spacetime. A discrete generalization of the usual U(N ) curvature is also constructed. An alternate interpretation of these results in terms of superimposed U(1 ) Maxwell fields and SU(N ) gauge fields is discussed in the Appendix. Numerical simulations are also presented, which explore the convergence of the DTQWs towards their continuous limit and which also compare the DTQWs with classical (i.e., nonquantum) motions in classical SU(2 ) fields. The results presented in this paper constitute a first step towards quantum simulations of generic Yang-Mills gauge theories through DTQWs.

  10. Current-Current Interactions, Dynamical Symmetry - and Quantum Chromodynamics.

    NASA Astrophysics Data System (ADS)

    Neuenschwander, Dwight Edward, Jr.

    Quantum Chromodynamics with massive gluons (gluon mass (TBOND) xm(,p)) in a contact-interaction limit called CQCD (strong coupling g (--->) (INFIN); x (--->) (INFIN)), despite its non-renormalizability and lack of hope of confinement, is nevertheless interesting for at least two reasons. (1) Some authors have suggested a relation between 4-Fermi and Yang-Mills theories. If g/x('2) << 1, then CQCD is not merely a 4-Fermi interaction, but includes 4, 6, 8, ...-Fermi non-Abelian contact interactions. (2) With the possibility of infrared slavery, perturbative evaluation of QCD in the infrared is a dubious practice. However, if g('2)/x('2) << 1 in CQCD, then the simplest 4-Fermi interaction is dominant, and CQCD admits perturbative treatment, but only in the infrared. With the dominant interaction, a dynamical Nambu-Goldstone realization of chiral symmetry -breaking (XSB) is found. Although in QCD the relation between confinement and XSB is controversial, XSB occurs in CQCD provided confinement is sacrificed.

  11. Partial restoration of chiral symmetry in a confining string

    SciTech Connect

    Kharzeev, Dmitri E.; Loshaj, F.

    2014-08-01

    Here, we attempt to describe the interplay of confinement and chiral symmetry breaking in QCD by using the string model. We argue that in the quasi-Abelian picture of confinement based on the condensation of magnetic monopoles and the dual Meissner effect, the world sheet dynamics of the confining string can be effectively described by the 1+1 dimensional massless electrodynamics, which is exactly soluble. The transverse plane distribution of the chromoelectric field stretched between the quark and antiquark sources can then be attributed to the fluctuations in the position of the string. The dependence of the chiral condensate in the string on the (chromo-)electric field can be evaluated analytically, and is determined by the chiral anomaly and the θ-vacuum structure. Moreover, our picture allows us to predict the distribution of the chiral condensate in the plane transverse to the axis connecting the quark and antiquark. This prediction is compared to the lattice QCD results; a good agreement is found.

  12. Symmetry in Sign Language Poetry

    ERIC Educational Resources Information Center

    Sutton-Spence, Rachel; Kaneko, Michiko

    2007-01-01

    This paper considers the range of ways that sign languages use geometric symmetry temporally and spatially to create poetic effect. Poets use this symmetry in sign language art to highlight duality and thematic contrast, and to create symbolic representations of beauty, order and harmony. (Contains 8 tables, 14 figures and 6 notes.)

  13. Symmetry in the Car Park

    ERIC Educational Resources Information Center

    Hancock, Karen

    2007-01-01

    In this article, the author presents a lesson on rotational symmetry which she developed for her students. The aim of the lesson was "to identify objects with rotational symmetry in the staff car park" and the success criteria were "pictures or sketches of at least six objects with different orders of rotation". After finding examples of…

  14. Asymptotic symmetries on Killing horizons

    NASA Astrophysics Data System (ADS)

    Koga, Jun-Ichirou

    2001-12-01

    We investigate asymptotic symmetries regularly defined on spherically symmetric Killing horizons in Einstein theory with or without the cosmological constant. These asymptotic symmetries are described by asymptotic Killing vectors, along which the Lie derivatives of perturbed metrics vanish on a Killing horizon. We derive the general form of the asymptotic Killing vectors and find that the group of asymptotic symmetries consists of rigid O(3) rotations of a horizon two-sphere and supertranslations along the null direction on the horizon, which depend arbitrarily on the null coordinate as well as the angular coordinates. By introducing the notion of asymptotic Killing horizons, we also show that local properties of Killing horizons are preserved not only under diffeomorphisms but also under nontrivial transformations generated by the asymptotic symmetry group. Although the asymptotic symmetry group contains the Diff(S1) subgroup, which results from supertranslations dependent only on the null coordinate, it is shown that the Poisson brackets algebra of the conserved charges conjugate to asymptotic Killing vectors does not acquire nontrivial central charges. Finally, by considering extended symmetries, we discuss the fact that unnatural reduction of the symmetry group is necessary in order to obtain the Virasoro algebra with nontrivial central charges, which is not justified when we respect the spherical symmetry of Killing horizons.

  15. Duality, Gauge Symmetries, Renormalization Groups and the BKT Transition

    NASA Astrophysics Data System (ADS)

    José, Jorge V.

    2013-06-01

    In this chapter, I will briefly review, from my own perspective, the situation within theoretical physics at the beginning of the 1970s, and the advances that played an important role in providing a solid theoretical and experimental foundation for the Berezinskii-Kosterlitz-Thouless theory (BKT). Over this period, it became clear that the Abelian gauge symmetry of the 2D-XY model had to be preserved to get the right phase structure of the model. In previous analyses, this symmetry was broken when using low order calculational approximations. Duality transformations at that time for two-dimensional models with compact gauge symmetries were introduced by José, Kadanoff, Nelson and Kirkpatrick (JKKN). Their goal was to analyze the phase structure and excitations of XY and related models, including symmetry breaking fields which are experimentally important. In a separate context, Migdal had earlier developed an approximate Renormalization Group (RG) algorithm to implement Wilson's RG for lattice gauge theories. Although Migdal's RG approach, later extended by Kadanoff, did not produce a true phase transition for the XY model, it almost did asymptotically in terms of a non-perturbative expansion in the coupling constant with an essential singularity. Using these advances, including work done on instantons (vortices), JKKN analyzed the behavior of the spin-spin correlation functions of the 2D XY-model in terms of an expansion in temperature and vortex-pair fugacity. Their analysis led to a perturbative derivation of RG equations for the XY model which are the same as those first derived by Kosterlitz for the two-dimensional Coulomb gas. JKKN's results gave a theoretical formulation foundation and justification for BKT's sound physical assumptions and for the validity of their calculational approximations that were, in principle, strictly valid only at very low temperatures, away from the critical TBKT temperature. The theoretical predictions were soon tested

  16. Duality, Gauge Symmetries, Renormalization Groups and the BKT Transition

    NASA Astrophysics Data System (ADS)

    José, Jorge V.

    2017-03-01

    In this chapter, I will briefly review, from my own perspective, the situation within theoretical physics at the beginning of the 1970s, and the advances that played an important role in providing a solid theoretical and experimental foundation for the Berezinskii-Kosterlitz-Thouless theory (BKT). Over this period, it became clear that the Abelian gauge symmetry of the 2D-XY model had to be preserved to get the right phase structure of the model. In previous analyses, this symmetry was broken when using low order calculational approximations. Duality transformations at that time for two-dimensional models with compact gauge symmetries were introduced by José, Kadanoff, Nelson and Kirkpatrick (JKKN). Their goal was to analyze the phase structure and excitations of XY and related models, including symmetry breaking fields which are experimentally important. In a separate context, Migdal had earlier developed an approximate Renormalization Group (RG) algorithm to implement Wilson’s RG for lattice gauge theories. Although Migdal’s RG approach, later extended by Kadanoff, did not produce a true phase transition for the XY model, it almost did asymptotically in terms of a non-perturbative expansion in the coupling constant with an essential singularity. Using these advances, including work done on instantons (vortices), JKKN analyzed the behavior of the spin-spin correlation functions of the 2D XY-model in terms of an expansion in temperature and vortex-pair fugacity. Their analysis led to a perturbative derivation of RG equations for the XY model which are the same as those first derived by Kosterlitz for the two-dimensional Coulomb gas. JKKN’s results gave a theoretical formulation foundation and justification for BKT’s sound physical assumptions and for the validity of their calculational approximations that were, in principle, strictly valid only at very low temperatures, away from the critical TBKT temperature. The theoretical predictions were soon tested

  17. Hyperbolic-symmetry vector fields.

    PubMed

    Gao, Xu-Zhen; Pan, Yue; Cai, Meng-Qiang; Li, Yongnan; Tu, Chenghou; Wang, Hui-Tian

    2015-12-14

    We present and construct a new kind of orthogonal coordinate system, hyperbolic coordinate system. We present and design a new kind of local linearly polarized vector fields, which is defined as the hyperbolic-symmetry vector fields because the points with the same polarization form a series of hyperbolae. We experimentally demonstrate the generation of such a kind of hyperbolic-symmetry vector optical fields. In particular, we also study the modified hyperbolic-symmetry vector optical fields with the twofold and fourfold symmetric states of polarization when introducing the mirror symmetry. The tight focusing behaviors of these vector fields are also investigated. In addition, we also fabricate micro-structures on the K9 glass surfaces by several tightly focused (modified) hyperbolic-symmetry vector fields patterns, which demonstrate that the simulated tightly focused fields are in good agreement with the fabricated micro-structures.

  18. PREFACE: Symmetries and Integrability of Difference Equations

    NASA Astrophysics Data System (ADS)

    Doliwa, Adam; Korhonen, Risto; Lafortune, Stéphane

    2007-10-01

    The notion of integrability was first introduced in the 19th century in the context of classical mechanics with the definition of Liouville integrability for Hamiltonian flows. Since then, several notions of integrability have been introduced for partial and ordinary differential equations. Closely related to integrability theory is the symmetry analysis of nonlinear evolution equations. Symmetry analysis takes advantage of the Lie group structure of a given equation to study its properties. Together, integrability theory and symmetry analysis provide the main method by which nonlinear evolution equations can be solved explicitly. Difference equations (DE), like differential equations, are important in numerous fields of science and have a wide variety of applications in such areas as mathematical physics, computer visualization, numerical analysis, mathematical biology, economics, combinatorics, and quantum field theory. It is thus crucial to develop tools to study and solve DEs. While the theory of symmetry and integrability for differential equations is now largely well-established, this is not yet the case for discrete equations. Although over recent years there has been significant progress in the development of a complete analytic theory of difference equations, further tools are still needed to fully understand, for instance, the symmetries, asymptotics and the singularity structure of difference equations. The series of SIDE meetings on Symmetries and Integrability of Difference Equations started in 1994. Its goal is to provide a platform for an international and interdisciplinary communication for researchers working in areas associated with integrable discrete systems, such as classical and quantum physics, computer science and numerical analysis, mathematical biology and economics, discrete geometry and combinatorics, theory of special functions, etc. The previous SIDE meetings took place in Estérel near Montréal, Canada (1994), at the University of

  19. PREFACE: Symmetries in Science XVI

    NASA Astrophysics Data System (ADS)

    2014-10-01

    -session, topics ranging from theoretical chemistry and molecular physics via fundamental problems in quantum theory to thermodynamics, nonlinear dynamics, soliton theory and finally cosmology, were examined and lively discussed. Nearly all the talks can also be viewed on the conference website. The majority of participants contributed to these Proceedings but some were unable to do so as their results were either previously submitted or published elsewhere. We refer to: · Quesne C 2013, J. Math. Phys. 54, 102102. · Spera M 2013, (Nankai Series in Pure, Applied Mathematics and Theoretical Physics): 11 Symmetries and Groups in Contemporary Physics: pp. 593-598 Proceedings of the XXIX International Colloquium on Group-Theoretical Methods in Physics Tianjin, China, 20 - 26 August 2012 (World Scientific, Singapore) · Snobl L and Winternitz P 2014, Classification and Identification of Lie Algebras, CRM Monograph Series 33 (Montreal) ISBN-10: 0-8218-4355-9, ISBN-13: 978-0-8218-4355-0 (http://www.ams.org/bookstore?fn=20&arg1=crmmseries&ikey=CRMM-33). Our personal thanks to Daniel and family! Endless support from the Schenk Family who, among other things, sponsored (yet again) the entire conference dinner (including wines and banquet hall) meant that some costs could be alleviated. We could therefore assist various colleagues from economically-weak countries, despite the lack of external funding. A financial deficit meant we would have had to forego the Conference Proceedings, published in previous years by IOP. After long deliberations, and with donations from Gerhard Berssenbrügge, Dr. Dr. Stephan Hauk and Dr. Volker Weisswange, this could be facilitated. We are very grateful to these private donors for their generous and wholehearted support. The staff of Collegium Mehrerau is also to be thanked for their hospitality. Finally, our sincere thanks to Yvette not only for her preparatory work and support during the conference, but also for her persistent interest and help in producing

  20. Anatomy of a deformed symmetry: Field quantization on curved momentum space

    SciTech Connect

    Arzano, Michele

    2011-01-15

    In certain scenarios of deformed relativistic symmetries relevant for noncommutative field theories particles exhibit a momentum space described by a non-Abelian group manifold. Starting with a formulation of phase space for such particles which allows for a generalization to include group-valued momenta we discuss quantization of the corresponding field theory. Focusing on the particular case of {kappa}-deformed phase space we construct the one-particle Hilbert space and show how curvature in momentum space leads to an ambiguity in the quantization procedure reminiscent of the ambiguities one finds when quantizing fields in curved space-times. The tools gathered in the discussion on quantization allow for a clear definition of the basic deformed field mode operators and two-point function for {kappa}-quantum fields.

  1. Renormalization group improvement and dynamical breaking of symmetry in a supersymmetric Chern-Simons-matter model

    NASA Astrophysics Data System (ADS)

    Quinto, A. G.; Ferrari, A. F.; Lehum, A. C.

    2016-06-01

    In this work, we investigate the consequences of the Renormalization Group Equation (RGE) in the determination of the effective superpotential and the study of Dynamical Symmetry Breaking (DSB) in an N = 1 supersymmetric theory including an Abelian Chern-Simons superfield coupled to N scalar superfields in (2 + 1) dimensional spacetime. The classical Lagrangian presents scale invariance, which is broken by radiative corrections to the effective superpotential. We calculate the effective superpotential up to two-loops by using the RGE and the beta functions and anomalous dimensions known in the literature. We then show how the RGE can be used to improve this calculation, by summing up properly defined series of leading logs (LL), next-to-leading logs (NLL) contributions, and so on... We conclude that even if the RGE improvement procedure can indeed be applied in a supersymmetric model, the effects of the consideration of the RGE are not so dramatic as it happens in the non-supersymmetric case.

  2. Magnetic-field-tuned Aharonov-Bohm oscillations and evidence for non-Abelian anyons at ν = 5/2.

    PubMed

    Willett, R L; Nayak, C; Shtengel, K; Pfeiffer, L N; West, K W

    2013-11-01

    We show that the resistance of the ν = 5/2 quantum Hall state, confined to an interferometer, oscillates with the magnetic field consistent with an Ising-type non-Abelian state. In three quantum Hall interferometers of different sizes, resistance oscillations at ν = 7/3 and integer filling factors have the magnetic field period expected if the number of quasiparticles contained within the interferometer changes so as to keep the area and the total charge within the interferometer constant. Under these conditions, an Abelian state such as the (3, 3, 1) state would show oscillations with the same period as at an integer quantum Hall state. However, in an Ising-type non-Abelian state there would be a rapid oscillation associated with the "even-odd effect" and a slower one associated with the accumulated Abelian phase due to both the Aharonov-Bohm effect and the Abelian part of the quasiparticle braiding statistics. Our measurements at ν = 5/2 are consistent with the latter.

  3. PT Symmetry and Spontaneous Symmetry Breaking in a Microwave Billiard

    NASA Astrophysics Data System (ADS)

    Bittner, S.; Dietz, B.; Günther, U.; Harney, H. L.; Miski-Oglu, M.; Richter, A.; Schäfer, F.

    2012-01-01

    We demonstrate the presence of parity-time (PT) symmetry for the non-Hermitian two-state Hamiltonian of a dissipative microwave billiard in the vicinity of an exceptional point (EP). The shape of the billiard depends on two parameters. The Hamiltonian is determined from the measured resonance spectrum on a fine grid in the parameter plane. After applying a purely imaginary diagonal shift to the Hamiltonian, its eigenvalues are either real or complex conjugate on a curve, which passes through the EP. An appropriate basis choice reveals its PT symmetry. Spontaneous symmetry breaking occurs at the EP.

  4. 3d {N} = 2 mirror symmetry, pq-webs and monopole superpotentials

    NASA Astrophysics Data System (ADS)

    Benvenuti, Sergio; Pasquetti, Sara

    2016-08-01

    D3 branes stretching between webs of (p,q) 5branes provide an interesting class of 3 d {N} = 2 theories. For generic pq-webs however the low energy field theory is not known. We use 3d mirror symmetry and Type IIB S-duality to construct Abelian gauge theories corresponding to D3 branes ending on both sides of a pq-web made of many coincident N S5's intersecting one D5. These theories contain chiral monopole operators in the superpotential and enjoy a non trivial pattern of global symmetry enhancements. In the special case of the pq-web with one D5 and one N S5, the 3d low energy SCFT admits three dual formulations. This triality can be applied locally inside bigger quiver gauge theories. We prove our statements using partial mirror symmetry à la Kapustin-Strassler, showing the equality of the S b 3 partition functions and studying the quantum chiral rings.

  5. Functional Symmetry of Endomembranes

    PubMed Central

    2007-01-01

    In higher eukaryotic cells pleiomorphic compartments composed of vacuoles, tubules and vesicles move from the endoplasmic reticulum (ER) and the plasma membrane to the cell center, operating in early biosynthetic trafficking and endocytosis, respectively. Besides transporting cargo to the Golgi apparatus and lysosomes, a major task of these compartments is to promote extensive membrane recycling. The endocytic membrane system is traditionally divided into early (sorting) endosomes, late endosomes and the endocytic recycling compartment (ERC). Recent studies on the intermediate compartment (IC) between the ER and the Golgi apparatus suggest that it also consists of peripheral (“early”) and centralized (“late”) structures, as well as a third component, designated here as the biosynthetic recycling compartment (BRC). We propose that the ERC and the BRC exist as long-lived “mirror compartments” at the cell center that also share the ability to expand and become mobilized during cell activation. These considerations emphasize the functional symmetry of endomembrane compartments, which provides a basis for the membrane rearrangements taking place during cell division, polarization, and differentiation. PMID:17267686

  6. Symmetry algebras of linear differential equations

    NASA Astrophysics Data System (ADS)

    Shapovalov, A. V.; Shirokov, I. V.

    1992-07-01

    The local symmetries of linear differential equations are investigated by means of proven theorems on the structure of the algebra of local symmetries of translationally and dilatationally invariant differential equations. For a nonparabolic second-order equation, the absence of nontrivial nonlinear local symmetries is proved. This means that the local symmetries reduce to the Lie algebra of linear differential symmetry operators. For the Laplace—Beltrami equation, all local symmetries reduce to the enveloping algebra of the algebra of the conformal group.

  7. Understanding the physics of a possible non-Abelian fractional quantum hall effect state.

    SciTech Connect

    Pan, Wei; Crawford, Matthew; Tallakulam, Madhu; Ross, Anthony Joseph, III

    2010-10-01

    We wish to present in this report experimental results from a one-year Senior Council Tier-1 LDRD project that focused on understanding the physics of a possible non-Abelian fractional quantum Hall effect state. We first give a general introduction to the quantum Hall effect, and then present the experimental results on the edge-state transport in a special fractional quantum Hall effect state at Landau level filling {nu} = 5/2 - a possible non-Abelian quantum Hall state. This state has been at the center of current basic research due to its potential applications in fault-resistant topological quantum computation. We will also describe the semiconductor 'Hall-bar' devices we used in this project. Electron physics in low dimensional systems has been one of the most exciting fields in condensed matter physics for many years. This is especially true of quantum Hall effect (QHE) physics, which has seen its intellectual wealth applied in and has influenced many seemingly unrelated fields, such as the black hole physics, where a fractional QHE-like phase has been identified. Two Nobel prizes have been awarded for discoveries of quantum Hall effects: in 1985 to von Klitzing for the discovery of integer QHE, and in 1998 to Tsui, Stormer, and Laughlin for the discovery of fractional QHE. Today, QH physics remains one of the most vibrant research fields, and many unexpected novel quantum states continue to be discovered and to surprise us, such as utilizing an exotic, non-Abelian FQHE state at {nu} = 5/2 for fault resistant topological computation. Below we give a briefly introduction of the quantum Hall physics.

  8. Effective models of doped quantum ladders of non-Abelian anyons

    NASA Astrophysics Data System (ADS)

    Soni, Medha; Troyer, Matthias; Poilblanc, Didier

    2016-01-01

    Quantum spin models have been studied extensively in one and higher dimensions. Furthermore, these systems have been doped with holes to study t -J models of SU (2 ) spin-1/2. Their anyonic counterparts can be built from non-Abelian anyons, such as Fibonacci anyons described by SU (2) 3 theories, which are quantum deformations of the SU (2 ) algebra. Inspired by the physics of SU (2 ) spins, several works have explored ladders of Fibonacci anyons and also one-dimensional (1D) t -J models. Here, we aim to explore the combined effects of extended dimensionality and doping by studying ladders composed of coupled chains of interacting itinerant Fibonacci anyons. We show analytically that in the limit of strong rung couplings these models can be mapped onto effective 1D models. These effective models can either be gapped models of hole pairs, or gapless models described by t -J (or modified t -J -V ) chains of Fibonacci anyons, whose spectrum exhibits a fractionalization into charge and anyon degrees of freedom. The charge degrees of freedom are described by the hardcore boson spectra while the anyon sector is given by a chain of localized interacting anyons. By using exact diagonalizations for two-leg and three-leg ladders, we show that indeed the doped ladders show exactly the same behavior as that of t -J chains. In the strong ferromagnetic rung limit, we can obtain a new model that hosts two different kinds of Fibonacci particles, which we denote as the heavy τ 's and light τ 's. These two particle types carry the same (non-Abelian) topological charge but different (Abelian) electric charges. Once again, we map the two-dimensional ladder onto an effective chain carrying these heavy and light τ 's. We perform a finite size scaling analysis to show the appearance of gapless modes for certain anyon densities, whereas a topological gapped phase is suggested for another density regime.

  9. Non-Abelian quantum order in spin-orbit-coupled semiconductors: Search for topological Majorana particles in solid-state systems

    NASA Astrophysics Data System (ADS)

    Sau, Jay D.; Tewari, Sumanta; Lutchyn, Roman M.; Stanescu, Tudor D.; Das Sarma, S.

    2010-12-01

    We show that an ordinary semiconducting thin film with spin-orbit coupling can, under appropriate circumstances, be in a quantum topologically ordered state supporting exotic Majorana excitations which follow non-Abelian statistics. The key to the quantum topological order is the coexistence of spin-orbit coupling with proximity-induced s -wave superconductivity and an externally induced Zeeman coupling of the spins. For the Zeeman coupling below a critical value, the system is a nontopological (proximity-induced) s -wave superconductor. However, for a range of Zeeman coupling above the critical value, the lowest energy excited state inside a vortex is a zero-energy Majorana fermion state. The system, thus, has entered into a non-Abelian s -wave superconducting state via a topological quantum phase transition (TQPT) tuned by the Zeeman coupling. In the topological phase, since the time-reversal symmetry is explicitly broken by the Zeeman term in the Hamiltonian, the edge of the film constitutes a chiral Majorana wire. Just like the s -wave superconductivity, the Zeeman coupling can also be proximity induced in the film by an adjacent magnetic insulator. We show this by an explicit model tight-binding calculation for both types of proximity effects in the heterostructure geometry. Here we show that the same TQPT can be accessed by varying the interface transparency between the film and the superconductor. For the transparency below (above) a critical value, the system is a topological (regular) s -wave superconductor. In the one-dimensional version of the same structure and for the Zeeman coupling above the critical value, there are localized Majorana zero-energy modes at the two ends of a semiconducting quantum nanowire. In this case, the Zeeman coupling can be induced more easily by an external magnetic field parallel to the wire, obviating the need for a magnetic insulator. We show that, despite the fact that the superconducting pair potential in the nanowire is

  10. Non-Abelian Bremsstrahlung and Azimuthal Asymmetries in High Energy p+A Reactions

    DOE PAGES

    Gyulassy, Miklos; Vitev, Ivan Mateev; Levai, Peter; ...

    2014-09-25

    Here we apply the GLV reaction operator solution to the Vitev-Gunion-Bertsch (VGB) boundary conditions to compute the all-order in nuclear opacity non-abelian gluon bremsstrahlung of event- by-event uctuating beam jets in nuclear collisions. We evaluate analytically azimuthal Fourier moments of single gluon, vmore » $$M\\atop{n}$$ {1}, and even number 2ℓ gluon, v$$M\\atop{n}$$ {2ℓ} inclusive distributions in high energy p+A reactions as a function of harmonic $n$, target recoil cluster number, $M$, and gluon number, 2ℓ, at RHIC and LHC. Multiple resolved clusters of recoiling target beam jets together with the projectile beam jet form Color Scintillation Antenna (CSA) arrays that lead to character- istic boost non-invariant trapezoidal rapidity distributions in asymmetric B+A nuclear collisions. The scaling of intrinsically azimuthally anisotropic and long range in η nature of the non-Abelian bremsstrahlung leads to vn moments that are similar to results from hydrodynamic models, but due entirely to non-Abelian wave interference phenomena sourced by the fluctuating CSA. Our analytic non-flow solutions are similar to recent numerical saturation model predictions but differ by predicting a simple power-law hierarchy of both even and odd vn without invoking kT factorization. A test of CSA mechanism is the predicted nearly linear η rapidity dependence of the vn(kTη). Non- Abelian beam jet bremsstrahlung may thus provide a simple analytic solution to Beam Energy Scan (BES) puzzle of the near $$\\sqrt{s}$$ independence of vn(pT) moments observed down to 10 AGeV where large-x valence quark beam jets dominate inelastic dynamics. Recoil bremsstrahlung from multiple independent CSA clusters could also provide a partial explanation for the unexpected similarity of vn in p(D) + A and non-central A + A at same dN=dη multiplicity as observed at RHIC and LHC.« less

  11. Russian doll spectrum in a non-Abelian string-net ladder

    NASA Astrophysics Data System (ADS)

    Schulz, Marc Daniel; Dusuel, Sébastien; Vidal, Julien

    2015-04-01

    We study a string-net ladder in the presence of a string tension. Focusing on the simplest non-Abelian anyon theory with a quantum dimension larger than two, we determine the phase diagram and find a Russian doll spectrum featuring size-independent energy levels as well as highly degenerate zero-energy eigenstates. At the self-dual points, we compute the gap exactly by using a mapping onto the Temperley-Lieb chain. These results are in stark contrast with the ones obtained for Fibonacci or Ising theories.

  12. Renormalization of Tensorial Group Field Theories: Abelian U(1) Models in Four Dimensions

    NASA Astrophysics Data System (ADS)

    Carrozza, Sylvain; Oriti, Daniele; Rivasseau, Vincent

    2014-04-01

    We tackle the issue of renormalizability for Tensorial Group Field Theories (TGFT) including gauge invariance conditions, with the rigorous tool of multi-scale analysis, to prepare the ground for applications to quantum gravity models. In the process, we define the appropriate generalization of some key QFT notions, including connectedness, locality and contraction of (high) subgraphs. We also define a new notion of Wick ordering, corresponding to the subtraction of (maximal) melonic tadpoles. We then consider the simplest examples of dynamical 4-dimensional TGFT with gauge invariance conditions for the Abelian U(1) case. We prove that they are super-renormalizable for any polynomial interaction.

  13. Probing Non-Abelian Statistics of Majorana Fermions in Ultracold Atomic Superfluid

    SciTech Connect

    Zhu Shiliang; Shao, L.-B.; Wang, Z. D.; Duan, L.-M.

    2011-03-11

    We propose an experiment to directly probe the non-Abelian statistics of Majorana fermions by braiding them in an s-wave superfluid of ultracold atoms. We show that different orders of braiding operations give orthogonal output states that can be distinguished through Raman spectroscopy. Realization of Majorana states in an s-wave superfluid requires strong spin-orbital coupling and a controllable Zeeman field in the perpendicular direction. We present a simple laser configuration to generate the artificial spin-orbital coupling and the required Zeeman field in the dark-state subspace.

  14. Non-Abelian Bremsstrahlung and Azimuthal Asymmetries in High Energy p+A Reactions

    SciTech Connect

    Gyulassy, Miklos; Vitev, Ivan Mateev; Levai, Peter; Biro, Tamas S.

    2014-09-25

    Here we apply the GLV reaction operator solution to the Vitev-Gunion-Bertsch (VGB) boundary conditions to compute the all-order in nuclear opacity non-abelian gluon bremsstrahlung of event- by-event uctuating beam jets in nuclear collisions. We evaluate analytically azimuthal Fourier moments of single gluon, v$M\\atop{n}$ {1}, and even number 2ℓ gluon, v$M\\atop{n}$ {2ℓ} inclusive distributions in high energy p+A reactions as a function of harmonic $n$, target recoil cluster number, $M$, and gluon number, 2ℓ, at RHIC and LHC. Multiple resolved clusters of recoiling target beam jets together with the projectile beam jet form Color Scintillation Antenna (CSA) arrays that lead to character- istic boost non-invariant trapezoidal rapidity distributions in asymmetric B+A nuclear collisions. The scaling of intrinsically azimuthally anisotropic and long range in η nature of the non-Abelian bremsstrahlung leads to vn moments that are similar to results from hydrodynamic models, but due entirely to non-Abelian wave interference phenomena sourced by the fluctuating CSA. Our analytic non-flow solutions are similar to recent numerical saturation model predictions but differ by predicting a simple power-law hierarchy of both even and odd vn without invoking kT factorization. A test of CSA mechanism is the predicted nearly linear η rapidity dependence of the vn(kTη). Non- Abelian beam jet bremsstrahlung may thus provide a simple analytic solution to Beam Energy Scan (BES) puzzle of the near $\\sqrt{s}$ independence of vn(pT) moments observed down to 10 AGeV where large-x valence quark beam jets dominate inelastic dynamics. Recoil bremsstrahlung from multiple independent CSA clusters could also provide a partial explanation for the unexpected similarity of vn in p(D) + A and non-central A + A at same dN=dη multiplicity as observed at RHIC and LHC.

  15. Mimetic discretization of the Abelian Chern-Simons theory and link invariants

    SciTech Connect

    Di Bartolo, Cayetano; Grau, Javier; Leal, Lorenzo

    2013-12-15

    A mimetic discretization of the Abelian Chern-Simons theory is presented. The study relies on the formulation of a theory of differential forms in the lattice, including a consistent definition of the Hodge duality operation. Explicit expressions for the Gauss Linking Number in the lattice, which correspond to their continuum counterparts are given. A discussion of the discretization of metric structures in the space of transverse vector densities is presented. The study of these metrics could serve to obtain explicit formulae for knot an link invariants in the lattice.

  16. Some symmetry group aspects of a perfect plane plasticity system

    NASA Astrophysics Data System (ADS)

    Senashov, S. I.; Yakhno, A.

    2013-09-01

    In this paper, all the known classical solutions of a plane perfect plasticity system under the Saint Venant-Tresca-von Mises yield criterion are associated with some group of point symmetries. The equations of slip-line families for all solutions are constructed, which allows one to explicitly determine the boundaries of the plastic areas. It is shown how one can determine the compatible velocity solution for known stresses by considering symmetries. Some invariant solutions of velocities for Prandtl stresses are constructed. The mechanical sense of the obtained velocity fields is discussed. To the blessed memory of our teacher D D Ivlev

  17. Unifying left-right symmetry and 331 electroweak theories

    NASA Astrophysics Data System (ADS)

    Reig, Mario; Valle, José W. F.; Vaquera-Araujo, C. A.

    2017-03-01

    We propose a realistic theory based on the SU (3)c ⊗ SU (3)L ⊗ SU (3)R ⊗ U(1)X gauge group which requires the number of families to match the number of colors. In the simplest realization neutrino masses arise from the canonical seesaw mechanism and their smallness correlates with the observed V-A nature of the weak force. Depending on the symmetry breaking path to the Standard Model one recovers either a left-right symmetric theory or one based on the SU (3)c ⊗ SU (3)L ⊗ U (1) symmetry as the ;next; step towards new physics.

  18. PREFACE: Symmetries in Science XIV

    NASA Astrophysics Data System (ADS)

    Schuch, Dieter; Ramek, Michael

    2010-04-01

    also included in these Proceedings. It was especially rewarding and greatly appreciated that symposium-founder Bruno Gruber attended all the sessions and that Dr. Hubert Regner, a distinguished official of the provincial administration and ardent supporter of the symposia for over twenty years, honoured us with a visit and an encouraging address to the participants. We wish to express our sincere gratitude to the local community, particularly the Schenk Family and the staff of Collegium Mehrerau for the selfless friendship, generosity and kind hospitality they offered our gathering. It made a lasting impression on participants and guests alike and provided an excellent basis for fruitful scientific discussions and personal interactions. This and the positive resonance from participants have encouraged us to take the experiment a step further to "Symmetries in Science 2011"! Thanks also to Yvette for continuous and reliable support. The conference and proceedings would probably not have materialized without her. Frankfurt am Main and Graz, June 2010 Dieter Schuch Michael Ramek Conference photograph

  19. Physics of a two-dimensional electron gas with cold atoms in non-Abelian gauge potentials

    NASA Astrophysics Data System (ADS)

    Satija, Indubala I.; Dakin, Daniel C.; Vaishnav, J. Y.; Clark, Charles W.

    2008-04-01

    Motivated by the possibility of creating non-Abelian fields using cold atoms in optical lattices, we explore the richness and complexity of noninteracting two-dimensional electron gases (2DEGs) in a lattice, subjected to such fields. In the continuum limit, a non-Abelian system characterized by a two-component “magnetic flux” describes a harmonic oscillator existing in two different charge states (mimicking a particle-hole pair) where the coupling between the states is determined by the non-Abelian parameter, namely, the difference between the two components of the “magnetic flux.” A key feature of the non-Abelian system is a splitting of the Landau energy levels, which broaden into bands, as the spectrum depends explicitly on the transverse momentum. These Landau bands result in a coarse-grained “moth,” a continuum version of the generalized Hofstadter butterfly. Furthermore, the bands overlap, leading to effective relativistic effects. Importantly, similar features also characterize the corresponding two-dimensional lattice problem when at least one of the components of the magnetic flux is an irrational number. The lattice system with two competing “magnetic fluxes” penetrating the unit cell provides a rich environment in which to study localization phenomena. Some unique aspects of the transport properties of the non-Abelian system are the possibility of inducing localization by varying the quasimomentum, and the absence of localization of certain zero-energy states exhibiting a linear energy-momentum relation. Furthermore, non-Abelian systems provide an interesting localization scenario where the localization transition is accompanied by a transition from relativistic to nonrelativistic theory.

  20. Towards a Realization of the Condensed-Matter-Gravity Correspondence in String Theory via Consistent Abelian Truncation of the Aharony-Bergman-Jafferis-Maldacena Model

    NASA Astrophysics Data System (ADS)

    Mohammed, Asadig; Murugan, Jeff; Nastase, Horatiu

    2012-11-01

    We present an embedding of the three-dimensional relativistic Landau-Ginzburg model for condensed matter systems in an N=6, U(N)×U(N) Chern-Simons-matter theory [the Aharony-Bergman-Jafferis-Maldacena model] by consistently truncating the latter to an Abelian effective field theory encoding the collective dynamics of O(N) of the O(N2) modes. In fact, depending on the vacuum expectation value on one of the Aharony-Bergman-Jafferis-Maldacena scalars, a mass deformation parameter μ and the Chern-Simons level number k, our Abelianization prescription allows us to interpolate between the Abelian Higgs model with its usual multivortex solutions and a ϕ4 theory. We sketch a simple condensed matter model that reproduces all the salient features of the Abelianization. In this context, the Abelianization can be interpreted as giving a dimensional reduction from four dimensions.

  1. Towards a realization of the condensed-matter-gravity correspondence in string theory via consistent Abelian truncation of the Aharony-Bergman-Jafferis-Maldacena model.

    PubMed

    Mohammed, Asadig; Murugan, Jeff; Nastase, Horatiu

    2012-11-02

    We present an embedding of the three-dimensional relativistic Landau-Ginzburg model for condensed matter systems in an N = 6, U(N) × U(N) Chern-Simons-matter theory [the Aharony-Bergman-Jafferis-Maldacena model] by consistently truncating the latter to an Abelian effective field theory encoding the collective dynamics of O(N) of the O(N(2)) modes. In fact, depending on the vacuum expectation value on one of the Aharony-Bergman-Jafferis-Maldacena scalars, a mass deformation parameter μ and the Chern-Simons level number k, our Abelianization prescription allows us to interpolate between the Abelian Higgs model with its usual multivortex solutions and a Ø(4) theory. We sketch a simple condensed matter model that reproduces all the salient features of the Abelianization. In this context, the Abelianization can be interpreted as giving a dimensional reduction from four dimensions.

  2. Electroweak Symmetry Breaking: With Dynamics

    SciTech Connect

    Chivukula, R. Sekhar

    2005-03-22

    In this note I provide a brief description of models of dynamical electroweak symmetry breaking, including walking technicolor, top-color assisted technicolor, the top-quark seesaw model, and little higgs theories.

  3. Classification of spacetimes with symmetry

    NASA Astrophysics Data System (ADS)

    Hicks, Jesse W.

    Spacetimes with symmetry play a critical role in Einstein's Theory of General Relativity. Missing from the literature is a correct, usable, and computer accessible classification of such spacetimes. This dissertation fills this gap; specifically, we. i) give a new and different approach to the classification of spacetimes with symmetry using modern methods and tools such as the Schmidt method and computer algebra systems, resulting in ninety-two spacetimes; ii) create digital databases of the classification for easy access and use for researchers; iii) create software to classify any spacetime metric with symmetry against the new database; iv) compare results of our classification with those of Petrov and find that Petrov missed six cases and incorrectly normalized a significant number of metrics; v) classify spacetimes with symmetry in the book Exact Solutions to Einstein's Field Equations Second Edition by Stephani, Kramer, Macallum, Hoenselaers, and Herlt and in Komrakov's paper Einstein-Maxwell equation on four-dimensional homogeneous spaces using the new software.

  4. Symmetries from the solution manifold

    NASA Astrophysics Data System (ADS)

    Aldaya, Víctor; Guerrero, Julio; Lopez-Ruiz, Francisco F.; Cossío, Francisco

    2015-07-01

    We face a revision of the role of symmetries of a physical system aiming at characterizing the corresponding Solution Manifold (SM) by means of Noether invariants as a preliminary step towards a proper, non-canonical, quantization. To this end, "point symmetries" of the Lagrangian are generally not enough, and we must resort to the more general concept of contact symmetries. They are defined in terms of the Poincaré-Cartan form, which allows us, in turn, to find the symplectic structure on the SM, through some sort of Hamilton-Jacobi (HJ) transformation. These basic symmetries are realized as Hamiltonian vector fields, associated with (coordinate) functions on the SM, lifted back to the Evolution Manifold through the inverse of this HJ mapping, that constitutes an inverse of the Noether Theorem. The specific examples of a particle moving on S3, at the mechanical level, and nonlinear SU(2)-sigma model in field theory are sketched.

  5. Partial Dynamical Symmetry in Molecules

    NASA Astrophysics Data System (ADS)

    Ping, Jia-Lun; Chen, Jin-Quan

    1997-03-01

    It is shown that any Hamiltonian involving only one- and two-bond interactions for a molecule withnbonds and having a point groupPas its symmetry group may have theSn⊃Ppartial dynamical symmetry, i.e., the Hamiltonian can be solved analytically for a part of the states, called the unique states. For example, theXY6molecule has theS6⊃Ohpartial dynamical symmetry. The model of Iachello and Oss forncoupled anharmonic oscillators is revisited in terms of the partial dynamical symmetry. The energies are obtained analytically for the nine unique levels of theXY6molecule and the structures of the eigenstates are disclosed for the first time, while for non-unique states they are obtained by diagonalizing the Hamiltonian in theS6⊃Ohsymmetry adapted basis with greatly reduced dimension.

  6. Broken Symmetries and Magnetic Dynamos

    NASA Technical Reports Server (NTRS)

    Shebalin, John V.

    2007-01-01

    Phase space symmetries inherent in the statistical theory of ideal magnetohydrodynamic (MHD) turbulence are known to be broken dynamically to produce large-scale coherent magnetic structure. Here, results of a numerical study of decaying MHD turbulence are presented that show large-scale coherent structure also arises and persists in the presence of dissipation. Dynamically broken symmetries in MHD turbulence may thus play a fundamental role in the dynamo process.

  7. Possible violations of spacetime symmetries

    NASA Astrophysics Data System (ADS)

    Urrutia, Luis

    2016-10-01

    The identification of symmetries has played a fundamental role in our understanding of physical phenomena. Nevertheless, in most cases such symmetries constitute only a zeroth-order approximation and they need to be broken so that the predictions of the theory are consistent with experimental observation. In particular, the almost sacred CPT and Lorentz symmetries, which are certainly part of the fundamental ideas of modern physics, need to be probed experimentally. Recently, such efforts have been intensified because different theoretical approaches aiming to understand the microstructure of space-time suggest the possibility that such symmetries could present minute violations. Up to now, and with increasing experimental sensitivities, no signs of violation have been found. Nevertheless, we observe that even the persistence of such negative results will have a profound impact. On one hand, they will provide those symmetries with a firm experimental basis. On the other, they will set stringent experimental bounds to be compared with the possible emergence of such violations in quantum gravity models based upon a discrete structure of space. We present a very general perspective of the research on Lorentz symmetry breaking, together with a review of a few specific topics.

  8. A solenoidal synthetic field and the non-Abelian Aharonov-Bohm effects in neutral atoms

    NASA Astrophysics Data System (ADS)

    Huo, Ming-Xia; Nie, Wei; Hutchinson, David A. W.; Kwek, Leong Chuan

    2014-08-01

    Cold neutral atoms provide a versatile and controllable platform for emulating various quantum systems. Despite efforts to develop artificial gauge fields in these systems, realizing a unique ideal-solenoid-shaped magnetic field within the quantum domain in any real-world physical system remains elusive. Here we propose a scheme to generate a ``hairline'' solenoid with an extremely small size around 1 micrometer which is smaller than the typical coherence length in cold atoms. Correspondingly, interference effects will play a role in transport. Despite the small size, the magnetic flux imposed on the atoms is very large thanks to the very strong field generated inside the solenoid. By arranging different sets of Laguerre-Gauss (LG) lasers, the generation of Abelian and non-Abelian SU(2) lattice gauge fields is proposed for neutral atoms in ring- and square-shaped optical lattices. As an application, interference patterns of the magnetic type-I Aharonov-Bohm (AB) effect are obtained by evolving atoms along a circle over several tens of lattice cells. During the evolution, the quantum coherence is maintained and the atoms are exposed to a large magnetic flux. The scheme requires only standard optical access, and is robust to weak particle interactions.

  9. A solenoidal synthetic field and the non-Abelian Aharonov-Bohm effects in neutral atoms.

    PubMed

    Huo, Ming-Xia; Nie, Wei; Hutchinson, David A W; Kwek, Leong Chuan

    2014-08-08

    Cold neutral atoms provide a versatile and controllable platform for emulating various quantum systems. Despite efforts to develop artificial gauge fields in these systems, realizing a unique ideal-solenoid-shaped magnetic field within the quantum domain in any real-world physical system remains elusive. Here we propose a scheme to generate a "hairline" solenoid with an extremely small size around 1 micrometer which is smaller than the typical coherence length in cold atoms. Correspondingly, interference effects will play a role in transport. Despite the small size, the magnetic flux imposed on the atoms is very large thanks to the very strong field generated inside the solenoid. By arranging different sets of Laguerre-Gauss (LG) lasers, the generation of Abelian and non-Abelian SU(2) lattice gauge fields is proposed for neutral atoms in ring- and square-shaped optical lattices. As an application, interference patterns of the magnetic type-I Aharonov-Bohm (AB) effect are obtained by evolving atoms along a circle over several tens of lattice cells. During the evolution, the quantum coherence is maintained and the atoms are exposed to a large magnetic flux. The scheme requires only standard optical access, and is robust to weak particle interactions.

  10. Creating and manipulating non-Abelian anyons in cold atom systems using auxiliary bosons

    NASA Astrophysics Data System (ADS)

    Zhang, Yuhe; Sreejith, G. J.; Jain, J. K.

    2015-08-01

    The possibility of realizing bosonic fractional quantum Hall effect in ultracold atomic systems suggests a new route to producing and manipulating anyons, by introducing auxiliary bosons of a different species that capture quasiholes and thus inherit their nontrivial braiding properties. States with localized quasiholes at any desired locations can be obtained by annihilating the auxiliary bosons at those locations. We explore how this method can be used to generate non-Abelian quasiholes of the Moore-Read Pfaffian state for bosons at filling factor ν =1 . We show that a Hamiltonian with an appropriate three-body interaction can produce two-quasihole states in two distinct fusion channels of the topological "qubit." Characteristics of these states that are related to the non-Abelian nature can be probed and verified by a measurement of the effective relative angular momentum of the auxiliary bosons, which is directly related to their pair distribution function. Moore-Read states of more than two quasiholes can also be produced in a similar fashion. We investigate some issues related to the experimental feasibility of this approach, in particular, how large the systems should be for a realization of this physics and to what extent this physics carries over to systems with the more standard two-body contact interaction.

  11. Experimental Identification of Non-Abelian Topological Orders on a Quantum Simulator

    NASA Astrophysics Data System (ADS)

    Li, Keren; Wan, Yidun; Hung, Ling-Yan; Lan, Tian; Long, Guilu; Lu, Dawei; Zeng, Bei; Laflamme, Raymond

    2017-02-01

    Topological orders can be used as media for topological quantum computing—a promising quantum computation model due to its invulnerability against local errors. Conversely, a quantum simulator, often regarded as a quantum computing device for special purposes, also offers a way of characterizing topological orders. Here, we show how to identify distinct topological orders via measuring their modular S and T matrices. In particular, we employ a nuclear magnetic resonance quantum simulator to study the properties of three topologically ordered matter phases described by the string-net model with two string types, including the Z2 toric code, doubled semion, and doubled Fibonacci. The third one, non-Abelian Fibonacci order is notably expected to be the simplest candidate for universal topological quantum computing. Our experiment serves as the basic module, built on which one can simulate braiding of non-Abelian anyons and ultimately, topological quantum computation via the braiding, and thus provides a new approach of investigating topological orders using quantum computers.

  12. Wilson loop and magnetic monopole through a non-Abelian Stokes theorem

    SciTech Connect

    Kondo, Kei-Ichi

    2008-04-15

    I show that the Wilson loop operator for the SU(N) Yang-Mills gauge connection is exactly rewritten in terms of conserved gauge-invariant magnetic and electric currents through a non-Abelian Stokes theorem of the Diakonov-Petrov type. Here the magnetic current originates from the magnetic monopole derived in the gauge-invariant way from the pure Yang-Mills theory even in the absence of the Higgs scalar field, in sharp contrast to the 't Hooft-Polyakov magnetic monopole in the Georgi-Glashow gauge-Higgs model. The resulting representation indicates that the Wilson loop operator in fundamental representations can be a probe for a single magnetic monopole irrespective of N in SU(N) Yang-Mills theory, against the conventional wisdom. Moreover, I show that the quantization condition for the magnetic charge follows from the fact that the non-Abelian Stokes theorem does not depend on the surface chosen for writing the surface integral. The obtained geometrical and topological representations of the Wilson loop operator have important implications to understanding quark confinement according to the dual superconductor picture.

  13. Non-Abelian vortex in four dimensions as a critical string on a conifold

    NASA Astrophysics Data System (ADS)

    Koroteev, P.; Shifman, M.; Yung, A.

    2016-09-01

    Non-Abelian vortex strings supported in a certain four-dimensional N =2 Yang-Mills theory with fundamental matter were shown [1] to become critical superstrings. In addition to translational moduli, the non-Abelian strings under consideration carry orientational and size moduli. Their dynamics is described by the two-dimensional sigma model whose target space is a tautological bundle over the complex projective space. For the N =2 theory with the U (2 ) gauge group and four fundamental hypermultiplets, there are six orientational and size moduli. After combining with four translational moduli, they form a ten-dimensional target space, which is required for a superstring to be critical. For the theory in question, the target space of the sigma model is C2×Y6, where Y6 is a conifold. We study closed string states which emerge in four dimensions (4D) and identify them with hadrons of the 4D bulk N =2 theory. It turns out that most of the states arising from the ten-dimensional graviton spectrum are nondynamical in 4D. We find a single dynamical massless hypermultiplet associated with the deformation of the complex structure of the conifold. We interpret this degree of freedom as a monopole-monopole baryon of the 4D theory (at strong coupling).

  14. Non-Abelian S U (N -1 ) -singlet fractional quantum Hall states from coupled wires

    NASA Astrophysics Data System (ADS)

    Fuji, Y.; Lecheminant, P.

    2017-03-01

    The construction of fractional quantum Hall (FQH) states from the two-dimensional array of quantum wires provides a useful way to control strong interactions in microscopic models and has been successfully applied to the Laughlin, Moore-Read, and Read-Rezayi states. We extend this construction to the Abelian and non-Abelian S U (N -1 ) -singlet FQH states at filling fraction ν =k (N -1 )/[N +k (N -1 )m ] labeled by integers k and m , which are potentially realized in multicomponent quantum Hall systems or S U (N ) spin systems. Utilizing the bosonization approach and conformal field theory (CFT), we show that their bulk quasiparticles and gapless edge excitations are both described by an (N -1 ) -component free-boson CFT and the S U (N) k/[U(1 ) ] N -1 CFT known as the Gepner parafermion. Their generalization to different filling fractions is also proposed. In addition, we argue possible applications of these results to two kinds of lattice systems: bosons interacting via occupation-dependent correlated hoppings and an S U (N ) Heisenberg model.

  15. Non-abelian fractional quantum hall effect for fault-resistant topological quantum computation.

    SciTech Connect

    Pan, Wei; Thalakulam, Madhu; Shi, Xiaoyan; Crawford, Matthew; Nielsen, Erik; Cederberg, Jeffrey George

    2013-10-01

    Topological quantum computation (TQC) has emerged as one of the most promising approaches to quantum computation. Under this approach, the topological properties of a non-Abelian quantum system, which are insensitive to local perturbations, are utilized to process and transport quantum information. The encoded information can be protected and rendered immune from nearly all environmental decoherence processes without additional error-correction. It is believed that the low energy excitations of the so-called =5/2 fractional quantum Hall (FQH) state may obey non-Abelian statistics. Our goal is to explore this novel FQH state and to understand and create a scientific foundation of this quantum matter state for the emerging TQC technology. We present in this report the results from a coherent study that focused on obtaining a knowledge base of the physics that underpins TQC. We first present the results of bulk transport properties, including the nature of disorder on the 5/2 state and spin transitions in the second Landau level. We then describe the development and application of edge tunneling techniques to quantify and understand the quasiparticle physics of the 5/2 state.

  16. Experimental Identification of Non-Abelian Topological Orders on a Quantum Simulator.

    PubMed

    Li, Keren; Wan, Yidun; Hung, Ling-Yan; Lan, Tian; Long, Guilu; Lu, Dawei; Zeng, Bei; Laflamme, Raymond

    2017-02-24

    Topological orders can be used as media for topological quantum computing-a promising quantum computation model due to its invulnerability against local errors. Conversely, a quantum simulator, often regarded as a quantum computing device for special purposes, also offers a way of characterizing topological orders. Here, we show how to identify distinct topological orders via measuring their modular S and T matrices. In particular, we employ a nuclear magnetic resonance quantum simulator to study the properties of three topologically ordered matter phases described by the string-net model with two string types, including the Z_{2} toric code, doubled semion, and doubled Fibonacci. The third one, non-Abelian Fibonacci order is notably expected to be the simplest candidate for universal topological quantum computing. Our experiment serves as the basic module, built on which one can simulate braiding of non-Abelian anyons and ultimately, topological quantum computation via the braiding, and thus provides a new approach of investigating topological orders using quantum computers.

  17. Non-Abelian statistics and topological quantum information processing in 1D wire networks

    NASA Astrophysics Data System (ADS)

    Alicea, Jason; Oreg, Yuval; Refael, Gil; von Oppen, Felix; Fisher, Matthew P. A.

    2011-03-01

    Topological quantum computation provides an elegant way around decoherence, as one encodes quantum information in a non-local fashion that the environment finds difficult to corrupt. Here we establish that one of the key operations---braiding of non-Abelian anyons---can be implemented in one-dimensional semiconductor wire networks. Previous work [Lutchyn et al., arXiv:1002.4033 and Oreg et al., arXiv:1003.1145] provided a recipe for driving semiconducting wires into a topological phase supporting long-sought particles known as Majorana fermions that can store topologically protected quantum information. Majorana fermions in this setting can be transported, created, and fused by applying locally tunable gates to the wire. More importantly, we show that networks of such wires allow braiding of Majorana fermions and that they exhibit non-Abelian statistics like vortices in a p+ip superconductor. We propose experimental setups that enable the Majorana fusion rules to be probed, along with networks that allow for efficient exchange of arbitrary numbers of Majorana fermions. This work paves a new path forward in topological quantum computation that benefits from physical transparency and experimental realism.

  18. Wilson loop and magnetic monopole through a non-Abelian Stokes theorem

    NASA Astrophysics Data System (ADS)

    Kondo, Kei-Ichi

    2008-04-01

    I show that the Wilson loop operator for the SU(N) Yang-Mills gauge connection is exactly rewritten in terms of conserved gauge-invariant magnetic and electric currents through a non-Abelian Stokes theorem of the Diakonov-Petrov type. Here the magnetic current originates from the magnetic monopole derived in the gauge-invariant way from the pure Yang-Mills theory even in the absence of the Higgs scalar field, in sharp contrast to the ’t Hooft Polyakov magnetic monopole in the Georgi-Glashow gauge-Higgs model. The resulting representation indicates that the Wilson loop operator in fundamental representations can be a probe for a single magnetic monopole irrespective of N in SU(N) Yang-Mills theory, against the conventional wisdom. Moreover, I show that the quantization condition for the magnetic charge follows from the fact that the non-Abelian Stokes theorem does not depend on the surface chosen for writing the surface integral. The obtained geometrical and topological representations of the Wilson loop operator have important implications to understanding quark confinement according to the dual superconductor picture.

  19. Non-Abelian black string solutions of N = (2,0) , d = 6 supergravity

    NASA Astrophysics Data System (ADS)

    Cano, Pablo A.; Ortín, Tomás; Santoli, Camilla

    2016-12-01

    We show that, when compactified on a circle, N = (2, 0), d = 6 supergravity coupled to 1 tensor multiplet and n V vector multiplets is dual to N = (2 , 0) , d = 6 supergravity coupled to just n T = n V + 1 tensor multiplets and no vector multiplets. Both theories reduce to the same models of N = 2 , d = 5 supergravity coupled to n V 5 = n V + 2 vector fields. We derive Buscher rules that relate solutions of these theories (and of the theory that one obtains by dualizing the 3-form field strength) admitting an isometry. Since the relations between the fields of N = 2 , d = 5 supergravity and those of the 6-dimensional theories are the same with or without gaugings, we construct supersymmetric non-Abelian solutions of the 6-dimensional gauged theories by uplifting the recently found 5-dimensional supersymmetric non-Abelian black-hole solutions. The solutions describe the usual superpositions of strings and waves supplemented by a BPST instanton in the transverse directions, similar to the gauge dyonic string of Duff, Lü and Pope. One of the solutions obtained interpolates smoothly between two AdS3× S3 geometries with different radii.

  20. A solenoidal synthetic field and the non-Abelian Aharonov-Bohm effects in neutral atoms

    PubMed Central

    Huo, Ming-Xia; Nie, Wei; Hutchinson, David A. W.; Kwek, Leong Chuan

    2014-01-01

    Cold neutral atoms provide a versatile and controllable platform for emulating various quantum systems. Despite efforts to develop artificial gauge fields in these systems, realizing a unique ideal-solenoid-shaped magnetic field within the quantum domain in any real-world physical system remains elusive. Here we propose a scheme to generate a “hairline” solenoid with an extremely small size around 1 micrometer which is smaller than the typical coherence length in cold atoms. Correspondingly, interference effects will play a role in transport. Despite the small size, the magnetic flux imposed on the atoms is very large thanks to the very strong field generated inside the solenoid. By arranging different sets of Laguerre-Gauss (LG) lasers, the generation of Abelian and non-Abelian SU(2) lattice gauge fields is proposed for neutral atoms in ring- and square-shaped optical lattices. As an application, interference patterns of the magnetic type-I Aharonov-Bohm (AB) effect are obtained by evolving atoms along a circle over several tens of lattice cells. During the evolution, the quantum coherence is maintained and the atoms are exposed to a large magnetic flux. The scheme requires only standard optical access, and is robust to weak particle interactions. PMID:25103877

  1. Confining and repulsive potentials from effective non-Abelian gauge fields in graphene bilayers

    NASA Astrophysics Data System (ADS)

    González, J.

    2016-10-01

    We investigate the effect of shear and strain in graphene bilayers, under conditions where the distortion of the lattice gives rise to a smooth one-dimensional modulation in the stacking sequence of the bilayer. We show that strain and shear produce characteristic Moiré patterns which can have the same visual appearance on a large scale, but representing graphene bilayers with quite different electronic properties. The different features in the low-energy electronic bands can be ascribed to the effect of a fictitious non-Abelian gauge field mimicking the smooth modulation of the stacking order. Strained and sheared bilayers show a complementary behavior, which can be understood from the fact that the non-Abelian gauge field acts as a repulsive interaction in the former, expelling the electron density away from the stacking domain walls, while behaving as a confining interaction leading to localization of the electronic states in the sheared bilayers. In this latter case, the presence of the effective gauge field explains the development of almost flat low-energy bands, resembling the form of the zeroth Landau level characteristic of a Dirac fermion field. The estimate of the gauge field strength in those systems gives a magnitude of the order of several tens of tesla, implying a robust phenomenology that should be susceptible of being observed in suitably distorted bilayer samples.

  2. Chaos-order transition in Bianchi type I non-Abelian Born-Infeld cosmology

    NASA Astrophysics Data System (ADS)

    Dyadichev, Vladimir V.; Gal'Tsov, Dmitri V.; Moniz, Paulo Vargas

    2005-10-01

    We investigate the Bianchi I cosmology with the homogeneous SU(2) Yang-Mills field governed by the non-Abelian Born-Infeld action. A similar system with the standard Einstein-Yang-Mills (EYM) action is known to exhibit chaotic behavior induced by the Yang-Mills field. When the action is replaced by the Born-Infeld type non-Abelian action (NBI), the chaos-order transition is observed in the high-energy region. This is interpreted as a smothering effect due to (nonperturbative in α') string corrections to the classical EYM action. We give numerical evidence for the chaos-order transition and present an analytical proof of regularity of color oscillations in the limit of strong Born-Infeld nonlinearity. We also perform a general analysis of the Bianchi I NBI cosmology and derive an exact solution in the case of only the U(1) component excited. Our new exact solution generalizes the Rosen solution of the Bianchi I Einstein-Maxwell cosmology to the U(1) Einstein-Born-Infeld theory.

  3. Symmetry in polarimetric remote sensing

    NASA Technical Reports Server (NTRS)

    Nghiem, S. V.; Yueh, S. H.; Kwok, R.

    1993-01-01

    Relationships among polarimetric backscattering coefficients are derived from the viewpoint of symmetry groups. For both reciprocal and non-reciprocal media, symmetry encountered in remote sensing due to reflection, rotation, azimuthal, and centrical symmetry groups is considered. The derived properties are general and valid to all scattering mechanisms, including volume and surface scatterings and their interactions, in a given symmetrical configuration. The scattering coefficients calculated from theoretical models for layer random media and rough surfaces are shown to obey the symmetry relations. Use of symmetry properties in remote sensing of structural and environmental responses of scattering media is also discussed. Orientations of spheroidal scatterers described by spherical, uniform, planophile, plagiothile, erectophile, and extremophile distributions are considered to derive their polarimetric backscattering characteristics. These distributions can be identified from the observed scattering coefficients by comparison with theoretical symmetry calculations. A new parameter is then defined to study scattering structures in geophysical media. Observations from polarimetric data acquired by the Jet Propulsion Laboratory airborne synthetic aperture radar over forests, sea ice, and sea surface are presented. Experimental evidences of the symmetry relationships are shown and their use in polarimetric remote sensing is illustrated. For forests, the coniferous forest in Mt. Shasta area (California) and mixed forest near Presque Isle (Maine) exhibit characteristics of the centrical symmetry at C-band. For sea ice in the Beaufort Sea, multi-year sea ice has a cross-polarized ratio e close to e(sub 0), calculated from symmetry, due to the randomness in the scattering structure. First-year sea ice has e much smaller than e(sub 0) due to the preferential alignment of the columnar structure of the ice. From polarimetric data of a sea surface in the Bering Sea, it is

  4. Quantum graphs: PT -symmetry and reflection symmetry of the spectrum

    NASA Astrophysics Data System (ADS)

    Kurasov, P.; Majidzadeh Garjani, B.

    2017-02-01

    Not necessarily self-adjoint quantum graphs—differential operators on metric graphs—are considered. Assume in addition that the underlying metric graph possesses an automorphism (symmetry) P . If the differential operator is P T -symmetric, then its spectrum has reflection symmetry with respect to the real line. Our goal is to understand whether the opposite statement holds, namely, whether the reflection symmetry of the spectrum of a quantum graph implies that the underlying metric graph possesses a non-trivial automorphism and the differential operator is P T -symmetric. We give partial answer to this question by considering equilateral star-graphs. The corresponding Laplace operator with Robin vertex conditions possesses reflection-symmetric spectrum if and only if the operator is P T -symmetric with P being an automorphism of the metric graph.

  5. Symmetries in Three-Dimensional Superconformal Quantum Field Theories

    NASA Astrophysics Data System (ADS)

    Bashkirov, Denis

    Many examples of gauge-gravity duality and quantum equivalences of different-looking three-dimensional Quantum Field Theories indicate the existence of continuous symmetries whose currents are not built from elementary, or perturbative, fields used to write down the Lagrangian. These symmetries are called hidden or nonperturbative. We describe a method for studying continuous symmetries in a large class of three-dimensional supersymmetric gauge theories which, in particular, enables one to explore nonperturbative global symmetries and supersymmetries. As an application of the method, we prove conjectured supersymmetry enhancement in strongly coupled ABJM theory from N = 6 to N = 8 and find additional nonperturbative evidence for its duality to the N = 8 U(N) SYM theory for the minimal value of the Chern-Simons coupling. Hidden supersymmetry is also shown to occur in N = 4 d = 3 SQCD with one fundamental and one adjoint hypermultiplets. An infinite family of N = 6 d = 3 ABJ theories is proved to have hidden N = 8 superconformal symmetry and hidden parity on the quantum level. We test several conjectural dualities between ABJ theories and theories proposed by Bagger and Lambert, and Gustavsson by comparing superconformal indices of these theories. Comparison of superconformal indices is also used to test dualities between N = 2 d = 3 theories proposed by Aharony, the analysis of whose chiral rings teaches some general lessons about nonperturbative chiral operators of strongly coupled 3d supersymmetric gauge theories. As another application of our method we consider examples of hidden global symmetries in a class of quiver three-dimensional N = 4 superconformal gauge theories. Finally, we point out to the relations between some basic propeties of superconformal N ≥ 6 theories and their symmetries. The results presented in this thesis were obtained in a series of papers [1, 2, 3, 4, 5].

  6. Structure and Properties of High Symmetry Composites

    DTIC Science & Technology

    1990-07-27

    utilizing a 4-directional reinforcement. Reducing the close-to-cubic symmetry concept into practice in our laboratory by a three-dimensional braiding...modelled by utilizing the different elastic strain energy expressions produced by different combinations of symmetry elements. Symmetry in Materials The...rings is insignmicant. Utilizing the above assumptions, numerous textile structures possess holosymmetric cubic symmetry. This symmetry state is found in

  7. Molecular Eigensolution Symmetry Analysis and Fine Structure

    PubMed Central

    Harter, William G.; Mitchell, Justin C.

    2013-01-01

    Spectra of high-symmetry molecules contain fine and superfine level cluster structure related to J-tunneling between hills and valleys on rovibronic energy surfaces (RES). Such graphic visualizations help disentangle multi-level dynamics, selection rules, and state mixing effects including widespread violation of nuclear spin symmetry species. A review of RES analysis compares it to that of potential energy surfaces (PES) used in Born–Oppenheimer approximations. Both take advantage of adiabatic coupling in order to visualize Hamiltonian eigensolutions. RES of symmetric and D2 asymmetric top rank-2-tensor Hamiltonians are compared with Oh spherical top rank-4-tensor fine-structure clusters of 6-fold and 8-fold tunneling multiplets. Then extreme 12-fold and 24-fold multiplets are analyzed by RES plots of higher rank tensor Hamiltonians. Such extreme clustering is rare in fundamental bands but prevalent in hot bands, and analysis of its superfine structure requires more efficient labeling and a more powerful group theory. This is introduced using elementary examples involving two groups of order-6 (C6 and D3~C3v), then applied to families of Oh clusters in SF6 spectra and to extreme clusters. PMID:23344041

  8. Structural Symmetry in Membrane Proteins.

    PubMed

    Forrest, Lucy R

    2015-01-01

    Symmetry is a common feature among natural systems, including protein structures. A strong propensity toward symmetric architectures has long been recognized for water-soluble proteins, and this propensity has been rationalized from an evolutionary standpoint. Proteins residing in cellular membranes, however, have traditionally been less amenable to structural studies, and thus the prevalence and significance of symmetry in this important class of molecules is not as well understood. In the past two decades, researchers have made great strides in this area, and these advances have provided exciting insights into the range of architectures adopted by membrane proteins. These structural studies have revealed a similarly strong bias toward symmetric arrangements, which were often unexpected and which occurred despite the restrictions imposed by the membrane environment on the possible symmetry groups. Moreover, membrane proteins disproportionately contain internal structural repeats resulting from duplication and fusion of smaller segments. This article discusses the types and origins of symmetry in membrane proteins and the implications of symmetry for protein function.

  9. Symmetry Guide to Ferroaxial Transitions

    NASA Astrophysics Data System (ADS)

    Hlinka, J.; Privratska, J.; Ondrejkovic, P.; Janovec, V.

    2016-04-01

    The 212 species of the structural phase transitions with a macroscopic symmetry breaking are inspected with respect to the occurrence of the ferroaxial order parameter, the electric toroidal moment. In total, 124 ferroaxial species are found, some of them being also fully ferroelectric (62) or fully ferroelastic ones (61). This ensures a possibility of electrical or mechanical switching of ferroaxial domains. Moreover, there are 12 ferroaxial species that are neither ferroelectric nor ferroelastic. For each species, we have also explicitly worked out a canonical form for a set of representative equilibrium property tensors of polar and axial nature in both high-symmetry and low-symmetry phases. This information was gathered into the set of 212 mutually different symbolic matrices, expressing graphically the presence of nonzero independent tensorial components and the symmetry-imposed links between them, for both phases simultaneously. Symmetry analysis reveals the ferroaxiality in several currently debated materials, such as VO2 , LuFe2 O4 , and URu2 Si2 .

  10. Resonantly amplified vibronic symmetry breaking

    NASA Astrophysics Data System (ADS)

    Poliakoff, E. D.; Rathbone, G. J.; Bozek, J. D.; Lucchese, R. R.

    2002-05-01

    In photoelectron spectroscopy, it is normally assumed that excitation of a single quantum of a non-totally symmetric vibrational mode is forbidden owing to symmetry constraints. Using vibrationally resolved photoelectron spectroscopy over a broad spectral range, we have shown that a previously overlooked mechanism can lead to these nominally forbidden transitions. Specifically, the photoelectron can mediate the oscillator strength for such a transition via resonantly amplified vibronic symmetry breaking, and this effect results from intrachannel rather than interchannel coupling. In our first experiments, we focused on bending excitation accompanying CO2 photoionization. Photoelectron spectroscopy on the CO_2^+(C^2Σ_g^+) state showed that the excitation of the (010) vibrational mode is mediated by a shape resonant continuum electron. The degree of vibrational excitation can be substantial, and extensions to other types of symmetry breaking are currently being investigated.

  11. Self-dual configurations in Abelian Higgs models with k-generalized gauge field dynamics

    NASA Astrophysics Data System (ADS)

    Casana, R.; Cavalcante, A.; da Hora, E.

    2016-12-01

    We have shown the existence of self-dual solutions in new Maxwell-Higgs scenarios where the gauge field possesses a k-generalized dynamic, i.e., the kinetic term of gauge field is a highly nonlinear function of F μν F μν . We have implemented our proposal by means of a k-generalized model displaying the spontaneous symmetry breaking phenomenon. We implement consistently the Bogomol'nyi-Prasad-Sommerfield formalism providing highly nonlinear self-dual equations whose solutions are electrically neutral possessing total energy proportional to the magnetic flux. Among the infinite set of possible configurations, we have found families of k-generalized models whose self-dual equations have a form mathematically similar to the ones arising in the Maxwell-Higgs or Chern-Simons-Higgs models. Furthermore, we have verified that our proposal also supports infinite twinlike models with | ϕ|4-potential or | ϕ|6-potential. With the aim to show explicitly that the BPS equations are able to provide well-behaved configurations, we have considered a test model in order to study axially symmetric vortices. By depending of the self-dual potential, we have shown that the k-generalized model is able to produce solutions that for long distances have a exponential decay (as Abrikosov-Nielsen-Olesen vortices) or have a power-law decay (characterizing delocalized vortices). In all cases, we observe that the generalization modifies the vortex core size, the magnetic field amplitude and the bosonic masses but the total energy remains proportional to the quantized magnetic flux.

  12. Symmetries of coupled harmonic oscillators

    NASA Technical Reports Server (NTRS)

    Han, D.; Kim, Y. S.

    1993-01-01

    It is shown that the system of two coupled harmonic oscillators possesses many interesting symmetries. It is noted that the symmetry of a single oscillator is that of the three-parameter group Sp(2). Thus two uncoupled oscillator exhibits a direct product of two Sp(2) groups, with six parameters. The coupling can be achieved through a rotation in the two-dimensional space of two oscillator coordinates. The closure of the commutation relations for the generators leads to the ten-parameter group Sp(4) which is locally isomorphic to the deSitter group O(3,2).

  13. Iterates of maps with symmetry

    NASA Technical Reports Server (NTRS)

    Chossat, Pascal; Golubitsky, Martin

    1988-01-01

    Fixed-point bifurcation, period doubling, and Hopf bifurcation (HB) for iterates of equivariant mappings are investigated analytically, with a focus on HB in the presence of symmetry. An algebraic formulation for the hypotheses of the theorem of Ruelle (1973) is derived, and the case of standing waves in a system of ordinary differential equations with O(2) symmetry is considered in detail. In this case, it is shown that HB can lead directly to motion on an invariant 3-torus, with an unexpected third frequency due to drift of standing waves along the torus.

  14. The Broken Symmetry of Time

    SciTech Connect

    Kastner, Ruth E.

    2011-11-29

    This paper seeks to clarify features of time asymmetry in terms of symmetry breaking. It is observed that, in general, a contingent situation or event requires the breaking of an underlying symmetry. The distinction between the universal anisotropy of temporal processes and the irreversibility of certain physical processes is clarified. It is also proposed that the Transactional Interpretation of quantum mechanics offers an effective way to explain general thermodynamic asymmetry in terms of the time asymmetry of radiation, where prior such efforts have fallen short.

  15. Quantum Symmetries and Exceptional Collections

    NASA Astrophysics Data System (ADS)

    Karp, Robert L.

    2011-01-01

    We study the interplay between discrete quantum symmetries at certain points in the moduli space of Calabi-Yau compactifications, and the associated identities that the geometric realization of D-brane monodromies must satisfy. We show that in a wide class of examples, both local and compact, the monodromy identities in question always follow from a single mathematical statement. One of the simplest examples is the {{mathbb Z}_5} symmetry at the Gepner point of the quintic, and the associated D-brane monodromy identity.

  16. Symmetry analysis of cellular automata

    NASA Astrophysics Data System (ADS)

    García-Morales, V.

    2013-01-01

    By means of B-calculus [V. García-Morales, Phys. Lett. A 376 (2012) 2645] a universal map for deterministic cellular automata (CAs) has been derived. The latter is shown here to be invariant upon certain transformations (global complementation, reflection and shift). When constructing CA rules in terms of rules of lower range a new symmetry, “invariance under construction” is uncovered. Modular arithmetic is also reformulated within B-calculus and a new symmetry of certain totalistic CA rules, which calculate the Pascal simplices modulo an integer number p, is then also uncovered.

  17. Chiral symmetry in quarkyonic matter

    SciTech Connect

    Kojo, T.

    2012-05-15

    The 1/N{sub c} expansion classifies nuclear matter, deconfined quark matter, and Quarkyonic matter in low temperature region. We investigate the realization of chiral symmetry in Quarkyonic matter by taking into account condensations of chiral particle-hole pairs. It is argued that chiral symmetry and parity are locally violated by the formation of chiral spirals, <{psi}-bar exp (2i{mu}{sub q} z{gamma}{sup 0} {gamma}{sup z}){psi}> . An extension to multiple chiral spirals is also briefly discussed.

  18. Bell Inequalities and Group Symmetry

    NASA Astrophysics Data System (ADS)

    Bolonek-Lasoń, Katarzyna

    2017-03-01

    Recently the method based on irreducible representations of finite groups has been proposed as a tool for investigating the more sophisticated versions of Bell inequalities (V. Ugǔr Gűney, M. Hillery, Phys. Rev. A90, 062121 ([2014]) and Phys. Rev. A91, 052110 ([2015])). In the present paper an example based on the symmetry group S 4 is considered. The Bell inequality violation due to the symmetry properties of regular tetrahedron is described. A nonlocal game based on the inequalities derived is described and it is shown that the violation of Bell inequality implies that the quantum strategies outperform their classical counterparts.

  19. Nonsupersymmetric Dualities from Mirror Symmetry

    NASA Astrophysics Data System (ADS)

    Kachru, Shamit; Mulligan, Michael; Torroba, Gonzalo; Wang, Huajia

    2017-01-01

    We study supersymmetry breaking perturbations of the simplest dual pair of (2 +1 )-dimensional N =2 supersymmetric field theories—the free chiral multiplet and N =2 super QED with a single flavor. We find dual descriptions of a phase diagram containing four distinct massive phases. The equivalence of the intervening critical theories gives rise to several nonsupersymmetric avatars of mirror symmetry: we find dualities relating scalar QED to a free fermion and Wilson-Fisher theories to both scalar and fermionic QED. Thus, mirror symmetry can be viewed as the multicritical parent duality from which these nonsupersymmetric dualities directly descend.

  20. Chiral symmetry on the lattice

    SciTech Connect

    Creutz, M.

    1994-11-01

    The author reviews some of the difficulties associated with chiral symmetry in the context of a lattice regulator. The author discusses the structure of Wilson Fermions when the hopping parameter is in the vicinity of its critical value. Here one flavor contrasts sharply with the case of more, where a residual chiral symmetry survives anomalies. The author briefly discusses the surface mode approach, the use of mirror Fermions to cancel anomalies, and finally speculates on the problems with lattice versions of the standard model.

  1. Non-Abelian evolution of electromagnetic waves in a weakly anisotropic inhomogeneous medium

    NASA Astrophysics Data System (ADS)

    Bliokh, K. Yu.; Frolov, D. Yu.; Kravtsov, Yu. A.

    2007-05-01

    A theory of electromagnetic wave propagation in a weakly anisotropic smoothly inhomogeneous medium is developed, based on the quantum-mechanical diagonalization procedure applied to Maxwell equations. The equations of motion for the translational (ray) and intrinsic (polarization) degrees of freedom are derived ab initio. The ray equations take into account the optical Magnus effect (spin Hall effect of photons) as well as trajectory variations owing to the medium anisotropy. Polarization evolution is described by the precession equation for the Stokes vector. In the generic case, the evolution of wave turns out to be non-Abelian: it is accompanied by mutual conversion of the normal modes and periodic oscillations of the ray trajectories analogous to electron zitterbewegung. The general theory is applied to examples of wave evolution in media with circular and linear birefringence.

  2. Anisotopic inflation with a non-abelian gauge field in Gauss-Bonnet gravity

    NASA Astrophysics Data System (ADS)

    Lahiri, Sayantani

    2017-01-01

    In presence of Gauss-Bonnet corrections, we study anisotropic inflation aided by a massless SU(2) gauge field where both the gauge field and the Gauss-Bonnet term are non-minimally coupled to the inflaton. In this scenario, under slow-roll approximations, the anisotropic inflation is realized as an attractor solution with quadratic forms of inflaton potential and Gauss-Bonnet coupling function. We show that the degree of anisotropy is proportional to the additive combination of two slow-roll parameters of the theory. The anisotropy may become either positive or negative similar to the non-Gauss-Bonnet framework, a feature of the model for anisotropic inflation supported by a non-abelian gauge field but the effect of Gauss-Bonnet term further enhances or suppresses the generated anisotropy.

  3. Demonstrating non-Abelian braiding of surface code defects in a five qubit experiment

    NASA Astrophysics Data System (ADS)

    Wootton, James R.

    2017-03-01

    Currently, the mainstream approach to quantum computing is through surface codes. One way to store and manipulate quantum information with these to create defects in the codes which can be moved and used as if they were particles. Specifically, they simulate the behaviour of exotic particles known as Majoranas, which are a kind of non-Abelian anyon. By exchanging these particles, important gates for quantum computation can be implemented. Here we investigate the simplest possible exchange operation for two surface code Majoranas. This is found to act non-trivially on only five qubits. The system is then truncated to these five qubits, so that the exchange process can be run on the IBM 5Q processor. The results demonstrate the expected effect of the exchange. This paper has been written in a style that should hopefully be accessible to both professional and amateur scientists.

  4. Low-energy signals from kinetic mixing with a warped abelian hidden sector

    NASA Astrophysics Data System (ADS)

    McDonald, Kristian L.; Morrissey, David E.

    2011-02-01

    We investigate the detailed phenomenology of a light Abelian hidden sector in the Randall-Sundrum framework. Relative to other works with light hidden sectors, the main new feature is a tower of hidden Kaluza-Klein vectors that kinetically mix with the Standard Model photon and Z. We investigate the decay properties of the hidden sector fields in some detail, and develop an approach for calculating processes initiated on the ultraviolet brane of a warped space with large injection momentum relative to the infrared scale. Using these results, we determine the detailed bounds on the light warped hidden sector from precision electroweak measurements and low-energy experiments. We find viable regions of parameter space that lead to significant production rates for several of the hidden Kaluza-Klein vectors in meson factories and fixed-target experiments. This offers the possibility of exploring the structure of an extra spacetime dimension with lower-energy probes.

  5. Robustness of non-Abelian holonomic quantum gates against parametric noise

    SciTech Connect

    Solinas, Paolo; Zanghi, Nino; Zanardi, Paolo

    2004-10-01

    We present a numerical study of the robustness of a specific class of non-Abelian holonomic quantum gates. We take into account the parametric noise due to stochastic fluctuations of the control fields which drive the time-dependent Hamiltonian along an adiabatic loop. The performance estimator used is the state fidelity between noiseless and noisy holonomic gates. We carry over our analysis with different correlation times and we find out that noisy holonomic gates seem to be close to the noiseless ones for 'short' and 'long' noise correlation times. This result can be interpreted as a consequence of the geometric nature of the holonomic operator. Our simulations have been performed by using parameters relevant to the excitonic proposal for the implementation of holonomic quantum computation [P. Solinas et al., Phys. Rev. B 67, 121307 (2003)].

  6. Low energy dynamics of slender monopoles in non-Abelian superconductor

    NASA Astrophysics Data System (ADS)

    Arai, M.; Blaschke, F.; Eto, M.; Sakai, N.

    2016-01-01

    Low energy dynamics of magnetic monopoles and anti-monopoles in the U(2)c gauge theory is studied in the Higgs (non-Abelian superconducting) phase. The monopoles in this phase are slender ellipsoids, pierced by a vortex string. We investigate scattering of monopole with anti-monopole and find that they do not always decay into radiation, contrary to our naive intuition. They can repel, make bound states (magnetic mesons) or resonances. We point out that some part of solutions in 1 + 3 dimensions can be mapped exactly onto the sine-Gordon system in 1 + 1 dimensions in the first non-trivial order of rigid-body approximation and we provide analytic formulas for such solutions there.

  7. Beta function in the non-Abelian Nambu-Jona-Lasinio model in four dimensions

    SciTech Connect

    Alves, Van Sergio; Pinheiro, S. V. L.; Nascimento, Leonardo; Pena, Francisco

    2009-08-15

    In this paper we present the structure of the renormalization group in non-Abelian Nambu-Jona-Lasinio model up to 1-loop order. The model is not perturbatively renormalizable in the usual power counting sense, but it is treated as an effective theory, valid in a scale of energy in which p<<{lambda}, where p is the external momenta of the loop and {lambda} is a massive parameter that characterizes the couplings of the nonrenormalizable vertex. We clarify the tensorial structure of the interaction vertices and calculate the functions of the renormalization group. The analysis of the fixed points of the theory is also presented using Zimmermann's procedure for reducing the coupling constants. We find that the origin is an infrared-stable fixed point at low energies and also there is a nontrivial ultraviolet stable fixed point, indicating that the theory could be perturbatively investigated in the low momentum regime.

  8. Bounds on topological Abelian string-vortex and string-cigar from information-entropic measure

    NASA Astrophysics Data System (ADS)

    Correa, R. A. C.; Dantas, D. M.; Almeida, C. A. S.; da Rocha, Roldão

    2016-04-01

    In this work we obtain bounds on the topological Abelian string-vortex and on the string-cigar, by using a new measure of configurational complexity, known as configurational entropy. In this way, the information-theoretical measure of six-dimensional braneworlds scenarios is capable to probe situations where the parameters responsible for the brane thickness are arbitrary. The so-called configurational entropy (CE) selects the best value of the parameter in the model. This is accomplished by minimizing the CE, namely, by selecting the most appropriate parameters in the model that correspond to the most organized system, based upon the Shannon information theory. This information-theoretical measure of complexity provides a complementary perspective to situations where strictly energy-based arguments are inconclusive. We show that the higher the energy the higher the CE, what shows an important correlation between the energy of the a localized field configuration and its associated entropic measure.

  9. Dynamical programming approach for controlling the directed Abelian Dhar-Ramaswamy model.

    PubMed

    Cajueiro, Daniel O; Andrade, R F S

    2010-09-01

    A dynamical programming approach is used to deal with the problem of controlling the directed abelian Dhar-Ramaswamy model on two-dimensional square lattice. Two strategies are considered to obtain explicit results to this task. First, the optimal solution of the problem is characterized by the solution of the Bellman equation obtained by numerical algorithms. Second, the solution is used as a benchmark to value how far from the optimum other heuristics that can be applied to larger systems are. This approach is the first attempt on the direction of schemes for controlling self-organized criticality that are based on optimization principles that consider explicitly a tradeoff between the size of the avalanches and the cost of intervention.

  10. Non-Abelian localization for supersymmetric Yang-Mills-Chern-Simons theories on a Seifert manifold

    NASA Astrophysics Data System (ADS)

    Ohta, Kazutoshi; Yoshida, Yutaka

    2012-11-01

    We derive non-Abelian localization formulas for supersymmetric Yang-Mills-Chern-Simons theory with matters on a Seifert manifold M, which is the three-dimensional space of a circle bundle over a two-dimensional Riemann surface Σ, by using the cohomological approach introduced by Källén. We find that the partition function and the vacuum expectation value of the supersymmetric Wilson loop reduces to a finite dimensional integral and summation over classical flux configurations labeled by discrete integers. We also find that the partition function reduces further to just a discrete sum over integers in some cases, and evaluate the supersymmetric index (Witten index) exactly on S1×Σ. The index completely agrees with the previous prediction from field theory and branes. We discuss a vacuum structure of the Aharony-Bergman-Jafferis-Maldacena theory deduced from the localization.

  11. Non-Abelian evolution of electromagnetic waves in a weakly anisotropic inhomogeneous medium

    SciTech Connect

    Bliokh, K. Yu.; Frolov, D. Yu.; Kravtsov, Yu. A.

    2007-05-15

    A theory of electromagnetic wave propagation in a weakly anisotropic smoothly inhomogeneous medium is developed, based on the quantum-mechanical diagonalization procedure applied to Maxwell equations. The equations of motion for the translational (ray) and intrinsic (polarization) degrees of freedom are derived ab initio. The ray equations take into account the optical Magnus effect (spin Hall effect of photons) as well as trajectory variations owing to the medium anisotropy. Polarization evolution is described by the precession equation for the Stokes vector. In the generic case, the evolution of wave turns out to be non-Abelian: it is accompanied by mutual conversion of the normal modes and periodic oscillations of the ray trajectories analogous to electron zitterbewegung. The general theory is applied to examples of wave evolution in media with circular and linear birefringence.

  12. Three phases in the three-dimensional Abelian-Higgs model with nonlocal gauge interactions

    SciTech Connect

    Takashima, Shunsuke; Ichinose, Ikuo; Matsui, Tetsuo; Sakakibara, Kazuhiko

    2006-08-15

    We study the phase structure of the three-dimensional (3D) nonlocal compact U(1) lattice gauge theory coupled with a Higgs field by Monte Carlo simulations. The nonlocal interactions among gauge variables are along the temporal direction and mimic the effect of local coupling to massless particles. In contrast to the 3D local Abelian-Higgs model having only the confinement phase, the present model exhibits the confinement, Higgs, and Coulomb phases separated by three second-order transition lines emanating from a triple point. This result is relevant not only to the 3D massless QED coupled with a Higgs field but also to electron fractionalization phenomena in strongly correlated electron systems like the high-T{sub c} superconductors and the fractional quantum Hall effect.

  13. Wire constructions of Abelian topological phases in three or more dimensions

    NASA Astrophysics Data System (ADS)

    Iadecola, Thomas; Neupert, Titus; Chamon, Claudio; Mudry, Christopher

    2016-05-01

    Coupled-wire constructions have proven to be useful tools to characterize Abelian and non-Abelian topological states of matter in two spatial dimensions. In many cases, their success has been complemented by the vast arsenal of other theoretical tools available to study such systems. In three dimensions, however, much less is known about topological phases. Since the theoretical arsenal in this case is smaller, it stands to reason that wire constructions, which are based on one-dimensional physics, could play a useful role in developing a greater microscopic understanding of three-dimensional topological phases. In this paper, we provide a comprehensive strategy, based on the geometric arrangement of commuting projectors in the toric code, to generate and characterize coupled-wire realizations of strongly interacting three-dimensional topological phases. We show how this method can be used to construct pointlike and linelike excitations, and to determine the topological degeneracy. We also point out how, with minor modifications, the machinery already developed in two dimensions can be naturally applied to study the surface states of these systems, a fact that has implications for the study of surface topological order. Finally, we show that the strategy developed for the construction of three-dimensional topological phases generalizes readily to arbitrary dimensions, vastly expanding the existing landscape of coupled-wire theories. Throughout the paper, we discuss Zm topological order in three and four dimensions as a concrete example of this approach, but the approach itself is not limited to this type of topological order.

  14. Spin symmetry in the antinucleon spectrum.

    PubMed

    Zhou, Shan-Gui; Meng, Jie; Ring, P

    2003-12-31

    We discuss spin and pseudospin symmetry in the spectrum of single nucleons and single antinucleons in a nucleus. As an example we use relativistic mean field theory to investigate single antinucleon spectra. We find a very well developed spin symmetry in single antineutron and single antiproton spectra. The dominant components of the wave functions of the spin doublet are almost identical. This spin symmetry in antiparticle spectra and the pseudospin symmetry in particle spectra have the same origin. However, it turns out that the spin symmetry in antinucleon spectra is much better developed than the pseudospin symmetry in normal nuclear single particle spectra.

  15. Charge symmetry at the partonic level

    SciTech Connect

    Londergan, J. T.; Peng, J. C.; Thomas, A. W.

    2010-07-01

    This review article discusses the experimental and theoretical status of partonic charge symmetry. It is shown how the partonic content of various structure functions gets redefined when the assumption of charge symmetry is relaxed. We review various theoretical and phenomenological models for charge symmetry violation in parton distribution functions. We summarize the current experimental upper limits on charge symmetry violation in parton distributions. A series of experiments are presented, which might reveal partonic charge symmetry violation, or alternatively might lower the current upper limits on parton charge symmetry violation.

  16. Conditions for the emergence of gauge bosons from spontaneous Lorentz symmetry breaking

    NASA Astrophysics Data System (ADS)

    Escobar, C. A.; Urrutia, L. F.

    2015-07-01

    The emergence of gauge particles (e.g., photons and gravitons) as Goldstone bosons arising from spontaneous symmetry breaking is an interesting hypothesis which would provide a dynamical setting for the gauge principle. We investigate this proposal in the framework of a general SO (N ) non-Abelian Nambu model (NANM), effectively providing spontaneous Lorentz symmetry breaking in terms of the corresponding Goldstone bosons. Using a nonperturbative Hamiltonian analysis, we prove that the SO (N ) Yang-Mills (YM) theory is equivalent to the corresponding NANM, after both current conservation and the Gauss laws are imposed as initial conditions for the latter. This equivalence is independent of any gauge fixing in the YM theory. A substantial conceptual and practical improvement in the analysis arises by choosing a particular parametrization that solves the nonlinear constraint defining the NANM. This choice allows us to show that the relation between the NANM canonical variables and the corresponding ones of the YM theory, Aia and Eb j , is given by a canonical transformation. In terms of the latter variables, the NANM Hamiltonian has the same form as the YM Hamiltonian, except that the Gauss laws do not arise as first-class constraints. The dynamics of the NANM further guarantees that it is sufficient to impose them only as initial conditions, in order to recover the full equivalence. It is interesting to observe that this particular parametrization exhibits the NANM as a regular theory, thus providing a substantial simplification in the calculations.

  17. Permutation symmetry in spinor quantum gases: selection rules, conservation laws, and correlations.

    PubMed

    Yurovsky, Vladimir A

    2014-11-14

    Many-body systems of identical arbitrary-spin particles, with separable spin and spatial degrees of freedom, are considered. Their eigenstates can be classified by Young diagrams, corresponding to nontrivial permutation symmetries (beyond the conventional paradigm of symmetric-antisymmetric states). The present work obtains the following. (a) Selection rules for additional nonseparable (dependent on spins and coordinates) k-body interactions: the Young diagrams, associated with the initial and final states of a transition, can differ by relocation of no more than k boxes between their rows. (b) Correlation rules in which eigenstate-averaged local correlations of k particles vanish if k exceeds the number of columns (for bosons) or rows (for fermions) in the associated Young diagram. It also elucidates the physical meaning of the quantities conserved due to permutation symmetry-in 1929, Dirac identified those with characters of the symmetric group-relating them to experimentally observable correlations of several particles. The results provide a way to control the formation of entangled states belonging to multidimensional non-Abelian representations of the symmetric group. These states can find applications in quantum computation and metrology.

  18. Turning Students into Symmetry Detectives

    ERIC Educational Resources Information Center

    Wilders, Richard; VanOyen, Lawrence

    2011-01-01

    Exploring mathematical symmetry is one way of increasing students' understanding of art. By asking students to search designs and become pattern detectives, teachers can potentially increase their appreciation of art while reinforcing their perception of the use of math in their day-to-day lives. This article shows teachers how they can interest…

  19. Platonic Symmetry and Geometric Thinking

    ERIC Educational Resources Information Center

    Zsombor-Murray, Paul

    2007-01-01

    Cubic symmetry is used to build the other four Platonic solids and some formalism from classical geometry is introduced. Initially, the approach is via geometric construction, e.g., the "golden ratio" is necessary to construct an icosahedron with pentagonal faces. Then conventional elementary vector algebra is used to extract quantitative…

  20. Concomitant Ordering and Symmetry Lowering

    ERIC Educational Resources Information Center

    Boo, William O. J.; Mattern, Daniell L.

    2008-01-01

    Examples of concomitant ordering include magnetic ordering, Jahn-Teller cooperative ordering, electronic ordering, ionic ordering, and ordering of partially-filled sites. Concomitant ordering sets in when a crystal is cooled and always lowers the degree of symmetry of the crystal. Concomitant ordering concepts can also be productively applied to…

  1. Circular codes, symmetries and transformations.

    PubMed

    Fimmel, Elena; Giannerini, Simone; Gonzalez, Diego Luis; Strüngmann, Lutz

    2015-06-01

    Circular codes, putative remnants of primeval comma-free codes, have gained considerable attention in the last years. In fact they represent a second kind of genetic code potentially involved in detecting and maintaining the normal reading frame in protein coding sequences. The discovering of an universal code across species suggested many theoretical and experimental questions. However, there is a key aspect that relates circular codes to symmetries and transformations that remains to a large extent unexplored. In this article we aim at addressing the issue by studying the symmetries and transformations that connect different circular codes. The main result is that the class of 216 C3 maximal self-complementary codes can be partitioned into 27 equivalence classes defined by a particular set of transformations. We show that such transformations can be put in a group theoretic framework with an intuitive geometric interpretation. More general mathematical results about symmetry transformations which are valid for any kind of circular codes are also presented. Our results pave the way to the study of the biological consequences of the mathematical structure behind circular codes and contribute to shed light on the evolutionary steps that led to the observed symmetries of present codes.

  2. Baryon and chiral symmetry breaking

    SciTech Connect

    Gorsky, A.; Krikun, A.

    2014-07-23

    We briefly review the generalized Skyrmion model for the baryon recently suggested by us. It takes into account the tower of vector and axial mesons as well as the chiral symmetry breaking. The generalized Skyrmion model provides the qualitative explanation of the Ioffe’s formula for the baryon mass.

  3. From symmetries to number theory

    SciTech Connect

    Tempesta, P.

    2009-05-15

    It is shown that the finite-operator calculus provides a simple formalism useful for constructing symmetry-preserving discretizations of quantum-mechanical integrable models. A related algebraic approach can also be used to define a class of Appell polynomials and of L series.

  4. The Symmetry of Natural Laws.

    ERIC Educational Resources Information Center

    Brown, Laurie M.

    This document is a monograph intended for advanced undergraduate students, or beginning graduate students, who have some knowledge of modern physics as well as classical physics, including the elementary quantum mechanical treatment of the hydrogen atom and angular momentum. The first chapter introduces symmetry and relates it to the mathematical…

  5. Resonantly amplified vibronic symmetry breaking

    NASA Astrophysics Data System (ADS)

    Rathbone, G. J.; Poliakoff, E. D.; Bozek, John D.; Lucchese, R. R.

    2001-05-01

    The energy dependence of the vibrational branching ratio for exciting one quantum of bending is determined for CO2 4σg-1 photoionization. This nominally forbidden transition becomes allowed for a photoionization transition as a result of instantaneous symmetry breaking due to zero point motion, and is strongly enhanced by a continuum shape resonance.

  6. Hidden local symmetry and beyond

    NASA Astrophysics Data System (ADS)

    Yamawaki, Koichi

    Gerry Brown was a godfather of our hidden local symmetry (HLS) for the vector meson from the birth of the theory throughout his life. The HLS is originated from very nature of the nonlinear realization of the symmetry G based on the manifold G/H, and thus is universal to any physics based on the nonlinear realization. Here, I focus on the Higgs Lagrangian of the Standard Model (SM), which is shown to be equivalent to the nonlinear sigma model based on G/H = SU(2)L ×SU(2)R/SU(2)V with additional symmetry, the nonlinearly-realized scale symmetry. Then, the SM does have a dynamical gauge boson of the SU(2)V HLS, “SM ρ meson”, in addition to the Higgs as a pseudo-dilaton as well as the NG bosons to be absorbed in to the W and Z. Based on the recent work done with Matsuzaki and Ohki, I discuss a novel possibility that the SM ρ meson acquires kinetic term by the SM dynamics itself, which then stabilizes the skyrmion dormant in the SM as a viable candidate for the dark matter, what we call “dark SM skyrmion (DSMS)”.

  7. Monster symmetry and extremal CFTs

    NASA Astrophysics Data System (ADS)

    Gaiotto, Davide

    2012-11-01

    We test some recent conjectures about extremal selfdual CFTs, which are the candidate holographic duals of pure gravity in AdS 3. We prove that no c = 48 extremal selfdual CFT or SCFT may possess Monster symmetry. Furthermore, we disprove a recent argument against the existence of extremal selfdual CFTs of large central charge.

  8. Superdeformations and fermion dynamical symmetries

    SciTech Connect

    Wu, Cheng-Li . Dept. of Physics and Atmospheric Science Tennessee Univ., Knoxville, TN . Dept. of Physics and Astronomy Joint Inst. for Heavy Ion Research, Oak Ridge, TN )

    1990-01-01

    In this talk, I will present a link between nuclear collective motions and their underlying fermion dynamical symmetries. In particular, I will focus on the microscopic understanding of deformations. It is shown that the SU{sub 3} of the one major shell fermion dynamical symmetry model (FDSM) is responsible for the physics of low and high spins in normal deformation. For the recently observed phenomena of superdeformation, the physics of the problem dictates a generalization to a supershell structure (SFDSM), which also has an SU{sub 3} fermion dynamical symmetry. Many recently discovered feature of superdeformation are found to be inherent in such an SU{sub 3} symmetry. In both cases the dynamical Pauli effect plays a vital role. A particularly noteworthy discovery from this model is that the superdeformed ground band is not the usual unaligned band but the D-pair aligned (DPA) band, which sharply crosses the excited bands. The existence of such DPA band is a key point to understand many properties of superdeformation. Our studies also poses new experimental challenge. This is particularly interesting since there are now plans to build new and exciting {gamma}-ray detecting systems, like the GAMMASPHERE, which could provide answers to some of these challenges. 34 refs., 11 figs., 5 tabs.

  9. Two elementary proofs of the Wigner theorem on symmetry in quantum mechanics

    NASA Astrophysics Data System (ADS)

    Simon, R.; Mukunda, N.; Chaturvedi, S.; Srinivasan, V.

    2008-11-01

    In quantum theory, symmetry has to be defined necessarily in terms of the family of unit rays, the state space. The theorem of Wigner asserts that a symmetry so defined at the level of rays can always be lifted into a linear unitary or an antilinear antiunitary operator acting on the underlying Hilbert space. We present two proofs of this theorem which are both elementary and economical. Central to our proofs is the recognition that a given Wigner symmetry can, by post-multiplication by a unitary symmetry, be taken into either the identity or complex conjugation. Our analysis often focuses on the behaviour of certain two-dimensional subspaces of the Hilbert space under the action of a given Wigner symmetry, but the relevance of this behaviour to the larger picture of the whole Hilbert space is made transparent at every stage.

  10. Symmetry Breaking During Drosophila Oogenesis

    PubMed Central

    Roth, Siegfried; Lynch, Jeremy A.

    2009-01-01

    The orthogonal axes of Drosophila are established during oogenesis through a hierarchical series of symmetry-breaking steps, most of which can be traced back to asymmetries inherent in the architecture of the ovary. Oogenesis begins with the formation of a germline cyst of 16 cells connected by ring canals. Two of these 16 cells have four ring canals, whereas the others have fewer. The first symmetry-breaking step is the selection of one of these two cells to become the oocyte. Subsequently, the germline cyst becomes surrounded by somatic follicle cells to generate individual egg chambers. The second symmetry-breaking step is the posterior positioning of the oocyte within the egg chamber, a process mediated by adhesive interactions with a special group of somatic cells. Posterior oocyte positioning is accompanied by a par gene-dependent repolarization of the microtubule network, which establishes the posterior cortex of the oocyte. The next two steps of symmetry breaking occur during midoogenesis after the volume of the oocyte has increased about 10-fold. First, a signal from the oocyte specifies posterior follicle cells, polarizing a symmetric prepattern present within the follicular epithelium. Second, the posterior follicle cells send a signal back to the oocyte, which leads to a second repolarization of the oocyte microtubule network and the asymmetric migration of the oocyte nucleus. This process again requires the par genes. The repolarization of the microtubule network results in the transport of bicoid and oskar mRNAs, the anterior and posterior determinants, respectively, of the embryonic axis, to opposite poles of the oocyte. The asymmetric positioning of the oocyte nucleus defines a cortical region of the oocyte where gurken mRNA is localized, thus breaking the dorsal–ventral symmetry of the egg and embryo. PMID:20066085

  11. Universal Formulation For Symmetries In Computed Flows

    NASA Technical Reports Server (NTRS)

    Pao, S. Paul; Abdol-Hamid, Khaled S.

    1995-01-01

    Universal formulation for high-order symmetries in boundary conditions on flows devised. Eliminates need for special procedures to incorporate symmetries and corresponding boundary conditions into computer codes solving Navier-Stokes and Euler equations of flow.

  12. An Elementary Course in Mathematical Symmetry.

    ERIC Educational Resources Information Center

    Rose, Bruce I.; Stafford, Robert D.

    1981-01-01

    A college course designed to teach students about the mathematics of symmetry using pieces of wallpaper and cloth designs is presented. Mathematical structures and the symmetry of graphic designs provide the starting point for instruction. (MP)

  13. Snake states and their symmetries in graphene

    NASA Astrophysics Data System (ADS)

    Tiwari, Rakesh; Liu, Yang; Brada, Matej; Bruder, C.; Kusmartsev, F. V.; Mele, E. J.

    Snake states are open trajectories for charged particles moving in two dimensions under the influence of a spatially varying perpendicular magnetic field. They can also occur in a constant perpendicular magnetic field when the particle density is made nonuniform as realized at a pn junction in a semiconductor, or in graphene. We examine the correspondence of such trajectories in monolayer graphene in the quantum limit for two families of domain walls: (a) a uniform doped carrier density in an antisymmetric perpendicular magnetic field and (b) antisymmetric carrier density distribution in a uniform perpendicular magnetic field. Although, these families support different internal symmetries, the pattern of the boundary and interface currents is the same in both cases. We demonstrate that these two physically different situations are gauge equivalent when rewritten in a Nambu doubled formulation of the two limiting problems. Using gauge transformations in particle-hole space to connect these two problems, we map the protected interfacial modes to the Bogoliubov quasiparticles of an interfacial one-dimensional p-wave paired state.

  14. Snake states and their symmetries in graphene

    NASA Astrophysics Data System (ADS)

    Liu, Yang; Tiwari, Rakesh P.; Brada, Matej; Bruder, C.; Kusmartsev, F. V.; Mele, E. J.

    2015-12-01

    Snake states are open trajectories for charged particles propagating in two dimensions under the influence of a spatially varying perpendicular magnetic field. In the quantum limit they are protected edge modes that separate topologically inequivalent ground states and can also occur when the particle density rather than the field is made nonuniform. We examine the correspondence of snake trajectories in single-layer graphene in the quantum limit for two families of domain walls: (a) a uniform doped carrier density in an antisymmetric field profile and (b) antisymmetric carrier distribution in a uniform field. These families support different internal symmetries but the same pattern of boundary and interface currents. We demonstrate that these physically different situations are gauge equivalent when rewritten in a Nambu doubled formulation of the two limiting problems. Using gauge transformations in particle-hole space to connect these problems, we map the protected interfacial modes to the Bogoliubov quasiparticles of an interfacial one-dimensional p -wave paired state. A variational model is introduced to interpret the interfacial solutions of both domain wall problems.

  15. Symmetry perception in humans and macaques.

    PubMed

    Beck, Diane M; Pinsk, Mark A; Kastner, Sabine

    2005-09-01

    The human ability to detect symmetry has been a topic of interest to psychologists and philosophers since the 19th century, yet surprisingly little is known about the neural basis of symmetry perception. In a recent fMRI study, Sasaki and colleagues begin to remedy this situation. By identifying the neural structures that respond to symmetry in both humans and macaques, the authors lay the groundwork for understanding the neural mechanisms underlying symmetry perception.

  16. Flavored Peccei-Quinn symmetry

    NASA Astrophysics Data System (ADS)

    Ahn, Y. H.

    2015-03-01

    In an attempt to uncover any underlying physics in the standard model (SM), we suggest a μ - τ power law in the lepton sector, such that relatively large 13 mixing angle with bilarge ones can be derived. On the basis of this, we propose a neat and economical model for both the fermion mass hierarchy problem of the SM and a solution to the strong charge parity (C P ) problem, in a way that no domain wall problem occurs, based on A4×U (1 )X symmetry in a supersymmetric framework. Here we refer to the global U (1 )X symmetry that can explain the above problems as "flavored Peccei-Quinn symmetry." In the model, a direct coupling of the SM gauge singlet flavon fields responsible for spontaneous symmetry breaking to ordinary quarks and leptons, both of which are charged under U (1 )X, comes to pass through Yukawa interactions, and all vacuum expectation values breaking the symmetries are connected to each other. So the scale of Peccei-Quinn symmetry breaking is shown to be roughly located around the 1 012 GeV section through its connection to the fermion masses. The model predictions are shown to lie on the testable regions in the very near future through on-going experiments for neutrino oscillation, neutrinoless double beta decay, and the axion. We examine the model predictions, arisen from the μ - τ power law, on leptonic C P violation, neutrinoless double beta decay, and atmospheric mixing angle, and show that the fermion mass and mixing hierarchies are in good agreement with the present data. Interestingly, we show the model predictions on the axion mass ma≃2.53 ×1 0-5 eV and the axion coupling to photon ga γ γ≃1.33 ×1 0-15 GeV-1 . And subsequently the square of the ratio between them is shown to be one or two orders of magnitude lower than that of the conventional axion model.

  17. Modular Extensions of Unitary Braided Fusion Categories and 2+1D Topological/SPT Orders with Symmetries

    NASA Astrophysics Data System (ADS)

    Lan, Tian; Kong, Liang; Wen, Xiao-Gang

    2017-04-01

    A finite bosonic or fermionic symmetry can be described uniquely by a symmetric fusion category E. In this work, we propose that 2+1D topological/SPT orders with a fixed finite symmetry E are classified, up to {E_8} quantum Hall states, by the unitary modular tensor categories C over E and the modular extensions of each C. In the case C=E, we prove that the set M_{ext}(E) of all modular extensions of E has a natural structure of a finite abelian group. We also prove that the set M_{ext}(C) of all modular extensions of E, if not empty, is equipped with a natural M_{ext}(C)-action that is free and transitive. Namely, the set M_{ext}(C) is an M_{ext}(E)-torsor. As special cases, we explain in detail how the group M_{ext}(E) recovers the well-known group-cohomology classification of the 2+1D bosonic SPT orders and Kitaev's 16 fold ways. We also discuss briefly the behavior of the group M_{ext}(E) under the symmetry-breaking processes and its relation to Witt groups.

  18. Generalized partial dynamical symmetry in nuclei.

    PubMed

    Leviatan, A; Isacker, P Van

    2002-11-25

    We introduce the notion of a generalized partial dynamical-symmetry for which part of the eigenstates have part of the dynamical symmetry. This general concept is illustrated with the example of Hamiltonians with a partial dynamical O(6) symmetry in the framework of the interacting boson model. The resulting spectrum and electromagnetic transitions are compared with empirical data in 162Dy.

  19. Noether symmetries and duality transformations in cosmology

    NASA Astrophysics Data System (ADS)

    Paliathanasis, Andronikos; Capozziello, Salvatore

    2016-09-01

    We discuss the relation between Noether (point) symmetries and discrete symmetries for a class of minisuperspace cosmological models. We show that when a Noether symmetry exists for the gravitational Lagrangian, then there exists a coordinate system in which a reversal symmetry exists. Moreover, as far as concerns, the scale-factor duality symmetry of the dilaton field, we show that it is related to the existence of a Noether symmetry for the field equations, and the reversal symmetry in the normal coordinates of the symmetry vector becomes scale-factor duality symmetry in the original coordinates. In particular, the same point symmetry as also the same reversal symmetry exists for the Brans-Dicke scalar field with linear potential while now the discrete symmetry in the original coordinates of the system depends on the Brans-Dicke parameter and it is a scale-factor duality when ωBD = 1. Furthermore, in the context of the O’Hanlon theory for f(R)-gravity, it is possible to show how a duality transformation in the minisuperspace can be used to relate different gravitational models.

  20. Superalgebra and fermion-boson symmetry

    PubMed Central

    Miyazawa, Hironari

    2010-01-01

    Fermions and bosons are quite different kinds of particles, but it is possible to unify them in a supermultiplet, by introducing a new mathematical scheme called superalgebra. In this article we discuss the development of the concept of symmetry, starting from the rotational symmetry and finally arriving at this fermion-boson (FB) symmetry. PMID:20228617

  1. Symmetry Breaking for Black-Scholes Equations

    NASA Astrophysics Data System (ADS)

    Yang, Xuan-Liu; Zhang, Shun-Li; Qu, Chang-Zheng

    2007-06-01

    Black-Scholes equation is used to model stock option pricing. In this paper, optimal systems with one to four parameters of Lie point symmetries for Black-Scholes equation and its extension are obtained. Their symmetry breaking interaction associated with the optimal systems is also studied. As a result, symmetry reductions and corresponding solutions for the resulting equations are obtained.

  2. Facial symmetry in robust anthropometrics.

    PubMed

    Kalina, Jan

    2012-05-01

    Image analysis methods commonly used in forensic anthropology do not have desirable robustness properties, which can be ensured by robust statistical methods. In this paper, the face localization in images is carried out by detecting symmetric areas in the images. Symmetry is measured between two neighboring rectangular areas in the images using a new robust correlation coefficient, which down-weights regions in the face violating the symmetry. Raw images of faces without usual preliminary transformations are considered. The robust correlation coefficient based on the least weighted squares regression yields very promising results also in the localization of such faces, which are not entirely symmetric. Standard methods of statistical machine learning are applied for comparison. The robust correlation analysis can be applicable to other problems of forensic anthropology.

  3. Symmetry breaking around a wormhole

    NASA Astrophysics Data System (ADS)

    Choudhury, A. L.

    1996-11-01

    We have modified the extended version Coule and Maeda's version (D. H. Coule and Kei-ichi Maeda, Class.Quant.Grav.7,995(1990)) of the Gidding-Strominger model (S. B. Giddings and A. Strominger, Nucl.Phys. B307, 854(l988)) of the euclidean gravitational field interacting with axion. The new model has R-symmetry in contrast to the previous model. At the lowest perturbation case the model retains a wormhole solution. We assume that the scalar expands adiabatically and satisfies ideal gas law in a crude first approximation. Under the Higg's mechanism the symmetry can be broken at the tree approximation. This mechanism, we hope, can be used to introduce the degeneracy of quark masses.

  4. Broken symmetries in multilayered perceptrons

    NASA Astrophysics Data System (ADS)

    Barkai, E.; Hansel, D.; Sompolinsky, H.

    1992-03-01

    The statistical mechanics of two-layered perceptrons with N input units, K hidden units, and a single output unit that makes a decision based on a majority rule (Committee Machine) are studied. Two architectures are considered. In the nonoverlapping case the hidden units do not share common inputs. In the fully connected case each hidden unit is connected to the entire input layer. In both cases the network realizes a random dichotomy of P inputs. The statistical properties of the space of solutions as a function of P is studied, using the replica method, and by numerical simulations, in the regime where N>>K. In the nonoverlapping architecture with continuously varying weights the capacity, defined as the maximal number of P per weight, (αc) is calculated under a replica-symmetric (RS) ansatz. At large K, αc diverges as K1/2 in contradiction with the rigorous upper bound, αcsymmetry-breaking effect. The instability of the RS solution is shown to occur at a value of α which remains finite in the large-K limit. A one-step replica-symmetry-breaking (RSB) ansatz is studied for K=3 and in the limit K goes to infinity. The results indicate that αc(K) diverges with K, probably logarithmically. The occurrence of RSB far below the capacity limit is confirmed by comparison of the theoretical results with numerical simulations for K=3. This symmetry breaking implies that unlike the single-layer perceptron case, the space of solutions of the two-layer perceptron breaks, beyond a critical value of α, into many disjoint subregions. The entropies of the connected subregions are almost degenerate, their relative difference being of order 1/N. In the case of a nonoverlapping Committee Machine with binary, i.e., +/-1 weights, αc<=1 is an upper bound for all K. The RS theory predicts αc=0.92 for K=3 and αc=0.95 for the large-K limit

  5. Symmetry of cardiac function assessment

    PubMed Central

    Bai, Xu-Fang; Ma, Amy X

    2016-01-01

    Both right and left ventricles are developed from two adjacent segments of the primary heart tube. Though they are different with regard to shape and power, they mirror each other in terms of behavior. This is the first level of symmetry in cardiac function assessment. Both cardiac muscle contraction and relaxation are active. This constructs the second level of symmetry in cardiac function assessment. Combination of the two levels will help to find some hidden indexes or approaches to evaluate cardiac function. In this article, four major indexes from echocardiography were analyzed under this principal, another seventeen indexes or measurement approaches came out of the shadow, which is very helpful in the assessment of cardiac function, especially for the right cardiac function and diastolic cardiac function. PMID:27582768

  6. Proposed Aharonov-Casher interference measurement of non-Abelian vortices in chiral p-wave superconductors

    NASA Astrophysics Data System (ADS)

    Grosfeld, Eytan; Seradjeh, Babak; Vishveshwara, Smitha

    2011-03-01

    We propose a two-path vortex interferometry experiment based on the Aharonov-Casher effect for detecting the non-Abelian nature of vortices in a chiral P-wave superconductor. The effect is based on observing vortex interference patterns upon enclosing a finite charge of externally controllable magnitude within the interference path. We predict that when the interfering vortices enclose an odd number of identical vortices in their path, the interference pattern disappears only for non-Abelian vortices. When pairing involves two distinct spin species, we derive the mutual statistics between half quantum and full quantum vortices and show that, remarkably, our predictions still hold for the situation of a full quantum vortex enclosing a half quantum vortex in its path. We discuss the experimentally relevant conditions under which these effects can be observed.

  7. Non-Abelian Stokes theorem for the Wilson loop operator in an arbitrary representation and its implication to quark confinement

    NASA Astrophysics Data System (ADS)

    Matsudo, Ryutaro; Kondo, Kei-Ichi

    2015-12-01

    We give a gauge-independent definition of magnetic monopoles in the S U (N ) Yang-Mills theory through the Wilson loop operator. For this purpose, we give an explicit proof of the Diakonov-Petrov version of the non-Abelian Stokes theorem for the Wilson loop operator in an arbitrary representation of the S U (N ) gauge group to derive a new form for the non-Abelian Stokes theorem. The new form is used to extract the magnetic-monopole contribution to the Wilson loop operator in a gauge-invariant way, which enables us to discuss confinement of quarks in any representation from the viewpoint of the dual superconductor vacuum.

  8. Non-Abelian phases in two-component ν =2 /3 fractional quantum Hall states: Emergence of Fibonacci anyons

    NASA Astrophysics Data System (ADS)

    Liu, Zhao; Vaezi, Abolhassan; Lee, Kyungmin; Kim, Eun-Ah

    2015-08-01

    Recent theoretical insights into the possibility of non-Abelian phases in ν =2 /3 fractional quantum Hall states revived the interest in the numerical phase diagram of the problem. We investigate the effect of various kinds of two-body interlayer couplings on the (330) bilayer state and exactly solve the Hamiltonian for up to 14 electrons on sphere and torus geometries. We consider interlayer tunneling, short-ranged repulsive/attractive pseudopotential interactions, and Coulomb repulsion. We find a 6-fold ground-state degeneracy on the torus when the interlayer hollow-core interaction is dominant. To identify the topological nature of this phase we measure the orbital-cut entanglement spectrum, quasihole counting, topological entanglement entropy, and wave-function overlap. Comparing the numerical results to the theoretical predictions, we interpret this 6-fold ground-state degeneracy phase to be the non-Abelian bilayer Fibonacci state.

  9. Skein theory and topological quantum registers: Braiding matrices and topological entanglement entropy of non-Abelian quantum Hall states

    SciTech Connect

    Hikami, Kazuhiro

    2008-07-15

    We study topological properties of quasi-particle states in the non-Abelian quantum Hall states. We apply a skein-theoretic method to the Read-Rezayi state whose effective theory is the SU(2){sub K} Chern-Simons theory. As a generalization of the Pfaffian (K = 2) and the Fibonacci (K = 3) anyon states, we compute the braiding matrices of quasi-particle states with arbitrary spins. Furthermore we propose a method to compute the entanglement entropy skein-theoretically. We find that the entanglement entropy has a nontrivial contribution called the topological entanglement entropy which depends on the quantum dimension of non-Abelian quasi-particle intertwining two subsystems.

  10. Symmetries in Lagrangian Field Theory

    NASA Astrophysics Data System (ADS)

    Búa, Lucia; Bucataru, Ioan; León, Manuel de; Salgado, Modesto; Vilariño, Silvia

    2015-06-01

    By generalising the cosymplectic setting for time-dependent Lagrangian mechanics, we propose a geometric framework for the Lagrangian formulation of classical field theories with a Lagrangian depending on the independent variables. For that purpose we consider the first-order jet bundles J1π of a fiber bundle π : E → ℝk where ℝk is the space of independent variables. Generalized symmetries of the Lagrangian are introduced and the corresponding Noether theorem is proved.

  11. Fermion mass without symmetry breaking

    NASA Astrophysics Data System (ADS)

    Catterall, Simon

    2016-01-01

    We examine a model of reduced staggered fermions in three dimensions interacting through an SO (4) invariant four fermion interaction. The model is similar to that considered in a recent paper by Ayyer and Chandrasekharan [1]. We present theoretical arguments and numerical evidence which support the idea that the system develops a mass gap for sufficiently strong four fermi coupling without producing a symmetry breaking fermion bilinear condensate. Massless and massive phases appear to be separated by a continuous phase transition.

  12. Explaining quantum spontaneous symmetry breaking

    NASA Astrophysics Data System (ADS)

    Liu, Chuang; Emch, Gérard G.

    Two accounts of quantum symmetry breaking (SSB) in the algebraic approach are compared: the representational and the decompositional account. The latter account is argued to be superior for understanding quantum SSB. Two exactly solvable models are given as applications of our account: the Weiss-Heisenberg model for ferromagnetism and the BCS model for superconductivity. Finally, the decompositional account is shown to be more conducive to the causal explanation of quantum SSB.

  13. Dark matter and global symmetries

    NASA Astrophysics Data System (ADS)

    Mambrini, Yann; Profumo, Stefano; Queiroz, Farinaldo S.

    2016-09-01

    General considerations in general relativity and quantum mechanics are known to potentially rule out continuous global symmetries in the context of any consistent theory of quantum gravity. Assuming the validity of such considerations, we derive stringent bounds from gamma-ray, X-ray, cosmic-ray, neutrino, and CMB data on models that invoke global symmetries to stabilize the dark matter particle. We compute up-to-date, robust model-independent limits on the dark matter lifetime for a variety of Planck-scale suppressed dimension-five effective operators. We then specialize our analysis and apply our bounds to specific models including the Two-Higgs-Doublet, Left-Right, Singlet Fermionic, Zee-Babu, 3-3-1 and Radiative See-Saw models. Assuming that (i) global symmetries are broken at the Planck scale, that (ii) the non-renormalizable operators mediating dark matter decay have O (1) couplings, that (iii) the dark matter is a singlet field, and that (iv) the dark matter density distribution is well described by a NFW profile, we are able to rule out fermionic, vector, and scalar dark matter candidates across a broad mass range (keV-TeV), including the WIMP regime.

  14. Symmetry analysis of talus bone

    PubMed Central

    Islam, K.; Dobbe, A.; Komeili, A.; Duke, K.; El-Rich, M.; Dhillon, S.; Adeeb, S.; Jomha, N. M.

    2014-01-01

    Objective The main object of this study was to use a geometric morphometric approach to quantify the left-right symmetry of talus bones. Methods Analysis was carried out using CT scan images of 11 pairs of intact tali. Two important geometric parameters, volume and surface area, were quantified for left and right talus bones. The geometric shape variations between the right and left talus bones were also measured using deviation analysis. Furthermore, location of asymmetry in the geometric shapes were identified. Results Numerical results showed that talus bones are bilaterally symmetrical in nature, and the difference between the surface area of the left and right talus bones was less than 7.5%. Similarly, the difference in the volume of both bones was less than 7.5%. Results of the three-dimensional (3D) deviation analyses demonstrated the mean deviation between left and right talus bones were in the range of -0.74 mm to 0.62 mm. It was observed that in eight of 11 subjects, the deviation in symmetry occurred in regions that are clinically less important during talus surgery. Conclusions We conclude that left and right talus bones of intact human ankle joints show a strong degree of symmetry. The results of this study may have significance with respect to talus surgery, and in investigating traumatic talus injury where the geometric shape of the contralateral talus can be used as control. Cite this article: Bone Joint Res 2014;3:139–45. PMID:24802391

  15. Poincaré polynomials for Abelian symplectic quotients of pure r-qubits via wall-crossings

    NASA Astrophysics Data System (ADS)

    Molladavoudi, Saeid; Zainuddin, Hishamuddin

    2015-10-01

    In this paper, we compute a recursive wall-crossing formula for the Poincaré polynomials and Euler characteristics of Abelian symplectic quotients of a complex projective manifold under a special effective action of a torus with non-trivial characters. An analogy can be made with the space of pure states of a composite quantum system containing r-quantum bits under action of the maximal torus of Local Unitary operations.

  16. Absorption and emission of radiation by a sourceless Abelian gauge wall in a Robertson-Walker space-time.

    NASA Astrophysics Data System (ADS)

    Morris, J. R.

    1992-04-01

    A model of a sourceless Abelian "gauge wall" consisting of a singular magnetic field occupying the (y, z)-plane is examined in the context of a flat Robertson-Walker space-time background. Exact solutions are found for the gauge field structure function. The solutions may be static or time dependent. Dynamic solutions exist which describe the absorption and emission of gauge field radiation by the gauge wall.

  17. Minimally allowed beta beata 0_nu rates from approximate flavor symmetries

    SciTech Connect

    Jenkins, James

    2008-01-01

    Neutrinoless double beta decay ({beta}{beta}0{nu}) is the only realistic probe of Majorana neutrinos. In the standard scenario, dominated by light neutrino exchange, the process amplitude is proportional to m{sub ee} , the e - e element of the Majorana mass matrix. This is expected to hold true for small {beta}{beta}{nu} rates ({Gamma}{sub {beta}{beta}0{nu}}), even in the presence of new physics. Naively, current data allows for vanishing m{sub ee} , but this should be protected by an appropriate flavor symmetry. All such symmetries lead to mass matrices inconsistent with oscillation phenomenology. Hence, Majorana neutrinos imply nonzero {Gamma}{sub {beta}{beta}0{nu}}. I perform a spurion analysis to break all possible abelian symmetries that guarantee {Gamma}{sub {beta}{beta}0{nu}} = 0 and search for minimally allowed m{sub ee} values. Specifically, I survey 259 broken structures to yield m{sub ee} values and current phenomenological constraints under a variety of scenarios. This analysis also extracts predictions for both neutrino oscillation parameters and kinematic quantities. Assuming reasonable tuning levels, I find that m{sub ee} > 4 x 10{sup -6} eV at 99% confidence. Bounds below this value would indicate the Dirac neutrino nature or the existence of new light (eV-MeV scale) degrees of freedom that can potentially be probed elsewhere. This limit can be raised by improvements in neutrino parameter measurements, particularly of the reactor mixing angle, depending on the best fit parameter values. Such improvements will also significantly constrain the available model space and aid in future constructions.

  18. Phase diagram of a non-Abelian Aubry-André-Harper model with p -wave superfluidity

    NASA Astrophysics Data System (ADS)

    Wang, Jun; Liu, Xia-Ji; Xianlong, Gao; Hu, Hui

    2016-03-01

    We study theoretically a one-dimensional quasiperiodic Fermi system with topological p -wave superfluidity, which can be deduced from a topologically nontrivial tight-binding model on the square lattice in a uniform magnetic field and subject to a non-Abelian gauge field. The system may be regarded as a non-Abelian generalization of the well-known Aubry-André-Harper model. We investigate its phase diagram as a function of the strength of the quasidisorder and the amplitude of the p -wave order parameter through a number of numerical investigations, including a multifractal analysis. There are four distinct phases separated by three critical lines, i.e., two phases with all extended wave functions [(I) and (IV)], a topologically trivial phase (II) with all localized wave functions, and a critical phase (III) with all multifractal wave functions. Phase (I) is related to phase (IV) by duality. It also seems to be related to phase (II) by duality. Our proposed phase diagram may be observable in current cold-atom experiments, in view of simulating non-Abelian gauge fields and topological insulators/superfluids with ultracold atoms.

  19. Quark confinement: Dual superconductor picture based on a non-Abelian Stokes theorem and reformulations of Yang-Mills theory

    NASA Astrophysics Data System (ADS)

    Kondo, Kei-Ichi; Kato, Seikou; Shibata, Akihiro; Shinohara, Toru

    2015-05-01

    The purpose of this paper is to review the recent progress in understanding quark confinement. The emphasis of this review is placed on how to obtain a manifestly gauge-independent picture for quark confinement supporting the dual superconductivity in the Yang-Mills theory, which should be compared with the Abelian projection proposed by 't Hooft. The basic tools are novel reformulations of the Yang-Mills theory based on change of variables extending the decomposition of the SU(N) Yang-Mills field due to Cho, Duan-Ge and Faddeev-Niemi, together with the combined use of extended versions of the Diakonov-Petrov version of the non-Abelian Stokes theorem for the SU(N) Wilson loop operator. Moreover, we give the lattice gauge theoretical versions of the reformulation of the Yang-Mills theory which enables us to perform the numerical simulations on the lattice. In fact, we present some numerical evidences for supporting the dual superconductivity for quark confinement. The numerical simulations include the derivation of the linear potential for static interquark potential, i.e., non-vanishing string tension, in which the "Abelian" dominance and magnetic monopole dominance are established, confirmation of the dual Meissner effect by measuring the chromoelectric flux tube between quark-antiquark pair, the induced magnetic-monopole current, and the type of dual superconductivity, etc. In addition, we give a direct connection between the topological configuration of the Yang-Mills field such as instantons/merons and the magnetic monopole. We show especially that magnetic monopoles in the Yang-Mills theory can be constructed in a manifestly gauge-invariant way starting from the gauge-invariant Wilson loop operator and thereby the contribution from the magnetic monopoles can be extracted from the Wilson loop in a gauge-invariant way through the non-Abelian Stokes theorem for the Wilson loop operator, which is a prerequisite for exhibiting magnetic monopole dominance for quark

  20. The abelian confinement mechanism revisited: New aspects of the Georgi–Glashow model

    SciTech Connect

    Anber, Mohamed M.

    2014-02-15

    The confinement problem remains one of the most difficult problems in theoretical physics. An important step toward the solution of this problem is Polyakov’s work on abelian confinement. The Georgi–Glashow model is a natural testing ground for this mechanism which has been surprising us by its richness and wide applicability. In this work, we shed light on two new aspects of this model in 2+1 D. First, we develop a many-body description of the effective degrees of freedom. Namely, we consider a non-relativistic gas of W-bosons in the background of monopole–instanton plasma. Many-body treatment is a standard toolkit in condensed matter physics. However, we add a new twist by supplying the monopole–instantons as external background field. Using this construction along with a mean-field approximation, we calculate the form of the potential between two electric probes as a function of their separation. This potential is expressed in terms of the Meijer-G function which interpolates between logarithmic and linear behavior at small and large distances, respectively. Second, we develop a systematic approach to integrate out the effect of the W-bosons at finite temperature in the range 0≤Tabelian confinement in the Georgi–Glashow model from a new perspective. • We develop a many

  1. Generalization of Friedberg-Lee symmetry

    NASA Astrophysics Data System (ADS)

    Huang, Chao-Shang; Li, Tianjun; Liao, Wei; Zhu, Shou-Hua

    2008-07-01

    We study the possible origin of Friedberg-Lee symmetry. First, we propose the generalized Friedberg-Lee symmetry in the potential by including the scalar fields in the field transformations, which can be broken down to the Friedberg-Lee symmetry spontaneously. We show that the generalized Friedberg-Lee symmetry allows a typical form of Yukawa couplings, and the realistic neutrino masses and mixings can be generated via the seesaw mechanism. If the right-handed neutrinos transform nontrivially under the generalized Friedberg-Lee symmetry, we can have the testable TeV scale seesaw mechanism. Second, we present two models with the SO(3)×U(1) global flavor symmetry in the lepton sector. After the flavor symmetry breaking, we can obtain the charged lepton masses, and explain the neutrino masses and mixings via the seesaw mechanism. Interestingly, the complete neutrino mass matrices are similar to those of the above models with generalized Friedberg-Lee symmetry. So the Friedberg-Lee symmetry is the residual symmetry in the neutrino mass matrix after the SO(3)×U(1) flavor symmetry breaking.

  2. Enhanced Facial Symmetry Assessment in Orthodontists.

    PubMed

    Jackson, Tate H; Clark, Kait; Mitroff, Stephen R

    2013-01-01

    Assessing facial symmetry is an evolutionarily important process, which suggests that individual differences in this ability should exist. As existing data are inconclusive, the current study explored whether a group trained in facial symmetry assessment, orthodontists, possessed enhanced abilities. Symmetry assessment was measured using face and non-face stimuli among orthodontic residents and two control groups: university participants with no symmetry training and airport security luggage screeners, a group previously shown to possess expert visual search skills unrelated to facial symmetry. Orthodontic residents were more accurate at assessing symmetry in both upright and inverted faces compared to both control groups, but not for non-face stimuli. These differences are not likely due to motivational biases or a speed-accuracy tradeoff-orthodontic residents were slower than the university participants but not the security screeners. Understanding such individual differences in facial symmetry assessment may inform the perception of facial attractiveness.

  3. Symmetries in nuclei: New methods and applications

    NASA Astrophysics Data System (ADS)

    Caprio, Mark A.

    2011-04-01

    When a symmetry is a ``good'' symmetry of the nuclear system, as in the dynamical symmetries of the shell model and interacting boson model, this symmetry can directly give the spectroscopic properties of the nucleus, without the need for involved calculations. However, even if a symmetry is strongly broken, it nonetheless provides a calculational tool, classifying the basis states used in a full computational treatment of the many-body problem and greatly simplifying the underlying computational machinery. The symmetry then serves as the foundation for a physically meaningful truncation scheme for the calculation. This talk will provide an introduction to new applications of symmetry approaches to the nuclear problem, including the required mathematical developments. Supported by the US DOE under grant DE-FG02-95ER-40934 and by the Research Corporation for Science Advancement under a Cottrell Scholar Award.

  4. Enhanced Facial Symmetry Assessment in Orthodontists

    PubMed Central

    Jackson, Tate H.; Clark, Kait; Mitroff, Stephen R.

    2013-01-01

    Assessing facial symmetry is an evolutionarily important process, which suggests that individual differences in this ability should exist. As existing data are inconclusive, the current study explored whether a group trained in facial symmetry assessment, orthodontists, possessed enhanced abilities. Symmetry assessment was measured using face and non-face stimuli among orthodontic residents and two control groups: university participants with no symmetry training and airport security luggage screeners, a group previously shown to possess expert visual search skills unrelated to facial symmetry. Orthodontic residents were more accurate at assessing symmetry in both upright and inverted faces compared to both control groups, but not for non-face stimuli. These differences are not likely due to motivational biases or a speed-accuracy tradeoff—orthodontic residents were slower than the university participants but not the security screeners. Understanding such individual differences in facial symmetry assessment may inform the perception of facial attractiveness. PMID:24319342

  5. Dispersion relation for bianisotropic materials and its symmetry properties

    NASA Technical Reports Server (NTRS)

    Graglia, Roberto D.; Uslenghi, Piergiorgio L. E.; Zich, Riccardo E.

    1991-01-01

    The dispersion relation for an arbitrary general bianisotropic medium is derived in Cartesian coordinates, in a form well suited to imposing the boundary conditions when dealing with layered media with planar and parallel interfaces. Special cases of practical interest are also considered. Eleven fundamental coefficient families are identified by considering in detail all the symmetries present in the dispersion relation. An ad hoc expression of the determinant of the sum of two 3 x 3 matrices permits the use of a simple procedure to obtain the coefficients of the dispersion equation. The discussed symmetry properties have general validity, and this technique to evaluate the coefficients may be useful in other fields of application where dispersion relations are of importance.

  6. Spinor Bose gases: Symmetries, magnetism, and quantum dynamics

    NASA Astrophysics Data System (ADS)

    Stamper-Kurn, Dan M.; Ueda, Masahito

    2013-07-01

    Spinor Bose gases form a family of quantum fluids manifesting both magnetic order and superfluidity. This article reviews experimental and theoretical progress in understanding the static and dynamic properties of these fluids. The connection between system properties and the rotational symmetry properties of the atomic states and their interactions are investigated. Following a review of the experimental techniques used for characterizing spinor gases, their mean-field and many-body ground states, both in isolation and under the application of symmetry-breaking external fields, are discussed. These states serve as the starting point for understanding low-energy dynamics, spin textures, and topological defects, effects of magnetic-dipole interactions, and various nonequilibrium collective spin-mixing phenomena. The paper aims to form connections and establish coherence among the vast range of works on spinor Bose gases, so as to point to open questions and future research opportunities.

  7. Matter inflation with A{sub 4} flavour symmetry breaking

    SciTech Connect

    Antusch, Stefan; Nolde, David E-mail: david.nolde@unibas.ch

    2013-10-01

    We discuss model building in tribrid inflation, which is a framework for realising inflation in the matter sector of supersymmetric particle physics models. The inflaton is a D-flat combination of matter fields, and inflation ends by a phase transition in which some Higgs field obtains a vacuum expectation value. We first describe the general procedure for implementing tribrid inflation in realistic models of particle physics that can be applied to a wide variety of BSM particle physics models around the GUT scale. We then demonstrate how the procedure works for an explicit lepton flavour model based on an A{sub 4} family symmetry. The model is both predictive and phenomenologically viable, and illustrates how tribrid inflation connects cosmological and particle physics parameters. In particular, it predicts a relation between the neutrino Yukawa coupling and the running of the spectral index α{sub s}. We also show how topological defects from the flavour symmetry breaking can be avoided automatically.

  8. Symmetry and Structural Properties of Condensed Matter - Proceedings of the 4th International School on Theoretical Physics

    NASA Astrophysics Data System (ADS)

    Lulek, T.; Florek, W.; Lulek, B.

    1997-07-01

    The Table of Contents for the book is as follows: * Preface * Committees and Sponsors * Eugene Wigner and Translational Symmetries * PART A. GROUP ACTION ON SETS AND HIDDEN SYMMETRIES; BETHE ANSATZ * Physical Implications of Crystal Symmetry and Time Reversal * Bethe's Ansatz and the Marshall Rule * Symmetry Properties of Small Amounts of Matter: Clusters and Surface Reconstructions * Analyticity of Bloch and Wannier Functions -- Properties of Berry Phases * τ-Numeration, τ-Wavelets and Diffraction Formulas for the Fibonacci Chain * Dynamical Symmetry * Lorentz Group in Condensed Matter Physics * Geometric Properties of Potentials of Electric Charges * Quadratic Algebra as Dynamic Symmetry * Energy Eigenstates of High Symmetry Electron Systems by Means of Subspace Density Functionals * Optical Tensors in Spatially Modulated Magnetic Systems * Thermodynamic Properties of Spin Systems by Means of the Method of Hierarchy of Algebras * Isoenergetic Surfaces and the Density of States in Low-Symmetrical Crystals * Critical Comments on the Infinite Volume Limit * Orbit Spaces of Compact Linear Groups * The Orbit Space Approach to the Theory of Phase Transitions: The Non-Coregular Case * PART B. MOLECULAR PHYSICS, SYMMETRIC AND UNITARY GROUPS * Combinatorial Aspects of Representations of the Unitary Group * Plethysm in Physics and Chemistry Applications * Group Theory and the Meaning of Life? * Finite States and the Constructive Theory of Discrete Structures * Affine Kac-Moody Algebras and Their Representations * Quantum Systems with Finite Hilbert Space * Casimir Operators of the Unitary Group and Spectral Density Distribution Moments * Quasi-Exact Solvability of a System of Coupled Equations: The Canonical Form of the Rabi and E ⊗ ɛ Jahn-Teller Hamiltonians * Affine Kac-Moody Algebras and the D-Dimensional Hydrogen Atom * Symmetry Classification of Magnetic Excitations in Thulium Iron Garnet * Spectral Density of a Periodic J-Matrix * PART C. STATISTICS OF PARTICLES

  9. Vortices and magnetic bags in Abelian models with extended scalar sectors and some of their applications

    NASA Astrophysics Data System (ADS)

    Forgács, Péter; Lukács, Árpád

    2016-12-01

    A detailed study of vortices is presented in Ginzburg-Landau (or Abelian Higgs) models with two complex scalars (order parameters) assuming a general U (1 )×U (1 ) symmetric potential. Particular emphasis is given to the case in which only one of the scalars obtains a vacuum expectation value (VEV). It is found that for a significantly large domain in parameter space vortices with a scalar field condensate in their core [condensate core (CC)] coexist with Abrikosov-Nielsen-Olesen (ANO) vortices. Importantly, CC vortices are stable and have lower energy than the ANO ones. Magnetic bags or giant vortices of the order of 1000 flux quanta are favored to form for the range of parameters ("strong couplings") appearing for the superconducting state of liquid metallic hydrogen (LMH). Furthermore, it is argued that finite energy/unit length 1VEV vortices are smoothly connected to fractional flux 2VEV ones. Stable, finite energy CC-type vortices are also exhibited in the case when one of the scalar fields is neutral.

  10. Spin correlations and topological entanglement entropy in a non-Abelian spin-one spin liquid

    NASA Astrophysics Data System (ADS)

    Wildeboer, Julia; Bonesteel, N. E.

    2016-07-01

    We analyze the properties of a non-Abelian spin-one chiral spin liquid state proposed by Greiter and Thomale [Phys. Rev. Lett. 102, 207203 (2009), 10.1103/PhysRevLett.102.207203] using Monte Carlo. In this state the bosonic ν =1 Moore-Read Pfaffian wave function is used to describe a gas of bosonic spin flips on a square lattice with one flux quantum per plaquette. For toroidal geometries there is a three-dimensional space of these states corresponding to the topological degeneracy of the bosonic Moore-Read state on the torus. We show that spin correlations for different states in this space become indistinguishable for large system size. We also calculate the Renyi entanglement entropy for different system partitions to extract the topological entanglement entropy and provide evidence that the topological order of the lattice spin-liquid state is the same as that of the continuum Moore-Read state from which it is constructed.

  11. Non-Abelian dark forces and the relic densities of dark glueballs

    NASA Astrophysics Data System (ADS)

    Forestell, Lindsay; Morrissey, David E.; Sigurdson, Kris

    2017-01-01

    Our understanding of the Universe is known to be incomplete, and new gauge forces beyond those of the Standard Model might be crucial to describing its observed properties. A minimal and well-motivated possibility is a pure Yang-Mills non-Abelian dark gauge force with no direct connection to the Standard Model. We determine here the relic abundances of the glueball bound states that arise in such theories and investigate their cosmological effects. Glueballs are first formed in a confining phase transition, and their relic densities are set by a network of annihilation and transfer reactions. The lightest glueball has no lighter states to annihilate into, and its yield is set mainly by 3 →2 number-changing processes which persistently release energy into the glueball gas during freeze-out. The abundances of the heavier glueballs are dominated by 2 →2 transfer reactions and tend to be much smaller than the lightest state. We also investigate potential connectors between the dark force and the Standard Model that allow some or all of the dark glueballs to decay. If the connection is weak, the lightest glueball can be very long-lived or stable and is a viable dark matter candidate. For stronger connections, the lightest glueball will decay quickly, but other heavier glueball states can remain stable and contribute to the dark matter density.

  12. Quantum simulation of Abelian Wu–Yang monopoles in spin-1/2 systems

    NASA Astrophysics Data System (ADS)

    Zhang, Ze-Lin; Chen, Ming-Feng; Wu, Huai-Zhi; Yang, Zhen-Biao

    2017-04-01

    With the help of the Berry curvature and the first Chern number (C 1), we both analytically and numerically investigate and thus simulate artificial magnetic monopoles formed in parameter space of the Hamiltonian of a driven superconducting qubit. The topological structure of a spin-1/2 system (qubit) can be captured by the distribution of Berry curvature, which describes the geometry of eigenstates of the Hamiltonian. Degenerate points in parameter space act as sources (C 1  =  1, represented by quantum ground state manifold) or sinks (C 1  =  ‑1, represented by quantum excited state manifold) of the magnetic field. We note that the strength of the magnetic field (described by Berry curvature) has an apparent impact on the quantum states during the process of topological transition. It exhibits an unusual property that the transition of the quantum states is asymmetric when the degenerate point passes from outside to inside and again outside the manifold spanned by system parameters. Our results also pave the way to explore intriguing properties of Abelian Wu–Yang monopoles in other spin-1/2 systems.

  13. Localizing gauge fields on a topological Abelian string and the Coulomb law

    SciTech Connect

    Torrealba S, Rafael S.

    2010-07-15

    The confinement of electromagnetic field is studied in axial symmetrical, warped, six-dimensional brane world, using a recently proposed topological Abelian string-vortex solution as background. It was found, that the massless gauge field fluctuations follow four-dimensional Maxwell equations in the Lorenz gauge. The massless zero mode is localized when the thickness of the string vortex is less than 5{beta}/4{pi}e{sup 2}v{sup 2} and there are no other localized massless modes. There is also an infinite of nonlocalized massive Fourier modes, that follow four-dimensional Proca equations with a continuous spectrum. To compute the corrections to the Coulomb potential, a radial cutoff was introduced, in order to achieve a discrete mass spectrum. As a main result, a (R{sub o}/{beta}R{sup 2}) correction was found for the four-dimensional effective Coulomb law; the result is in correspondence with the observed behavior of the Coulomb potential at today's measurable distances.

  14. Symmetry breaking and wake instabilities

    NASA Astrophysics Data System (ADS)

    Sengupta, Raja

    A numerical technique has been developed in the context of spatio-temporal stability analysis. The convective/absolute nature of instability determines the time-asymptotic response of a linearly unstable flow, either in the form an oscillator or in the form of a noise amplifier. This depends on the location of pinch point singularities of the dispersion relations obtained via linear stability analyses. A new and efficient approach to locate such singularities is presented. Local analyticity of the dispersion relations was exploited via the Cauchy-Riemann equations in a quasi-Newton's root- finding procedure employing numerical Jacobians. Initial guesses provided by temporal stability analyses have been shown to converge to the pinch points even in the presence of multiple saddle points for various Falkner- Skan wedge profiles. This effort was motivated by the phenomenon of spontaneous symmetry breaking in flow over a cone. At large enough incidence, a pair of vortices develop on the leeward side of the cone which eventually become asymmetric as the angle of attack is increased further. A conical, thin-layer Navier-Stokes solver was employed to investigate the effect of flowfield saddles in this process. The approximate factorization scheme incorporated in the solver was shown analytically to be symmetric to eliminate possible sources of asymmetry. Local grid resolution studies were performed to demonstrate the importance of correctly computing the leeside saddle point and the secondary separation and reattchment points. Topological studies of the flow field as it loses symmetry agreed well with previous qualitative experimental observations. However, the original goal of this study, to settle an ongoing controversy regarding the nature of the instability responsible for symmetry breaking, could not be realized due to computational inadequacy. It is conjectured that the process is governed by an absolute instability similar to that observed in a flow over a circular

  15. Quasi-periodic continuation along a continuous symmetry

    NASA Astrophysics Data System (ADS)

    Salomone, Matthew David

    Given a system of differential equations which admits a continuous group of symmetries and possesses a periodic solution, we show that under certain nondegeneracy assumptions there always exists a continuous family containing infinitely many periodic and quasi-periodic trajectories. This generalizes the continuation method of Poincaré to orbits which are not necessarily periodic. We apply these results in the setting of the Lagrangian N -body problem of homogeneous potential to characterize an infinite family of rotating nonplanar "hip-hop" orbits in the four-body problem of equal masses, and show how some other trajectories in the N -body theory may be extended to infinite families of periodic and quasi-periodic trajectories.

  16. Duality symmetries and G+++ theories

    NASA Astrophysics Data System (ADS)

    Riccioni, Fabio; Steele, Duncan; West, Peter

    2008-02-01

    We show that the nonlinear realizations of all the very extended algebras G+++, except the B and C series which we do not consider, contain fields corresponding to all possible duality symmetries of the on-shell degrees of freedom of these theories. This result also holds for G+++2 and we argue that the nonlinear realization of this algebra accounts precisely for the form fields present in the corresponding supersymmetric theory. We also find a simple necessary condition for the roots to belong to a G+++ algebra.

  17. History of electroweak symmetry breaking

    NASA Astrophysics Data System (ADS)

    Kibble, T. W. B.

    2015-07-01

    In this talk, I recall the history of the development of the unified electroweak theory, incorporating the symmetry-breaking Higgs mechanism, as I saw it from my standpoint as a member of Abdus Salam's group at Imperial College. I start by describing the state of physics in the years after the Second World War, explain how the goal of a unified gauge theory of weak and electromagnetic interactions emerged, the obstacles encountered, in particular the Goldstone theorem, and how they were overcome, followed by a brief account of more recent history, culminating in the historic discovery of the Higgs boson in 2012.

  18. Contact symmetries and Hamiltonian thermodynamics

    SciTech Connect

    Bravetti, A.; Lopez-Monsalvo, C.S.; Nettel, F.

    2015-10-15

    It has been shown that contact geometry is the proper framework underlying classical thermodynamics and that thermodynamic fluctuations are captured by an additional metric structure related to Fisher’s Information Matrix. In this work we analyse several unaddressed aspects about the application of contact and metric geometry to thermodynamics. We consider here the Thermodynamic Phase Space and start by investigating the role of gauge transformations and Legendre symmetries for metric contact manifolds and their significance in thermodynamics. Then we present a novel mathematical characterization of first order phase transitions as equilibrium processes on the Thermodynamic Phase Space for which the Legendre symmetry is broken. Moreover, we use contact Hamiltonian dynamics to represent thermodynamic processes in a way that resembles the classical Hamiltonian formulation of conservative mechanics and we show that the relevant Hamiltonian coincides with the irreversible entropy production along thermodynamic processes. Therefore, we use such property to give a geometric definition of thermodynamically admissible fluctuations according to the Second Law of thermodynamics. Finally, we show that the length of a curve describing a thermodynamic process measures its entropy production.

  19. Symmetry-plane models of 3D Euler fluid equations: Analytical solutions and finite-time blowup using infinitesimal Lie-symmetry methods

    NASA Astrophysics Data System (ADS)

    Bustamante, Miguel D.

    2014-11-01

    We consider 3D Euler fluids endowed with a discrete symmetry whereby the velocity field is invariant under mirror reflections about a 2D surface known as the ``symmetry plane.'' This type of flow is widely used in numerical simulations of classical/magnetic/quantum turbulence and vortex reconnection. On the 2D symmetry plane, the governing equations are best written in terms of two scalars: vorticity and stretching rate of vorticity. These determine the velocity field on the symmetry plane. However, the governing equations are not closed, because of the contribution of a single pressure term that depends on the full 3D velocity profile. By modelling this pressure term we propose a one-parameter family of sensible models for the flow along the 2D symmetry plane. We apply the method of infinitesimal Lie symmetries and solve the governing equations analytically for the two scalars as functions of time. We show how the value of the model's parameter determines if the analytical solution has a finite-time blowup and obtain explicit formulae for the blowup time. We validate the models by showing that a particular choice of the model's parameter corresponds to a well-known exact solution of 3D Euler equations [Gibbon et al., Physica D 132, 497 (1999)]. We discuss practical applications. Supported by Science Foundation Ireland (SFI) under Grant Number 12/IP/1491.

  20. Symmetry properties in polarimetric remote sensing

    NASA Technical Reports Server (NTRS)

    Nghiem, S. V.; Yueh, S. H.; Kwok, R.; Li, F. K.

    1992-01-01

    This paper presents the relations among polarimetric backscattering coefficients from the viewpoint of symmetry groups. Symmetry of geophysical media encountered in remote sensing due to reflection, rotation, azimuthal, and centrical symmetry groups is considered for both reciprocal and nonreciprocal cases. On the basis of the invariance under symmetry transformations in the linear polarization basis, the scattering coefficients are related by a set of equations which restrict the number of independent parameters in the polarimetric covariance matrix. The properties derived under these transformations are general and apply to all scattering mechanisms in a given symmetrical configuration. The scattering coefficients calculated from theoretical models for layer random media and rough surfaces are shown to obey the derived symmetry relations. Use of symmetry properties in remote sensing of structural and environmental responses of scattering media is discussed. As a practical application, the results from this paper provide new methods for the external calibration of polarimetric radars without the deployment of man-made calibration targets.

  1. Symmetry energy of dilute warm nuclear matter.

    PubMed

    Natowitz, J B; Röpke, G; Typel, S; Blaschke, D; Bonasera, A; Hagel, K; Klähn, T; Kowalski, S; Qin, L; Shlomo, S; Wada, R; Wolter, H H

    2010-05-21

    The symmetry energy of nuclear matter is a fundamental ingredient in the investigation of exotic nuclei, heavy-ion collisions, and astrophysical phenomena. New data from heavy-ion collisions can be used to extract the free symmetry energy and the internal symmetry energy at subsaturation densities and temperatures below 10 MeV. Conventional theoretical calculations of the symmetry energy based on mean-field approaches fail to give the correct low-temperature, low-density limit that is governed by correlations, in particular, by the appearance of bound states. A recently developed quantum-statistical approach that takes the formation of clusters into account predicts symmetry energies that are in very good agreement with the experimental data. A consistent description of the symmetry energy is given that joins the correct low-density limit with quasiparticle approaches valid near the saturation density.

  2. Classification of topological phases with reflection symmetry

    NASA Astrophysics Data System (ADS)

    Yoshida, Tsuneya; Morimoto, Takahiro; Furusaki, Akira

    2015-03-01

    In Z2 topological band insulators, the time-reversal symmetry protects their topological structure. In these years such a notion is extended to correlated systems including bosonic systems, and these nontrivial phases are referred to as symmetry protected topological (SPT) phases. Parallel to this progress, a topological crystalline insulator, protected by spatial symmetry, is found for SnTe. Thus, SPT phases protected by this type of symmetry are naturally expected, and classifications of such phases are desired. In this article, we address this issue by focusing on a reflection symmetry. Our analysis based on the Chern-Simons approach proposes periodic tables for bosonic and fermionic SPT phases in two dimensions. Besides that, we show an SPT phase with the reflection symmetry is stabilized in a spin model of honeycomb lattice.

  3. Dynamics-dependent symmetries in Newtonian mechanics

    NASA Astrophysics Data System (ADS)

    Holland, Peter

    2014-01-01

    We exhibit two symmetries of one-dimensional Newtonian mechanics whereby a solution is built from the history of another solution via a generally nonlinear and complex potential-dependent transformation of the time. One symmetry intertwines the square roots of the kinetic and potential energies and connects solutions of the same dynamical problem (the potential is an invariant function). The other symmetry connects solutions of different dynamical problems (the potential is a scalar function). The existence of corresponding conserved quantities is examined using Noether's theorem and it is shown that the invariant-potential symmetry is correlated with energy conservation. In the Hamilton-Jacobi picture the invariant-potential transformation provides an example of a ‘field-dependent’ symmetry in point mechanics. It is shown that this transformation is not a symmetry of the Schrödinger equation.

  4. Dynamical symmetries of the Kepler problem

    NASA Astrophysics Data System (ADS)

    Cariglia, Marco; Silva Araújo, Eduardo

    2013-09-01

    This paper comes from a first-year undergraduate research project on hidden symmetries of the dynamics for classical Hamiltonian systems. For pedagogical reasons the main subject chosen was Kepler’s problem of motion under a central potential, since it is a completely solved system. It is well known that for this problem the group of dynamical symmetries is strictly larger than the isometry group O(3), the extra symmetries corresponding to hidden symmetries of the dynamics. By taking the point of view of examining the group action of the dynamical symmetries on the allowed trajectories, it is possible to teach the basic elements of many important physics subjects in the same project, including the Hamiltonian formalism, hidden symmetries, integrable systems, group theory and the use of manifolds.

  5. Symplectic and Killing symmetries of AdS3 gravity: holographic vs boundary gravitons

    NASA Astrophysics Data System (ADS)

    Compère, G.; Mao, P.; Seraj, A.; Sheikh-Jabbari, M. M.

    2016-01-01

    The set of solutions to the AdS3 Einstein gravity with Brown-Henneaux boundary conditions is known to be a family of metrics labeled by two arbitrary periodic functions, respectively left and right-moving. It turns out that there exists an appropriate presymplectic form which vanishes on-shell. This promotes this set of metrics to a phase space in which the Brown-Henneaux asymptotic symmetries become symplectic symmetries in the bulk of spacetime. Moreover, any element in the phase space admits two global Killing vectors. We show that the conserved charges associated with these Killing vectors commute with the Virasoro symplectic symmetry algebra, extending the Virasoro symmetry algebra with two U(1) generators. We discuss that any element in the phase space falls into the coadjoint orbits of the Virasoro algebras and that each orbit is labeled by the U(1) Killing charges. Upon setting the right-moving function to zero and restricting the choice of orbits, one can take a near-horizon decoupling limit which preserves a chiral half of the symplectic symmetries. Here we show two distinct but equivalent ways in which the chiral Virasoro symplectic symmetries in the near-horizon geometry can be obtained as a limit of the bulk symplectic symmetries.

  6. Neutrino sector with Majorana mass terms and Friedberg-Lee symmetry

    NASA Astrophysics Data System (ADS)

    Jarlskog, C.

    2008-04-01

    We examine a recently proposed symmetry/condition by Friedberg and Lee in a framework where three right-handed neutrinos are added to the spectrum of the three-family minimal standard model. It is found that the right-handed neutrinos are very special, with respect to this symmetry. In the symmetry limit the neutrinos are massless, which could possibly be a hint about why they are light. Imposed as a condition and not as a full symmetry, we find that one of the three right-handed neutrinos simply decouples (has only gravitational interactions) and one of the interacting neutrinos is massless. The possible relation of the model to the seesaw mechanism is briefly discussed.

  7. The new integrable symplectic map and the symmetry of integrable nonlinear lattice equation

    NASA Astrophysics Data System (ADS)

    Dong, Huanhe; Zhang, Yong; Zhang, Xiaoen

    2016-07-01

    A discrete matrix spectral problem is presented and the hierarchy of discrete integrable systems is derived. Their Hamiltonian structures are established. As to the discrete integrable system, nonlinearization of the spatial parts of the Lax pairs and the adjoint Lax pairs generate a new integrable symplectic map. Based on the theory, a new integrable symplectic map and a family of finite-dimension completely integrable systems are given. Especially, two explicit equations are obtained under the Bargmann constraint. Finally, the symmetry of the discrete equation is provided according to the recursion operator and the seed symmetry. Although the solutions of the discrete equations have been gained by many methods, there are few articles that solving the discrete equation via the symmetry. So the solution of the discrete lattice equation is obtained through the symmetry theory.

  8. Lie symmetry analysis of the Heisenberg equation

    NASA Astrophysics Data System (ADS)

    Zhao, Zhonglong; Han, Bo

    2017-04-01

    The Lie symmetry analysis is performed on the Heisenberg equation from the statistical physics. Its Lie point symmetries and optimal system of one-dimensional subalgebras are determined. The similarity reductions and invariant solutions are obtained. Using the multipliers, some conservation laws are obtained. We prove that this equation is nonlinearly self-adjoint. The conservation laws associated with symmetries of this equation are constructed by means of Ibragimov's method.

  9. Symmetry-protected single-photon subradiance

    NASA Astrophysics Data System (ADS)

    Cai, Han; Wang, Da-Wei; Svidzinsky, Anatoly A.; Zhu, Shi-Yao; Scully, Marlan O.

    2016-05-01

    We study the protection of subradiant states by the symmetry of the atomic distributions in the Dicke limit, in which collective Lamb shifts cannot be neglected. We find that antisymmetric states are subradiant states for distributions with reflection symmetry. Continuous symmetry can also be used to achieve subradiance. This study is relevant to the problem of robust quantum memory with long storage time and fast readout.

  10. Model dependence of the neutron-skin thickness on the symmetry energy

    NASA Astrophysics Data System (ADS)

    Mondal, C.; Agrawal, B. K.; Centelles, M.; Colò, G.; Roca-Maza, X.; Paar, N.; Viñas, X.; Singh, S. K.; Patra, S. K.

    2016-06-01

    The model dependence in the correlations of the neutron-skin thickness in heavy nuclei with various symmetry-energy parameters is analyzed by using several families of systematically varied microscopic mean-field models. Such correlations show a varying degree of model dependence once the results for all the different families are combined. Some mean-field models associated with similar values of the symmetry-energy slope parameter at saturation density L , and pertaining to different families, yield a greater-than-expected spread in the neutron-skin thickness of the 208Pb nucleus. The effective value of the symmetry-energy slope parameter Leff, determined by using the nucleon density profiles of the finite nucleus and the density derivative S'(ρ ) of the symmetry energy starting from about saturation density up to low densities typical of the surface of nuclei, seems to account for the spread in the neutron-skin thickness for the models with similar L . The differences in the values of Leff are mainly due to the small differences in the nucleon density distributions of heavy nuclei in the surface region and the behavior of the symmetry energy at subsaturation densities.

  11. Functional ferroic heterostructures with tunable integral symmetry.

    PubMed

    Becher, C; Trassin, M; Lilienblum, M; Nelson, C T; Suresha, S J; Yi, D; Yu, P; Ramesh, R; Fiebig, M; Meier, D

    2014-07-02

    The relation between symmetry and functionality was pinpointed by Pierre Curie who stated that it is the symmetry breaking that creates physical properties. This fundamental principle is nowadays used for engineering heterostructures whose integral symmetry leads to exotic phenomena such as one-way transparency. For switching devices, however, such symmetry-related functionalities cannot be used because the symmetry in conventional heterostructures is immutable once the material has been synthesized. Here we demonstrate a concept for post-growth symmetry control in PbZr0.2Ti0.8O3 and BiFeO3-based heterostructures. A conducting oxide is sandwiched between two ferroelectric layers, and inversion symmetry is reversibly switched on or off by layer-selective electric-field poling. The generalization of our approach to other materials and symmetries is discussed. We thus establish ferroic trilayer structures as device components with reversibly tunable symmetry and demonstrate their use as light emitters that can be activated and deactivated by applying moderate electric voltages.

  12. Discrete gauge symmetry in continuum theories

    SciTech Connect

    Krauss, L.M.; Wilczek, F.

    1989-03-13

    We point out that local symmetries can masquerade as discrete global symmetries to an observer equipped with only low-energy probes. The existence of the underlying local gauge invariance can, however, result in observable Aharonov-Bohm-type effects. Black holes can therefore carry discrete gauge charges: a form of nonclassical ''hair.'' Neither black-hole evaporation, wormholes, nor anything else can violate discrete gauge symmetries. In supersymmetric unified theories such discrete symmetries can forbid proton-decay amplitudes that might otherwise be catastrophic.

  13. Fake conformal symmetry in unimodular gravity

    NASA Astrophysics Data System (ADS)

    Oda, Ichiro

    2016-08-01

    We study Weyl symmetry (local conformal symmetry) in unimodular gravity. It is shown that the Noether currents for both Weyl symmetry and global scale symmetry vanish exactly as in conformally invariant scalar-tensor gravity. We clearly explain why in the class of conformally invariant gravitational theories, the Noether currents vanish by starting with conformally invariant scalar-tensor gravity. Moreover, we comment on both classical and quantum-mechanical equivalences in Einstein's general relativity, conformally invariant scalar-tensor gravity, and the Weyl-transverse gravity. Finally, we discuss the Weyl current in the conformally invariant scalar action and see that it is also vanishing.

  14. Nonlinear (super)symmetries and amplitudes

    NASA Astrophysics Data System (ADS)

    Kallosh, Renata

    2017-03-01

    There is an increasing interest in nonlinear supersymmetries in cosmological model building. Independently, elegant expressions for the all-tree amplitudes in models with nonlinear symmetries, like D3 brane Dirac-Born-Infeld-Volkov-Akulov theory, were recently discovered. Using the generalized background field method we show how, in general, nonlinear symmetries of the action, bosonic and fermionic, constrain amplitudes beyond soft limits. The same identities control, for example, bosonic E 7(7) scalar sector symmetries as well as the fermionic goldstino symmetries.

  15. Braiding and Berry's phases in non-Abelian quantum hall states

    NASA Astrophysics Data System (ADS)

    Zikos, Georgios

    If one could be built, a quantum computer would be capable of storing and manipulating quantum states with sufficient accuracy to carry out computations that no classical computer can do (most notably factoring integers in polynomial time). The greatest obstacle to building such a device is the problem of error and decoherence. Classical computers can exploit the physical robustness of ordered states to protect classical information (as in, for example, the magnetically ordered state of a hard drive). Remarkably, a type of quantum order known as topological order can, in principle, play the same role for quantum information. The best studied topologically ordered states are quantum Hall states. These states arise when a two-dimensional electron gas is placed in a strong magnetic field and cooled to low temperatures. Under the right conditions, the electrons condense into an incompressible quantum liquid whose excitations are particle-like objects with fractional charge (quasiparticles). Certain quantum Hall states are thought to be non Abelian. This means that when a finite number of quasiparticles are present and fixed in space there is a low energy Hilbert space with finite dimension, rather than a unique state. Unitary operations can then be carried out on this Hilbert space by adiabatically dragging quasiparticles around one another so that their world-lines sweep out braids in 2+1 dimensional space time. A quantum computer which stores quantum information in this Hilbert space and computes by braiding is known as a topological quantum computer. In this thesis I review our work on determining precisely how one would carry out a computation on a topological quantum computer. I focus on the so-called Fibonacci anyons---quasiparticles which may exist in the experimentally observed quantum Hall state at Landau level filling fraction nu = 12/5. I give explicit prescriptions for encoding qubits (quantum bits) using Fibonacci anyons, and show how one would carry out a

  16. Inflation, symmetry, and B-modes

    NASA Astrophysics Data System (ADS)

    Hertzberg, Mark P.

    2015-05-01

    We examine the role of using symmetry and effective field theory in inflationary model building. We describe the standard formulation of starting with an approximate shift symmetry for a scalar field, and then introducing corrections systematically in order to maintain control over the inflationary potential. We find that this leads to models in good agreement with recent data. On the other hand, there are attempts in the literature to deviate from this paradigm by envoking other symmetries and corrections. In particular: in a suite of recent papers, several authors have made the claim that standard Einstein gravity with a cosmological constant and a massless scalar carries conformal symmetry. They claim this conformal symmetry is hidden when the action is written in the Einstein frame, and so has not been fully appreciated in the literature. They further claim that such a theory carries another hidden symmetry; a global SO (1 , 1) symmetry. By deforming around the global SO (1 , 1) symmetry, they are able to produce a range of inflationary models with asymptotically flat potentials, whose flatness is claimed to be protected by these symmetries. These models tend to give rise to B-modes with small amplitude. Here we explain that standard Einstein gravity does not in fact possess conformal symmetry. Instead these authors are merely introducing a redundancy into the description, not an actual conformal symmetry. Furthermore, we explain that the only real (global) symmetry in these models is not at all hidden, but is completely manifest when expressed in the Einstein frame; it is in fact the shift symmetry of a scalar field. When analyzed systematically as an effective field theory, deformations do not generally produce asymptotically flat potentials and small B-modes as suggested in these recent papers. Instead, deforming around the shift symmetry systematically, tends to produce models of inflation with B-modes of appreciable amplitude. Such simple models typically

  17. Wormhole dynamics in spherical symmetry

    SciTech Connect

    Hayward, Sean A.

    2009-06-15

    A dynamical theory of traversable wormholes is detailed in spherical symmetry. Generically a wormhole consists of a tunnel of trapped surfaces between two mouths, defined as temporal outer trapping horizons with opposite senses, in mutual causal contact. In static cases, the mouths coincide as the throat of a Morris-Thorne wormhole, with surface gravity providing an invariant measure of the radial curvature or ''flaring-out''. The null energy condition must be violated at a wormhole mouth. Zeroth, first, and second laws are derived for the mouths, as for black holes. Dynamic processes involving wormholes are reviewed, including enlargement or reduction, and interconversion with black holes. A new area of wormhole thermodynamics is suggested.

  18. Electroweak symmetry breaking via QCD.

    PubMed

    Kubo, Jisuke; Lim, Kher Sham; Lindner, Manfred

    2014-08-29

    We propose a new mechanism to generate the electroweak scale within the framework of QCD, which is extended to include conformally invariant scalar degrees of freedom belonging to a larger irreducible representation of SU(3)c. The electroweak symmetry breaking is triggered dynamically via the Higgs portal by the condensation of the colored scalar field around 1 TeV. The mass of the colored boson is restricted to be 350  GeV≲mS≲3  TeV, with the upper bound obtained from perturbative renormalization group evolution. This implies that the colored boson can be produced at the LHC. If the colored boson is electrically charged, the branching fraction of the Higgs boson decaying into two photons can slightly increase, and moreover, it can be produced at future linear colliders. Our idea of nonperturbative electroweak scale generation can serve as a new starting point for more realistic model building in solving the hierarchy problem.

  19. Mirror symmetry for Enriques surfaces

    NASA Astrophysics Data System (ADS)

    Lakuriqi, Enkeleida

    In this thesis, we investigate three separate but related projects. In the first one, we describe the geometric backgrounds of Type II string theory which are given by Enriques surfaces and their mirrors. We also study the effect of various string dualities on such backgrounds, in particular phase change in Gauged Linear Sigma Models and mirror symmetry. In the second project, we investigate special Kahler geometry in order to find canonical coordinates on the moduli of generalised Calabi-Yau spaces and the associated (2, 2) superconformal field theories. In the third project, we develop a general technique for computing the massless spectrum of (0, 2) quantum field theory compactified on a proper stack or an orbifold. We produce general formulas for the contribution of the twisted sectors and compute specific examples of compactifications on gerbes on projective spaces and Calabi-Yau threefolds.

  20. Permutation symmetry for theta functions

    SciTech Connect

    Carlson, B.C.

    2011-01-21

    This paper does for combinations of theta functions most of what Carlson (2004) [1] did for Jacobian elliptic functions. In each case the starting point is the symmetric elliptic integral R{sub F} of the first kind. Its three arguments (formerly squared Jacobian elliptic functions but now squared combinations of theta functions) differ by constants. Symbols designating the constants can often be used to replace 12 equations by three with permutation symmetry (formerly in the letters c, d, n for the Jacobian case but now in the subscripts 2, 3, 4 for theta functions). Such equations include derivatives and differential equations, bisection and duplication relations, addition formulas (apparently new for theta functions), and an example of pseudoaddition formulas.

  1. The emergence of a heavy quark family on a lattice

    NASA Astrophysics Data System (ADS)

    Preparata, Giuliano; Xue, She-Sheng

    1996-02-01

    Within the framework of the “Rome approach” for a lattice chiral gauge theory, the four-quark interaction with flavour symmetry is included. We analyse spontaneous symmetry breaking and compute composite modes and their contributions to the ground state energy. As a result, it is shown that the emergence of a heavy quark family is the energetically favoured solution.

  2. The Emergence of a Heavy Quark Family on a Lattice

    NASA Astrophysics Data System (ADS)

    Xue, She-Sheng

    1996-03-01

    Within the framework of the "Rome approach" for a lattice chiral gauge theory, the four-quark interaction with flavour symmetry is included. We analyse spontaneous symmetry breaking and compute composite modes and their contributions to the ground state energy. As a result, it is shown that the emergence of a heavy quark family is the energetically favoured solution.

  3. Rare Isotopes and Fundamental Symmetries

    NASA Astrophysics Data System (ADS)

    Brown, B. Alex; Engel, Jonathan; Haxton, Wick; Ramsey-Musolf, Michael; Romalis, Michael; Savard, Guy

    2009-01-01

    Experiments searching for new interactions in nuclear beta decay / Klaus P. Jungmann -- The beta-neutrino correlation in sodium-21 and other nuclei / P. A. Vetter ... [et al.] -- Nuclear structure and fundamental symmetries/ B. Alex Brown -- Schiff moments and nuclear structure / J. Engel -- Superallowed nuclear beta decay: recent results and their impact on V[symbol] / J. C. Hardy and I. S. Towner -- New calculation of the isospin-symmetry breaking correlation to superallowed Fermi beta decay / I. S. Towner and J. C. Hardy -- Precise measurement of the [symbol]H to [symbol]He mass difference / D. E. Pinegar ... [et al.] -- Limits on scalar currents from the 0+ to 0+ decay of [symbol]Ar and isospin breaking in [symbol]Cl and [symbol]Cl / A. Garcia -- Nuclear constraints on the weak nucleon-nucleon interaction / W. C. Haxton -- Atomic PNC theory: current status and future prospects / M. S. Safronova -- Parity-violating nucleon-nucleon interactions: what can we learn from nuclear anapole moments? / B. Desplanques -- Proposed experiment for the measurement of the anapole moment in francium / A. Perez Galvan ... [et al.] -- The Radon-EDM experiment / Tim Chupp for the Radon-EDM collaboration -- The lead radius Eexperiment (PREX) and parity violating measurements of neutron densities / C. J. Horowitz -- Nuclear structure aspects of Schiff moment and search for collective enhancements / Naftali Auerbach and Vladimir Zelevinsky -- The interpretation of atomic electric dipole moments: Schiff theorem and its corrections / C. -P. Liu -- T-violation and the search for a permanent electric dipole moment of the mercury atom / M. D. Swallows ... [et al.] -- The new concept for FRIB and its potential for fundamental interactions studies / Guy Savard -- Collinear laser spectroscopy and polarized exotic nuclei at NSCL / K. Minamisono -- Environmental dependence of masses and coupling constants / M. Pospelov.

  4. Neutrino properties and fundamental symmetries

    SciTech Connect

    Bowles, T.J.

    1996-07-01

    This is the final report of a three-year, Laboratory-Directed Research and Development (LDRD) project at the Los Alamos National Laboratory (LANL). There are two components to this work. The first is a development of a new detection scheme for neutrinos. The observed deficit of neutrinos from the Sun may be due to either a lack of understanding of physical processes in the Sun or may be due to neutrinos oscillating from one type to another during their transit from the Sun to the Earth. The Sudbury Neutrino Observatory (SNO) is designed to use a water Cerenkov detector employing one thousand tonnes of heavy water to resolve this question. The ability to distinguish muon and tau neutrinos from electron neutrinos is crucial in order to carry out a model-independent test of neutrino oscillations. We describe a developmental exploration of a novel technique to do this using {sup 3}He proportional counters. Such a method offers considerable advantages over the initially proposed method of using Cerenkov light from capture on NaCl in the SNO. The second component of this work is an exploration of optimal detector geometry for a time-reversal invariance experiment. The question of why time moves only in the forward direction is one of the most puzzling problems in modern physics. We know from particle physics measurements of the decay of kaons that there is a charge-parity symmetry that is violated in nature, implying time-reversal invariance violation. Yet, we do not understand the origin of the violation of this symmetry. To promote such an understanding, we are developing concepts and prototype apparatus for a new, highly sensitive technique to search for time-reversal-invariance violation in the beta decay of the free neutron. The optimized detector geometry is seven times more sensitive than that in previous experiments. 15 refs.

  5. Flavor symmetries and fermion masses

    SciTech Connect

    Rasin, Andrija

    1994-04-01

    We introduce several ways in which approximate flavor symmetries act on fermions and which are consistent with observed fermion masses and mixings. Flavor changing interactions mediated by new scalars appear as a consequence of approximate flavor symmetries. We discuss the experimental limits on masses of the new scalars, and show that the masses can easily be of the order of weak scale. Some implications for neutrino physics are also discussed. Such flavor changing interactions would easily erase any primordial baryon asymmetry. We show that this situation can be saved by simply adding a new charged particle with its own asymmetry. The neutrality of the Universe, together with sphaleron processes, then ensures a survival of baryon asymmetry. Several topics on flavor structure of the supersymmetric grand unified theories are discussed. First, we show that the successful predictions for the Kobayashi-Maskawa mixing matrix elements, Vub/Vcb = √mu/mc and Vtd/Vts = √md/ms, are a consequence of a large class of models, rather than specific properties of a few models. Second, we discuss how the recent observation of the decay β → sγ constrains the parameter space when the ratio of the vacuum expectation values of the two Higgs doublets, tanβ, is large. Finally, we discuss the flavor structure of proton decay. We observe a surprising enhancement of the branching ratio for the muon mode in SO(10) models compared to the same mode in the SU(5) model.

  6. How to infer non-Abelian statistics and topological visibility from tunneling conductance properties of realistic Majorana nanowires

    NASA Astrophysics Data System (ADS)

    Das Sarma, S.; Nag, Amit; Sau, Jay D.

    2016-07-01

    We consider a simple conceptual question with respect to Majorana zero modes in semiconductor nanowires: can the measured nonideal values of the zero-bias-conductance-peak in the tunneling experiments be used as a characteristic to predict the underlying topological nature of the proximity induced nanowire superconductivity? In particular, we define and calculate the topological visibility, which is a variation of the topological invariant associated with the scattering matrix of the system as well as the zero-bias-conductance-peak heights in the tunneling measurements, in the presence of dissipative broadening, using precisely the same realistic nanowire parameters to connect the topological invariants with the zero-bias tunneling conductance values. This dissipative broadening is present in both (the existing) tunneling measurements and also (any future) braiding experiments as an inevitable consequence of a finite braiding time. The connection between the topological visibility and the conductance allows us to obtain the visibility of realistic braiding experiments in nanowires, and to conclude that the current experimentally accessible systems with nonideal zero-bias conductance peaks may indeed manifest (with rather low visibility) non-Abelian statistics for the Majorana zero modes. In general, we find that a large (small) superconducting gap (Majorana peak splitting) is essential for the manifestation of the non-Abelian braiding statistics, and in particular, a zero-bias conductance value of around half the ideal quantized Majorana value should be sufficient for the manifestation of non-Abelian statistics in experimental nanowires. Our work also establishes that as a matter of principle the topological transition associated with the emergence of Majorana zero modes in finite nanowires is always a crossover (akin to a quantum phase transition at finite temperature) requiring the presence of dissipative broadening (which must be larger than the Majorana energy

  7. Confinement, NonAbelian monopoles, and 2D ℂPN-1 model on the worldsheet of finite-length strings

    NASA Astrophysics Data System (ADS)

    Konishi, Kenichi

    2017-03-01

    Quark confinement is proposed to be dual Meissner effect of nonAbelian kind. Important hints come from physics of strongly-coupled infrared-fixed-point theories in N = 2 supersymmetric QCD, which turn into confining vacua under a small relevant perturbation. The quest for the semiclassical origin of these nonAbelian monopoles, ubiquitous as the infrared degrees of freedom in supersymmetric gauge theories, motivates us to study the quantum dynamics of 2D ℂPN-1 model defined on a finite-width worldstrip, with various boundary conditions. The model is found to possess a unique phase ("confinement phase"), independent of the length of the string, showing the quantum persistence of the nonAbelian monopole.

  8. Bäcklund Transformations and Non-Abelian Nonlinear Evolution Equations: a Novel Bäcklund Chart

    NASA Astrophysics Data System (ADS)

    Carillo, Sandra; Lo Schiavo, Mauro; Schiebold, Cornelia

    2016-08-01

    Classes of third order non-Abelian evolution equations linked to that of Korteweg-de Vries-type are investigated and their connections represented in a non-commutative Bäcklund chart, generalizing results in [Fuchssteiner B., Carillo S., Phys. A 154 (1989), 467-510]. The recursion operators are shown to be hereditary, thereby allowing the results to be extended to hierarchies. The present study is devoted to operator nonlinear evolution equations: general results are presented. The implied applications referring to finite-dimensional cases will be considered separately.

  9. The 'sleeping beauty' galaxy NGC 4826: an almost textbook example of the Abelian Higgs vorto-source (-sink)

    NASA Astrophysics Data System (ADS)

    Saniga, Metod

    1995-03-01

    It is demonstrated that the kinematic 'peculiarity' of the early Sab galaxy NGC 4826 can easily be understood in terms of the Abelian Higgs (AH) model of spiral galaxies. A cylindrically symmetric AH vorto-source (-sink) with a disk-to-bulge ratio Omega greater than 1 is discussed and the distributions of the diagonal components of the corresponding stress-energy tensor Tmu,nu are presented. It is argued that the sign-changing component Tphiphi could account for the existence of two counter-rotating gas disks while negative values of Trr imply inward gas motions as observed in the outer and transition regions of the galaxy.

  10. Exact entanglement studies of strongly correlated systems: role of long-range interactions and symmetries of the system.

    PubMed

    Sahoo, Shaon; Goli, V M L Durga Prasad; Ramasesha, S; Sen, Diptiman

    2012-03-21

    We study the bipartite entanglement of strongly correlated systems using exact diagonalization techniques. In particular, we examine how the entanglement changes in the presence of long-range interactions by studying the Pariser-Parr-Pople model with long-range interactions. We compare the results for this model with those obtained for the Hubbard and Heisenberg models with short-range interactions. This study helps us to understand why the density matrix renormalization group (DMRG) technique is so successful even in the presence of long-range interactions. To better understand the behavior of long-range interactions and why the DMRG works well with it, we study the entanglement spectrum of the ground state and a few excited states of finite chains. We also investigate if the symmetry properties of a state vector have any significance in relation to its entanglement. Finally, we make an interesting observation on the entanglement profiles of different states (across the energy spectrum) in comparison with the corresponding profile of the density of states. We use isotropic chains and a molecule with non-Abelian symmetry for these numerical investigations.

  11. Current-current interactions, dynamical symmetry-breaking, and quantum chromodynamics

    SciTech Connect

    Neuenschwander, D.E. Jr.

    1983-01-01

    Quantum Chromodynamics with massive gluons (gluon mass triple bond xm/sub p/) in a contact-interaction limit called CQCD (strong coupling g..-->..infinity; x..-->..infinity), despite its non-renormalizability and lack of hope of confinement, is nevertheless interesting for at least two reasons. Some authors have suggested a relation between 4-Fermi and Yang-Mills theories. If g/x/sup 2/ much less than 1, then CQCD is not merely a 4-Fermi interaction, but includes 4,6,8 etc-Fermi non-Abelian contact interactions. With possibility of infrared slavery, perturbative evaluation of QCD in the infrared is a dubious practice. However, if g/sup 2//x/sup 2/ much less than 1 in CQCD, then the simplest 4-Fermi interaction is dominant, and CQCD admits perturbative treatment, but only in the infrared. With the dominant interaction, a dynamical Nambu-Goldstone realization of chiral symmetry-breaking (XSB) is found. Although in QCD the relation between confinement and XSB is controversial, XSB occurs in CQCD provided confinement is sacrificed.

  12. Cubic Icosahedra? A Problem in Assigning Symmetry

    ERIC Educational Resources Information Center

    Lloyd, D. R.

    2010-01-01

    There is a standard convention that the icosahedral groups are classified separately from the cubic groups, but these two symmetry types have been conflated as "cubic" in some chemistry textbooks. In this note, the connection between cubic and icosahedral symmetries is examined, using a simple pictorial model. It is shown that octahedral and…

  13. Symmetry in critical random Boolean network dynamics.

    PubMed

    Hossein, Shabnam; Reichl, Matthew D; Bassler, Kevin E

    2014-04-01

    Using Boolean networks as prototypical examples, the role of symmetry in the dynamics of heterogeneous complex systems is explored. We show that symmetry of the dynamics, especially in critical states, is a controlling feature that can be used both to greatly simplify analysis and to characterize different types of dynamics. Symmetry in Boolean networks is found by determining the frequency at which the various Boolean output functions occur. There are classes of functions that consist of Boolean functions that behave similarly. These classes are orbits of the controlling symmetry group. We find that the symmetry that controls the critical random Boolean networks is expressed through the frequency by which output functions are utilized by nodes that remain active on dynamical attractors. This symmetry preserves canalization, a form of network robustness. We compare it to a different symmetry known to control the dynamics of an evolutionary process that allows Boolean networks to organize into a critical state. Our results demonstrate the usefulness and power of using the symmetry of the behavior of the nodes to characterize complex network dynamics, and introduce an alternative approach to the analysis of heterogeneous complex systems.

  14. Symmetry is less than meets the eye.

    PubMed

    Apthorp, Deborah; Bell, Jason

    2015-03-30

    Symmetry is a ubiquitous feature in the visual environment and can be detected by a variety of species, ranging from insects through to humans [1,2]. Here we show it can also bias estimates of basic scene properties. Mirror (reflective) symmetry can be detected in as little as 50 ms, in both natural and artificial visual scenes, and even when embedded within cluttered backgrounds [1]. In terms of its biological relevance, symmetry is a key determinant in mate selection; the degree of symmetry in a face is positively associated with perceived healthiness and attractiveness ratings [3]. In short, symmetry processing mechanisms are an important part of the neural machinery of vision. We reveal that the importance of symmetry extends beyond the processing of shape and objects. Mirror symmetry biases our perception of scene content, with symmetrical patterns appearing to have fewer components than their asymmetric counterparts. This demonstrates an interaction between two fundamental dimensions of visual analysis: symmetry [1] and number [4]. We propose that this numerical underestimation results from a processing bias away from the redundant information within mirror symmetrical displays, extending existing theories regarding redundancy in visual analysis [5,6].

  15. Symmetry in Critical Random Boolean Networks Dynamics

    NASA Astrophysics Data System (ADS)

    Bassler, Kevin E.; Hossein, Shabnam

    2014-03-01

    Using Boolean networks as prototypical examples, the role of symmetry in the dynamics of heterogeneous complex systems is explored. We show that symmetry of the dynamics, especially in critical states, is a controlling feature that can be used to both greatly simplify analysis and to characterize different types of dynamics. Symmetry in Boolean networks is found by determining the frequency at which the various Boolean output functions occur. Classes of functions occur at the same frequency. These classes are orbits of the controlling symmetry group. We find the nature of the symmetry that controls the dynamics of critical random Boolean networks by determining the frequency of output functions utilized by nodes that remain active on dynamical attractors. This symmetry preserves canalization, a form of network robustness. We compare it to a different symmetry known to control the dynamics of an evolutionary process that allows Boolean networks to organize into a critical state. Our results demonstrate the usefulness and power of using symmetry to characterize complex network dynamics, and introduce a novel approach to the analysis of heterogeneous complex systems. This work was supported by the NSF through grants DMR-0908286 and DMR-1206839, and by the AFSOR and DARPA through grant FA9550-12-1-0405.

  16. Symmetry in critical random Boolean network dynamics

    NASA Astrophysics Data System (ADS)

    Hossein, Shabnam; Reichl, Matthew D.; Bassler, Kevin E.

    2014-04-01

    Using Boolean networks as prototypical examples, the role of symmetry in the dynamics of heterogeneous complex systems is explored. We show that symmetry of the dynamics, especially in critical states, is a controlling feature that can be used both to greatly simplify analysis and to characterize different types of dynamics. Symmetry in Boolean networks is found by determining the frequency at which the various Boolean output functions occur. There are classes of functions that consist of Boolean functions that behave similarly. These classes are orbits of the controlling symmetry group. We find that the symmetry that controls the critical random Boolean networks is expressed through the frequency by which output functions are utilized by nodes that remain active on dynamical attractors. This symmetry preserves canalization, a form of network robustness. We compare it to a different symmetry known to control the dynamics of an evolutionary process that allows Boolean networks to organize into a critical state. Our results demonstrate the usefulness and power of using the symmetry of the behavior of the nodes to characterize complex network dynamics, and introduce an alternative approach to the analysis of heterogeneous complex systems.

  17. Order in the Universe: The Symmetry Principle.

    ERIC Educational Resources Information Center

    Foundation for Integrative Education, Inc., New York, NY.

    The first two papers in this booklet provide a review of the pervasiveness of symmetry in nature and art, discussing how symmetry can be traced through every domain open to our understanding, from all aspects of nature to the special provinces of man; the checks and balances of government, the concept of equal justice, and the aesthetic ordering…

  18. Partial dynamical symmetry in a fermion system

    PubMed

    Escher; Leviatan

    2000-02-28

    The relevance of the partial dynamical symmetry concept for an interacting fermion system is demonstrated. Hamiltonians with partial SU(3) symmetry are presented in the framework of the symplectic shell model of nuclei and shown to be closely related to the quadrupole-quadrupole interaction. Implications are discussed for the deformed light nucleus 20Ne.

  19. Teaching symmetry in the introductory physics curriculum

    SciTech Connect

    Hill, C. T.; Lederman, L. M.

    2000-01-01

    Modern physics is largely defined by fundamental symmetry principles and Noether's Theorem. Yet these are not taught, or rarely mentioned, to beginning students, thus missing an opportunity to reveal that the subject of physics is as lively and contemporary as molecular biology, and as beautiful as the arts. We prescribe a symmetry module to insert into the curriculum, of a week's length.

  20. Broken chiral symmetry on a null plane

    SciTech Connect

    Beane, Silas R.

    2013-10-15

    On a null-plane (light-front), all effects of spontaneous chiral symmetry breaking are contained in the three Hamiltonians (dynamical Poincaré generators), while the vacuum state is a chiral invariant. This property is used to give a general proof of Goldstone’s theorem on a null-plane. Focusing on null-plane QCD with N degenerate flavors of light quarks, the chiral-symmetry breaking Hamiltonians are obtained, and the role of vacuum condensates is clarified. In particular, the null-plane Gell-Mann–Oakes–Renner formula is derived, and a general prescription is given for mapping all chiral-symmetry breaking QCD condensates to chiral-symmetry conserving null-plane QCD condensates. The utility of the null-plane description lies in the operator algebra that mixes the null-plane Hamiltonians and the chiral symmetry charges. It is demonstrated that in a certain non-trivial limit, the null-plane operator algebra reduces to the symmetry group SU(2N) of the constituent quark model. -- Highlights: •A proof (the first) of Goldstone’s theorem on a null-plane is given. •The puzzle of chiral-symmetry breaking condensates on a null-plane is solved. •The emergence of spin-flavor symmetries in null-plane QCD is demonstrated.