Universality class of the conserved Manna model in one dimension
NASA Astrophysics Data System (ADS)
Lee, Sang Bub
2014-06-01
The nonequilibrium absorbing phase transition of the discrete conserved Manna model was studied via Monte Carlo simulations on a one-dimensional chain, using the natural initial states with a sequential update. The critical density of the particles was found to be smaller than the recently reported value, and the order-parameter exponent was considerably different from the directed percolation (DP) value. The influence of quenched disorder was also studied on a diluted strip of Lx×Ly lattice sites with Lx≫Ly, and the results were compared with those of the contact process (CP). It was found that the Manna model and the CP exhibited distinctly different behaviors; the CP exhibited nonuniversal power-law decreases of active-site densities in the Griffith phase, whereas the Manna model showed a standard critical behavior. These results consistently suggest that the Manna model belongs to a universality class that is different from the DP class.
Universality class of the conserved Manna model in one dimension.
Lee, Sang Bub
2014-06-01
The nonequilibrium absorbing phase transition of the discrete conserved Manna model was studied via Monte Carlo simulations on a one-dimensional chain, using the natural initial states with a sequential update. The critical density of the particles was found to be smaller than the recently reported value, and the order-parameter exponent was considerably different from the directed percolation (DP) value. The influence of quenched disorder was also studied on a diluted strip of L_{x}×L_{y} lattice sites with L_{x}≫L_{y}, and the results were compared with those of the contact process (CP). It was found that the Manna model and the CP exhibited distinctly different behaviors; the CP exhibited nonuniversal power-law decreases of active-site densities in the Griffith phase, whereas the Manna model showed a standard critical behavior. These results consistently suggest that the Manna model belongs to a universality class that is different from the DP class. PMID:25019704
Lee, Sang Bub
2014-06-01
The critical behavior of absorbing phase transitions for two typical models in the Manna universality class, the conserved Manna model and the conserved lattice gas model, both on a square lattice, was investigated using the natural initial states. Various critical exponents were estimated using the static and dynamic simulations. The exponents characterizing dynamics of active particles differ considerably from the known exponents obtained using the random initial states, whereas those associated with the steady-state quantities remain the same. The critical exponents for both models were consistent with errors of less than 1% and satisfied the known scaling relations; thus, the known violation of scaling relations for models with a conserved field was resolved using the natural initial states. The results differed by 7%∼12% from the directed percolation values. PMID:25019750
Two-component Abelian sandpile models.
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. PMID:19518280
Kwon, Sungchul; Kim, Jin Min
2015-12-01
For a fixed-energy (FE) Manna sandpile model in one dimension, we investigate the critical behavior for regular initial conditions in which activities are distributed at regular intervals on average. The FE Manna model conserves the density ρ of total particles and undergoes an absorbing phase transition at a critical ρ(c). For the regular initial conditions, we show via extensive simulations that the dynamical scaling behaviors differ from those of the random and the natural initial conditions. Off-critical scaling exponents β and ν(⊥) are also measured and shown to agree well with the values of the directed percolation (DP) class as reported by Basu et al. [Phys. Rev. Lett. 109, 015702 (2012)]. Our results suggest that the dynamical scaling behaviors depend on the characteristics of initial conditions, but the off-critical scaling behaviors in the steady state are independent of initial conditions and belong to the DP class. PMID:26764674
NASA Astrophysics Data System (ADS)
Kwon, Sungchul; Kim, Jin Min
2016-07-01
A fixed-energy Manna sandpile model undergoes an absorbing phase transition at a critical ρc, where an order parameter ϕ (t ) decays as t-α in time t . As the prototype of the Manna class, the model has been extensively studied in one dimension. However, the previous estimates of ρc and some critical exponents are different, depending on the types of initial conditions; random, natural, and regular conditions. The estimates of ρc for the random and the regular conditions are the lower and the upper bound among currently known estimates, respectively. In this work, for the random conditions, ρc and α are measured by taking into account finite-size (FS) effects. At the previous estimate of ρc, simulation results show that the temporal decay of ϕ (t ) is strongly affected by the FS effects up to much larger system size (˜106 ). For the sizes for which ϕ (t ) is independent up to t =2 ×107 , we estimate ρc=0.8925 (1 ) and α =0.110 (5 ) , which clearly differ from the previous results for the random conditions, ρc=0.89199 (5 ) and α =0.141 (24 ) . Instead, the present ρc agrees with ρc=0.89255 (2 ) of the regular conditions. In addition, the present α is substantially distinguishable from the results of the other types of initial conditions, α =0.159 (3 ) and 0.146 (2 ) for the natural and the regular conditions, respectively, which supports the claim of the initial condition dependence of dynamical exponents in the Manna class.
On whole Abelian model dynamics
Chauca, J.; Doria, R.
2012-09-24
Physics challenge is to determine the objects dynamics. However, there are two ways for deciphering the part. The first one is to search for the ultimate constituents; the second one is to understand its behaviour in whole terms. Therefore, the parts can be defined either from elementary constituents or as whole functions. Historically, science has been moving through the first aspect, however, quarks confinement and complexity are interrupting this usual approach. These relevant facts are supporting for a systemic vision be introduced. Our effort here is to study on the whole meaning through gauge theory. Consider a systemic dynamics oriented through the U(1) - systemic gauge parameter which function is to collect a fields set {l_brace}A{sub {mu}I}{r_brace}. Derive the corresponding whole gauge invariant Lagrangian, equations of motion, Bianchi identities, Noether relationships, charges and Ward-Takahashi equations. Whole Lorentz force and BRST symmetry are also studied. These expressions bring new interpretations further than the usual abelian model. They are generating a systemic system governed by 2N+ 10 classical equations plus Ward-Takahashi identities. A whole dynamics based on the notions of directive and circumstance is producing a set determinism where the parts dynamics are inserted in the whole evolution. A dynamics based on state, collective and individual equations with a systemic interdependence.
NASA Astrophysics Data System (ADS)
Kwon, Sungchul; Kim, Jin Min
2015-12-01
For a fixed-energy (FE) Manna sandpile model in one dimension, we investigate the critical behavior for regular initial conditions in which activities are distributed at regular intervals on average. The FE Manna model conserves the density ρ of total particles and undergoes an absorbing phase transition at a critical ρc. For the regular initial conditions, we show via extensive simulations that the dynamical scaling behaviors differ from those of the random and the natural initial conditions. Off-critical scaling exponents β and ν⊥ are also measured and shown to agree well with the values of the directed percolation (DP) class as reported by Basu et al. [Phys. Rev. Lett. 109, 015702 (2012), 10.1103/PhysRevLett.109.015702]. Our results suggest that the dynamical scaling behaviors depend on the characteristics of initial conditions, but the off-critical scaling behaviors in the steady state are independent of initial conditions and belong to the DP class.
Abelian and non-Abelian bosonization: The operator solution of the WZW. sigma. model
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.
Anomalous Abelian symmetry in the standard model
Ramond, P.
1995-12-31
The observed hierarchy of quark and lepton masses can be parametrized by nonrenormalizable operators with dimensions determined by an anomalous Abelian family symmetry, a gauge extension to the minimal supersymmetric standard model. Such an Abelian symmetry is generic to compactified superstring theories, with its anomalies compensated by the Green-Schwarz mechanism. If we assume these two symmetries to be the same, we find the electroweak mixing angle to be sin {sup 2}{theta}{sub {omega}} = 3/8 at the string scale, just by setting the ratio of the product of down quark to charged lepton masses equal to one at the string scale. This assumes no GUT structure. The generality of the result suggests a superstring origin for the standard model. We generalize our analysis to massive neutrinos, and mixings in the lepton sector.
Engineering complex topological memories from simple Abelian models
NASA Astrophysics Data System (ADS)
Wootton, James R.; Lahtinen, Ville; Doucot, Benoit; Pachos, Jiannis K.
2011-09-01
In three spatial dimensions, particles are limited to either bosonic or fermionic statistics. Two-dimensional systems, on the other hand, can support anyonic quasiparticles exhibiting richer statistical behaviors. An exciting proposal for quantum computation is to employ anyonic statistics to manipulate information. Since such statistical evolutions depend only on topological characteristics, the resulting computation is intrinsically resilient to errors. The so-called non-Abelian anyons are most promising for quantum computation, but their physical realization may prove to be complex. Abelian anyons, however, are easier to understand theoretically and realize experimentally. Here we show that complex topological memories inspired by non-Abelian anyons can be engineered in Abelian models. We explicitly demonstrate the control procedures for the encoding and manipulation of quantum information in specific lattice models that can be implemented in the laboratory. This bridges the gap between requirements for anyonic quantum computation and the potential of state-of-the-art technology.
Fun with the Abelian Higgs model
NASA Astrophysics Data System (ADS)
Malinský, Michal
2013-05-01
In calculations of the elementary scalar spectra of spontaneously broken gauge theories there are a number of subtleties which, though it is often unnecessary to deal with them in the order-of-magnitude type of calculations, have to be taken into account if fully consistent results are sought for. Within the "canonical" effective-potential approach these are, for instance: the need to handle infinite series of nested commutators of derivatives of field-dependent mass matrices, the need to cope with spurious IR divergences emerging in the consistent leading-order approximation and, in particular, the need to account for the fine interplay between the renormalization effects in the one- and two-point Green functions which, indeed, is essential for the proper stable vacuum identification and, thus, for the correct interpretation of the results. In this note we illustrate some of these issues in the realm of the minimal Abelian Higgs model and two of its simplest extensions including extra heavy scalars in the spectrum in attempt to exemplify the key aspects of the usual "hierarchy problem" lore in a very specific and simple setting. We emphasize that, regardless of the omnipresent polynomial cut-off dependence in the one-loop corrections to the scalar two-point function, the physical Higgs boson mass is always governed by the associated symmetry-breaking VEV and, as such, it is generally as UV-robust as all other VEV-driven masses in the theory.
Gauge invariance for a whole Abelian model
Chauca, J.; Doria, R.; Soares, W.
2012-09-24
Light invariance is a fundamental principle for physics be done. It generates Maxwell equations, relativity, Lorentz group. However there is still space for a fourth picture be developed which is to include fields with same Lorentz nature. It brings a new room for field theory. It says that light invariance does not work just to connect space and time but it also associates different fields with same nature. Thus for the ((1/2),(1/2)) representation there is a fields family {l_brace}A{sub {mu}I}{r_brace} to be studied. This means that given such fields association one should derive its corresponding gauge theory. This is the effort at this work. Show that there is a whole gauge theory to cover these fields relationships. Considering the abelian case, prove its gauge invariance. It yields the kinetic, massive, trilinear and quadrilinear gauge invariant terms.
Abelian cosmic string in the Starobinsky model of gravity
NASA Astrophysics Data System (ADS)
Morais Graça, J. P.
2016-03-01
In this paper, I analyze numerically the behaviour of the solutions corresponding to an Abelian string in the framework of the Starobinsky model. The role played by the quadratic term in the Lagrangian density f(R)=R+η {R}2 of this model is emphasized and the results are compared with the corresponding ones obtained in the framework of Einstein’s theory of gravity. I have found that the angular deficit generated by the string is lowered as the η parameter increases, allowing a well-behaved spacetime for a large range of values of the symmetry-breaking scale.
The Abelian Higgs model on Optical Lattice?
NASA Astrophysics Data System (ADS)
Meurice, Yannick; Tsai, Shan-Wen; Bazavov, Alexei; Zhang, Jin
2015-03-01
We study the Lattice Gauge Theory of the U(1)-Higgs model in 1+1 dimensions in the strongly coupled regime. We discuss the plaquette corrections to the effective theory where link variables are integrated out. We discuss matching with the second-order perturbation theory effective Hamiltonian for various Bose-Hubbard models. This correspondence can be exploited for building a lattice gauge theory simulator on optical lattices. We propose to implement the quantum rotors which appear in the Hamiltonian formulation using Bose mixtures or p-orbitals. Recent progress on magnetic effects in 2+1 dimensions will be discussed. Supported by the Army Research Office of the Department of Defense under Award Number W911NF-13-1-0119.
Effective action for the Abelian Higgs model in FLRW
George, Damien P.; Mooij, Sander; Postma, Marieke E-mail: smooij@nikhef.nl
2012-11-01
We compute the divergent contributions to the one-loop action of the U(1) Abelian Higgs model. The calculation allows for a Friedmann-Lemaitre-Robertson-Walker space-time and a time-dependent expectation value for the scalar field. Treating the time-dependent masses as two-point interactions, we use the in-in formalism to compute the first, second and third order graphs that contribute quadratic and logarithmic divergences to the effective scalar action. Working in R{sub ξ} gauge we show that the result is gauge invariant upon using the equations of motion.
The Abelian Sandpile Model on a Random Binary Tree
NASA Astrophysics Data System (ADS)
Redig, F.; Ruszel, W. M.; Saada, E.
2012-06-01
We study the abelian sandpile model on a random binary tree. Using a transfer matrix approach introduced by Dhar and Majumdar, we prove exponential decay of correlations, and in a small supercritical region (i.e., where the branching process survives with positive probability) exponential decay of avalanche sizes. This shows a phase transition phenomenon between exponential decay and power law decay of avalanche sizes. Our main technical tools are: (1) A recursion for the ratio between the numbers of weakly and strongly allowed configurations which is proved to have a well-defined stochastic solution; (2) quenched and annealed estimates of the eigenvalues of a product of n random transfer matrices.
On discrete symmetries for a whole Abelian model
NASA Astrophysics Data System (ADS)
Chauca, J.; Doria, R.
2012-10-01
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 {Dμ,Xiμ} and the physical basis {GμI}. 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 {GμI} 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.
On discrete symmetries for a whole Abelian model
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.
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.
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.
Minimal non-Abelian model of atomic dark matter
NASA Astrophysics Data System (ADS)
Choquette, Jeremie; Cline, James M.
2015-12-01
A dark sector resembling the Standard Model, where the abundance of matter is explained by baryon and lepton asymmetries and stable constituents bind to form atoms, is a theoretically appealing possibility. We show that a minimal model with a hidden SU(2) gauge symmetry broken to U(1), with a Dirac fermion doublet, suffices to realize this scenario. Supplemented with a dark Higgs doublet that gets no vacuum expectation value, we readily achieve the dark matter asymmetry through leptogenesis. The model can simultaneously have three portals to the Standard Model, through the Higgs, non-Abelian kinetic mixing, and the heavy neutrino, with interesting phenomenology for direct and collider searches, as well as cosmologically relevant dark matter self-interactions. Exotic bound states consisting of two fermions and a doubly charged vector boson can exist in one phase of the theory.
Height probabilities in the Abelian sandpile model on the generalized finite Bethe lattice
NASA Astrophysics Data System (ADS)
Chen, Haiyan; Zhang, Fuji
2013-08-01
In this paper, we study the sandpile model on the generalized finite Bethe lattice with a particular boundary condition. Using a combinatorial method, we give the exact expressions for all single-site probabilities and some two-site joint probabilities. As a by-product, we prove that the height probabilities of bulk vertices are all the same for the Bethe lattice with certain given boundary condition, which was found from numerical evidence by Grassberger and Manna ["Some more sandpiles," J. Phys. (France) 51, 1077-1098 (1990)], 10.1051/jphys:0199000510110107700 but without a proof.
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.
Fixed point structure of the Abelian Higgs model
NASA Astrophysics Data System (ADS)
Fejős, G.; Hatsuda, T.
2016-06-01
The order of the superconducting phase transition is analyzed via the functional renormalization group approach. For the first time, we derive fully analytic expressions for the β functions of the charge and the self-coupling in the Abelian Higgs model with one complex scalar field in d =3 dimensions that support the existence of two charged fixed points: an infrared (IR) stable fixed point describing a second-order phase transition and a tricritical fixed point controlling the region of the parameter space that is attracted by the former one. It is found that the region separating first- and second-order transitions can be uniquely characterized by the Ginzburg-Landau parameter κ , and the system undergoes a second-order transition only if κ >κc≈0.62 /√{2 }.
Nonrelativistic limit of the abelianized ABJM model and the ADS/CMT correspondence
NASA Astrophysics Data System (ADS)
Lopez-Arcos, Cristhiam; Murugan, Jeff; Nastase, Horatiu
2016-05-01
We consider the nonrelativistic limit of the abelian reduction of the massive ABJM model proposed in [1], obtaining a supersymmetric version of the Jackiw-Pi model. The system exhibits an N=2 Super-Schrödinger symmetry with the Jackiw-Pi vortices emerging as BPS solutions. We find that this (2 + 1)-dimensional abelian field theory is dual to a certain (3+1)-dimensional gravity theory that differs somewhat from previously considered abelian condensed matter stand-ins for the ABJM model. We close by commenting on progress in the top-down realization of the AdS/CMT correspondence in a critical string theory.
A study of the Earth-Manna multithreaded system
Hum, H.H.J.; Maquelin, O.; Theobald, K.B.; Tian, Xinmin; Gao, G.R.; Hendren, L.J.
1996-08-01
Multithreaded architectures have been proposed for future multiprocessor systems. However, some open issues remain. Can multithreading be supported in a multiprocessor so that it can tolerate synchronization and communication latencies, with little intrusion on the performance of sequentially-executed code? How much does such support contribute to scalable performance when communication and synchronization demands are high? In this paper, we describe the design of EARTH, an architecture which addresses these issues. Each processor in EARTH has an off-the-shelf Execution Unit (EU) for executing threads, and an ASIC Synchronization Unit (SU) supporting dataflow-like thread synchronizations, scheduling, and remote requests. In preparation for an implementation of the SU, we have emulated a basic EARTH model on MANNA 2.0, an existing multiprocessor whose hardware configuration closely matches EARTH. This EARTH-MANNA testbed is fully functional, enabling us to experiment with large benchmarks with impressive speed. With this platform, we demonstrate that multithreading support can be efficiently implemented (with little emulation overhead) in a multiprocessor without a major impact on uniprocessor performance. Also, we measure how much basic multithreading support can help in tolerating increasing communication/synchronization demands.
Enhancing Gauge Symmetries of Non-Abelian Supersymmetric Chern-Simons Model
NASA Astrophysics Data System (ADS)
Gharavi, Kh. Bahalke; Monemzadeh, M.; Nejad, S. Abarghouei
2016-07-01
In this article, we study gauge symmetries of the Non-Abelian Supersymmetric Chern-Simons model (SCS) of SU(2) group at (2+1)-dimensions in the framework of the formalism of constrained systems. Since, broken gauge symmetries in this physical system lead to the presence of nonphysical degrees of freedom, the Non-Abelian SCS model is strictly constrained to second-class constraints. Hence, by introducing some auxiliary fields and using finite order BFT method, we obtain a gauge symmetric model by converting second-class constraint to first-class ones. Ultimately, the partition function of the model is obtained in the extended phase space.
An Abelian Model of Gravity and Canonical Quantization by Means of Path Integrals
NASA Astrophysics Data System (ADS)
Bracken, Paul
An Abelian model of gravity is introduced and its constraint structure is obtained. The main task is to show that the model with constraints can be canonically quantized by means of the canonical path integral formalism using the Faddeev-Popov approach. It is shown how the path integral can be simplified by carrying out the integrals over those variables for which the integrals can be computed.
Abelian p-form (p = 1, 2, 3) gauge theories as the field theoretic models for the Hodge theory
NASA Astrophysics Data System (ADS)
Kumar, R.; Krishna, S.; Shukla, A.; Malik, R. P.
2014-09-01
Taking the simple examples of an Abelian 1-form gauge theory in two (1+1)-dimensions, a 2-form gauge theory in four (3+1)-dimensions and a 3-form gauge theory in six (5+1)-dimensions of space-time, we establish that such gauge theories respect, in addition to the gauge symmetry transformations that are generated by the first-class constraints of the theory, additional continuous symmetry transformations. We christen the latter symmetry transformations as the dual-gauge transformations. We generalize the above gauge and dual-gauge transformations to obtain the proper (anti-)BRST and (anti-)dual-BRST transformations for the Abelian 3-form gauge theory within the framework of BRST formalism. We concisely mention such symmetries for the 2D free Abelian 1-form and 4D free Abelian 2-form gauge theories and briefly discuss their topological aspects in our present endeavor. We conjecture that any arbitrary Abelian p-form gauge theory would respect the above cited additional symmetry in D = 2p(p = 1, 2, 3, …) dimensions of space-time. By exploiting the above inputs, we establish that the Abelian 3-form gauge theory, in six (5+1)-dimensions of space-time, is a perfect model for the Hodge theory whose discrete and continuous symmetry transformations provide the physical realizations of all aspects of the de Rham cohomological operators of differential geometry. As far as the physical utility of the above nilpotent symmetries is concerned, we demonstrate that the 2D Abelian 1-form gauge theory is a perfect model of a new class of topological theory and 4D Abelian 2-form as well as 6D Abelian 3-form gauge theories are the field theoretic models for the quasi-topological field theory.
Haag duality for Kitaev’s quantum double model for abelian groups
NASA Astrophysics Data System (ADS)
Fiedler, Leander; Naaijkens, Pieter
2015-11-01
We prove Haag duality for cone-like regions in the ground state representation corresponding to the translational invariant ground state of Kitaev’s quantum double model for finite abelian groups. This property says that if an observable commutes with all observables localized outside the cone region, it actually is an element of the von Neumann algebra generated by the local observables inside the cone. This strengthens locality, which says that observables localized in disjoint regions commute. As an application, we consider the superselection structure of the quantum double model for abelian groups on an infinite lattice in the spirit of the Doplicher-Haag-Roberts program in algebraic quantum field theory. We find that, as is the case for the toric code model on an infinite lattice, the superselection structure is given by the category of irreducible representations of the quantum double.
Exact Mapping of the Stochastic Field Theory for Manna Sandpiles to Interfaces in Random Media
NASA Astrophysics Data System (ADS)
Le Doussal, Pierre; Wiese, Kay Jörg
2015-03-01
We show that the stochastic field theory for directed percolation in the presence of an additional conservation law [the conserved directed-percolation (C-DP) class] can be mapped exactly to the continuum theory for the depinning of an elastic interface in short-range correlated quenched disorder. Along one line of the parameters commonly studied, this mapping leads to the simplest overdamped dynamics. Away from this line, an additional memory term arises in the interface dynamics; we argue that this does not change the universality class. Since C-DP is believed to describe the Manna class of self-organized criticality, this shows that Manna stochastic sandpiles and disordered elastic interfaces (i.e., the quenched Edwards-Wilkinson model) share the same universal large-scale behavior.
Exact mapping of the stochastic field theory for Manna sandpiles to interfaces in random media.
Le Doussal, Pierre; Wiese, Kay Jörg
2015-03-20
We show that the stochastic field theory for directed percolation in the presence of an additional conservation law [the conserved directed-percolation (C-DP) class] can be mapped exactly to the continuum theory for the depinning of an elastic interface in short-range correlated quenched disorder. Along one line of the parameters commonly studied, this mapping leads to the simplest overdamped dynamics. Away from this line, an additional memory term arises in the interface dynamics; we argue that this does not change the universality class. Since C-DP is believed to describe the Manna class of self-organized criticality, this shows that Manna stochastic sandpiles and disordered elastic interfaces (i.e., the quenched Edwards-Wilkinson model) share the same universal large-scale behavior. PMID:25839253
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.
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.
Phase structure, magnetic monopoles, and vortices in the lattice Abelian Higgs model
Ranft, J.; Kripfganz, J.; Ranft, G.
1983-07-15
We present Monte Carlo calculations of lattice Abelian Higgs models in four dimensions and with charges of the Higgs particles equal to q = 1, 2, and 6. The phase transitions are studied in the plane of the two coupling constants considering separately average plaquette and average link expectation values. The density of topological excitations is studied. In the confinement phase we find finite densities of magnetic-monopole currents, electric currents, and vortex currents. The magnetic-monopole currents vanish exponentially in the Coulomb phase. The density of electric currents and vortex currents is finite in the Coulomb phase and vanishes exponentially in the Higgs phase.
A simple model for the evolution of a non-Abelian cosmic string network
NASA Astrophysics Data System (ADS)
Cella, G.; Pieroni, M.
2016-06-01
In this paper we present the results of numerical simulations intended to study the behavior of non-Abelian cosmic strings networks. In particular we are interested in discussing the variations in the asymptotic behavior of the system as we variate the number of generators for the topological defects. A simple model which allows for cosmic strings is presented and its lattice discretization is discussed. The evolution of the generated cosmic string networks is then studied for different values for the number of generators for the topological defects. Scaling solution appears to be approached in most cases and we present an argument to justify the lack of scaling for the residual cases.
The Abelian Higgs model and a minimal length in an un-particle scenario
NASA Astrophysics Data System (ADS)
Gaete, Patricio; Spallucci, Euro
2014-01-01
We consider both the Abelian Higgs model and the impact of a minimal length in the un-particle sector. It is shown that even if the Higgs field takes a non-vanishing vacuum expectation value (v.e.v.), gauge interaction keeps its long-range character leading to an effective gauge symmetry restoration. The effect of a quantum-gravity-induced minimal length on a physical observable is then estimated by using a physically based alternative to the usual Wilson loop approach. Interestingly, we obtain an ultraviolet finite interaction energy described by a confluent hypergeometric function, which shows a remarkable richness of behavior.
Non-Abelian dark matter: Models and constraints
NASA Astrophysics Data System (ADS)
Chen, Fang; Cline, James M.; Frey, Andrew R.
2009-10-01
Numerous experimental anomalies hint at the existence of a dark matter (DM) multiplet χi with small mass splittings. We survey the simplest such models which arise from DM in the low representations of a new SU(2) gauge symmetry, whose gauge bosons have a small mass μ≲1GeV. We identify preferred parameters Mχ≅1TeV, μ˜100MeV, αg˜0.04, and the χχ→4e annihilation channel, for explaining PAMELA, Fermi, and INTEGRAL/SPI lepton excesses, while remaining consistent with constraints from relic density, diffuse gamma rays, and the CMB. This consistency is strengthened if DM annihilations occur mainly in subhalos, while excitations (relevant to the excited DM proposal to explain the 511 keV excess) occur in the galactic center, due to higher velocity dispersions in the galactic center, induced by baryons. We derive new constraints and predictions which are generic to these models. Notably, decays of excited DM states χ'→χγ arise at one loop and could provide a new signal for INTEGRAL/SPI; big bang nucleosynthesis constraints on the density of dark SU(2) gauge bosons imply a lower bound on the mixing parameter γ between the SU(2) gauge bosons and photon. These considerations rule out the possibility of the gauge bosons that decay into e+e- being long-lived. We study in detail models of doublet, triplet, and quintuplet DM, showing that both normal and inverted mass hierarchies can occur, with mass splittings that can be parametrically smaller [e.g., O(100)keV] than the generic MeV scale of splittings. A systematic treatment of Z2 symmetry, which insures the stability of the intermediate DM state, is given for cases with inverted mass hierarchy, of interest for boosting the 511 keV signal from the excited dark matter mechanism.
Light supersymmetric axion in an anomalous Abelian extension of the standard model
Coriano, Claudio; Guzzi, Marco; Mariano, Antonio; Morelli, Simone
2009-08-01
We present a supersymmetric extension of the standard model (USSM-A) with an anomalous U(1) and Stueckelberg axions for anomaly cancellation, generalizing similar nonsupersymmetric constructions. The model, built by a bottom-up approach, is expected to capture the low-energy supersymmetric description of axionic symmetries in theories with gauged anomalous Abelian interactions, previously explored in the nonsupersymmetric case for scenarios with intersecting branes. The choice of a USSM-like superpotential, with one extra singlet superfield and an extra Abelian symmetry, allows a physical axionlike particle in the spectrum. We describe some general features of this construction and, in particular, the modification of the dark-matter sector which involves both the axion and several neutralinos with an axino component. The axion is expected to be very light in the absence of phases in the superpotential but could acquire a mass which can also be in the few GeV range or larger. In particular, the gauging of the anomalous symmetry allows independent mass/coupling interaction to the gauge fields of this particle, a feature which is absent in traditional (invisible) axion models. We comment on the general implications of our study for the signature of moduli from string theory due to the presence of these anomalous symmetries.
Coverings of topological semi-abelian algebras
NASA Astrophysics Data System (ADS)
Mucuk, Osman; Demir, Serap
2016-08-01
In this work, we study on a category of topological semi-abelian algebras which are topological models of given an algebraic theory T whose category of models is semi-abelian; and investigate some results on the coverings of topological models of such theories yielding semi-abelian categories. We also consider the internal groupoid structure in the semi-abelian category of T-algebras, and give a criteria for the lifting of internal groupoid structure to the covering groupoids.
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(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. PMID:23215268
Extended hubbard model with ring exchange: a route to a non-Abelian topological phase.
Freedman, Michael; Nayak, Chetan; Shtengel, Kirill
2005-02-18
We propose an extended Hubbard model on a 2D kagome lattice with an additional ring exchange term. The particles can be either bosons or spinless fermions. We analyze the model at the special filling fraction 1/6, where it is closely related to the quantum dimer model. We show how to arrive at an exactly soluble point whose ground state is the "d-isotopy" transition point into a stable phase with a certain type of non-Abelian topological order. Near the "special" values, d=2cos(pi/(k+2), this topological phase has anyonic excitations closely related to SU(2) Chern-Simons theory at level k. PMID:15783757
NASA Astrophysics Data System (ADS)
Escobar, C. A.; Urrutia, L. F.
2015-07-01
After imposing current conservation together with the Gauss law as initial conditions on the Abelian Nambu model, we prove that the resulting theory is equivalent to standard QED in the nonlinear gauge (AμAμ-n2M2) =0 , to all orders in perturbation theory. We show this by writing both models in terms of the same variables, which produce identical Feynman rules for the interactions and propagators. A crucial point is to verify that the Faddeev-Popov ghosts arising from the gauge fixing procedure in the QED sector decouple to all orders. We verify this decoupling by following a method like that employed in Yang-Mills theories when investigating the behavior of axial gauges. The equivalence between the two theories supports the idea that gauge particles can be envisaged as the Goldstone bosons originating from spontaneous Lorentz symmetry breaking.
Beta function in the non-Abelian Nambu-Jona-Lasinio model in four dimensions
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.
Three phases in the three-dimensional Abelian-Higgs model with nonlocal gauge interactions
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.
Probing the QCD vacuum with an Abelian chromomagnetic field: A study within an effective model
Campanelli, L.; Ruggieri, M.
2009-08-01
We study the response of the QCD vacuum to an external Abelian chromomagnetic field in the framework of a nonlocal Nambu-Jona-Lasinio model with the Polyakov loop. We use the lattice results on the deconfinement temperature of the pure gauge theory to compute the same quantity in the presence of dynamical quarks. We find a linear relationship between the deconfinement temperature with quarks and the squared root of the applied field strength, gH, in qualitative (and to some extent also quantitative) agreement with existing lattice calculations. On the other hand, we find a discrepancy on the approximate chiral symmetry restoration: while lattice results suggest the deconfinement and the chiral restoration remain linked even at a nonzero value of gH, our results are consistent with a scenario in which the two transitions are separated as gH is increased.
The abelian confinement mechanism revisited: New aspects of the Georgi–Glashow model
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≤T
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.
Velocity-dependent models for non-Abelian/entangled string networks
Avgoustidis, A.; Shellard, E. P. S.
2008-11-15
We develop velocity-dependent models describing the evolution of string networks that involve several types of interacting strings, each with a different tension. These incorporate the formation of Y-type junctions with links stretching between colliding strings, while always ensuring energy conservation. These models can be used to describe network evolution for non-Abelian strings as well as cosmic superstrings. The application to Z{sub N} strings in which interactions are topologically constrained, demonstrates that a scaling regime is generally reached which involves a hierarchy of string densities with the lightest most abundant. We also study hybrid networks of cosmic superstrings, where energetic considerations are more important in determining interaction outcomes. We again find that networks tend towards scaling, with the three lightest network components being dominant and having comparable number densities, while the heavier string states are suppressed. A more quantitative analysis depends on the precise calculation of the string interaction matrix using the underlying string or field theory. Nevertheless, these results provide further evidence that the presence of junctions in a string network does not obstruct scaling.
Phase transitions at strong coupling in the 2+1-d abelian Higgs model
NASA Astrophysics Data System (ADS)
MacKenzie, R. B.; Nebia-Rahal, Faïza; Paranjape, M. B.
2013-12-01
We study, using numerical Monte-Carlo simulations, an effective description of the 2+1 dimensional Abelian Higgs model which is valid at strong coupling, in the broken symmetry sector. In this limit, the massive gauge boson and the massive neutral Higgs decouple leaving only the massive vortices. The vortices have no long range interactions. We find a phase transition as the mass of the vortices is made lighter and lighter. At the transition, the contributions to the functional integral come from a so-called infinite vortex anti-vortex loop. Adding the Chern-Simons term simply counts the linking number between the vortices. We find that the Wilson loop exhibits perimeter law behaviour in both phases, although the polarization cloud increases by an order of magnitude at the transition. We also study the 't Hooft loop. We find the 't Hooft loop exhibits perimeter law behaviour in the presence of the Chern-Simons term but is trivial in its absence. Thus we have a theory with perimeter law for both the Wilson loop and the 't Hooft loop, but contains no massless particles.
Peristaltic modes of a single vortex in the Abelian Higgs model
Kojo, Toru; Suganuma, Hideo; Tsumura, Kyosuke
2007-05-15
Using the Abelian Higgs model, we study the radial excitations of single vortex and their propagation modes along the vortex line. We call such beyond-stringy modes peristaltic modes of single vortex. With the profile of the static vortex, we derive the vortex-induced potential, i.e., single-particle potential for the Higgs and the photon field fluctuations around the static vortex, and investigate the coherently propagating fluctuations which correspond to the vibration of the vortex. We derive, analyze, and numerically solve the field equations of the Higgs and the photon field fluctuations around the static vortex with various Ginzburg-Landau parameter {kappa} and topological charge n. Around the Bogomol'nyi-Prasad-Sommerfield value or critical coupling {kappa}{sup 2}=1/2, there appears a significant correlation between the Higgs and the photon field fluctuations mediated by the static vortex. As a result, for {kappa}{sup 2}=1/2, we find the characteristic new-type discrete pole of the peristaltic mode corresponding to the quasibound state of coherently fluctuating fields and the static vortex. We investigate its excitation energy, correlation energy of coherent fluctuations, spatial distributions, and the resulting magnetic flux behavior in detail. Our investigation covers not only usual type-II vortices with n=1 but also type-I and type-II vortices with n set-membership sign Z for the application to various general systems where the vortexlike objects behave as the essential degrees of freedom.
The abelian confinement mechanism revisited: New aspects of the Georgi-Glashow model
NASA Astrophysics Data System (ADS)
Anber, Mohamed M.
2014-02-01
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≤T
Constraints on abelian extensions of the Standard Model from two-loop vacuum stability and U(1) B- L
NASA Astrophysics Data System (ADS)
Corianò, Claudio; Rose, Luigi Delle; Marzo, Carlo
2016-02-01
We present a renormalization group study of the scalar potential in a minimal U(1) B- L extension of the Standard Model involving one extra heavier Higgs and three heavy right-handed neutrinos with family universal B-L charge assignments. We implement a type-I seesaw for the masses of the light neutrinos of the Standard Model. In particular, compared to a previous study, we perform a two-loop extension of the evolution, showing that two-loop effects are essential for the study of the stability of the scalar potential up to the Planck scale. The analysis includes the contribution of the kinetic mixing between the two abelian gauge groups, which is radiatively generated by the evolution, and the one-loop matching conditions at the electroweak scale. By requiring the stability of the potential up to the Planck mass, significant constraints on the masses of the heavy neutrinos, on the gauge couplings and the mixing in the Higgs sector are identified.
Bevis, Neil; Hindmarsh, Mark; Kunz, Martin; Urrestilla, Jon
2007-03-15
We present the first field-theoretic calculations of the contribution made by cosmic strings to the temperature power spectrum of the cosmic microwave background (CMB). Unlike previous work, in which strings were modeled as idealized one-dimensional objects, we evolve the simplest example of an underlying field theory containing local U(1) strings, the Abelian Higgs model. Limitations imposed by finite computational volumes are overcome using the scaling property of string networks and a further extrapolation related to the lessening of the string width in comoving coordinates. The strings and their decay products, which are automatically included in the field theory approach, source metric perturbations via their energy-momentum tensor, the unequal-time correlation functions of which are used as input into the CMB calculation phase. These calculations involve the use of a modified version of CMBEASY, with results provided over the full range of relevant scales. We find that the string tension {mu} required to normalize to the WMAP 3-year data at multipole l=10 is G{mu}=[2.04{+-}0.06(stat.){+-}0.12(sys.)]x10{sup -6}, where we have quoted statistical and systematic errors separately, and G is Newton's constant. This is a factor 2-3 higher than values in current circulation.
Hidden Q-structure and Lie 3-algebra for non-abelian superconformal models in six dimensions
NASA Astrophysics Data System (ADS)
Lavau, Sylvain; Samtleben, Henning; Strobl, Thomas
2014-12-01
We disclose the mathematical structure underlying the gauge field sector of the recently constructed non-abelian superconformal models in six space-time dimensions. This is a coupled system of 1-form, 2-form, and 3-form gauge fields. We show that the algebraic consistency constraints governing this system permit to define a Lie 3-algebra, generalizing the structural Lie algebra of a standard Yang-Mills theory to the setting of a higher bundle. Reformulating the Lie 3-algebra in terms of a nilpotent degree 1 BRST-type operator Q, this higher bundle can be compactly described by means of a Q-bundle; its fiber is the shifted tangent of the Q-manifold corresponding to the Lie 3-algebra and its base the odd tangent bundle of space-time equipped with the de Rham differential. The generalized Bianchi identities can then be retrieved concisely from Q2 = 0, which encode all the essence of the structural identities. Gauge transformations are identified as vertical inner automorphisms of such a bundle, their algebra being determined from a Q-derived bracket.
NASA Astrophysics Data System (ADS)
Andrist, Ruben S.; Wootton, James R.; Katzgraber, Helmut G.
2015-04-01
Current approaches for building quantum computing devices focus on two-level quantum systems which nicely mimic the concept of a classical bit, albeit enhanced with additional quantum properties. However, rather than artificially limiting the number of states to two, the use of d -level quantum systems (qudits) could provide advantages for quantum information processing. Among other merits, it has recently been shown that multilevel quantum systems can offer increased stability to external disturbances. In this study we demonstrate that topological quantum memories built from qudits, also known as Abelian quantum double models, exhibit a substantially increased resilience to noise. That is, even when taking into account the multitude of errors possible for multilevel quantum systems, topological quantum error-correction codes employing qudits can sustain a larger error rate than their two-level counterparts. In particular, we find strong numerical evidence that the thresholds of these error-correction codes are given by the hashing bound. Considering the significantly increased error thresholds attained, this might well outweigh the added complexity of engineering and controlling higher-dimensional quantum systems.
Infrared Maximally Abelian Gauge
Mendes, Tereza; Cucchieri, Attilio; Mihara, Antonio
2007-02-27
The confinement scenario in Maximally Abelian gauge (MAG) is based on the concepts of Abelian dominance and of dual superconductivity. Recently, several groups pointed out the possible existence in MAG of ghost and gluon condensates with mass dimension 2, which in turn should influence the infrared behavior of ghost and gluon propagators. We present preliminary results for the first lattice numerical study of the ghost propagator and of ghost condensation for pure SU(2) theory in the MAG.
Berezinskii-Kosterlitz-Thouless phase transitions in two-dimensional non-Abelian spin models
NASA Astrophysics Data System (ADS)
Borisenko, Oleg; Chelnokov, Volodymyr; Cuteri, Francesca; Papa, Alessandro
2016-07-01
It is argued that two-dimensional U(N ) spin models for any N undergo a Berezinskii-Kosterlitz-Thouless (BKT)-like phase transition, similarly to the famous X Y model. This conclusion follows from the Berezinskii-like calculation of the two-point correlation function in U(N ) models, approximate renormalization group analysis, and numerical investigations of the U(2 ) model. It is shown, via Monte Carlo simulations, that the universality class of the U(2 ) model coincides with that of the X Y model. Moreover, preliminary numerical results point out that two-dimensional SU(N ) spin models with the fundamental and adjoint terms and N >4 exhibit two phase transitions of BKT type, similarly to Z (N ) vector models.
Berezinskii-Kosterlitz-Thouless phase transitions in two-dimensional non-Abelian spin models.
Borisenko, Oleg; Chelnokov, Volodymyr; Cuteri, Francesca; Papa, Alessandro
2016-07-01
It is argued that two-dimensional U(N) spin models for any N undergo a Berezinskii-Kosterlitz-Thouless (BKT)-like phase transition, similarly to the famous XY model. This conclusion follows from the Berezinskii-like calculation of the two-point correlation function in U(N) models, approximate renormalization group analysis, and numerical investigations of the U(2) model. It is shown, via Monte Carlo simulations, that the universality class of the U(2) model coincides with that of the XY model. Moreover, preliminary numerical results point out that two-dimensional SU(N) spin models with the fundamental and adjoint terms and N>4 exhibit two phase transitions of BKT type, similarly to Z(N) vector models. PMID:27575078
Functional scale-free networks in the two-dimensional Abelian sandpile model
NASA Astrophysics Data System (ADS)
Zarepour, M.; Niry, M. D.; Valizadeh, A.
2015-07-01
Recently, the similarity of the functional network of the brain and the Ising model was investigated by Chialvo [Nat. Phys. 6, 744 (2010), 10.1038/nphys1803]. This similarity supports the idea that the brain is a self-organized critical system. In this study we derive a functional network of the two-dimensional Bak-Tang-Wiesenfeld sandpile model as a self-organized critical model, and compare its characteristics with those of the functional network of the brain, obtained from functional magnetic resonance imaging.
Non-Abelian {SU}{(3)}_{k} anyons: inversion identities for higher rank face models
NASA Astrophysics Data System (ADS)
Frahm, Holger; Karaiskos, Nikos
2015-12-01
The spectral problem for an integrable system of particles satisfying the fusion rules of {SU}{(3)}k is expressed in terms of exact inversion identities satisfied by the commuting transfer matrices of the integrable fused {A}2(1) interaction round a face model of Jimbo, Miwa and Okado. The identities are proven using local properties of the Boltzmann weights, in particular the Yang-Baxter equation and unitarity. They are closely related to the consistency conditions for the construction of eigenvalues obtained in the separation of variables approach to integrable vertex models.
Abelian gauge extension of the standard model: Dark matter and radiative neutrino mass
NASA Astrophysics Data System (ADS)
Borah, Debasish; Adhikari, Rathin
2012-05-01
We study a simple extension of the standard model where the gauge group is extended by an additional U(1)X gauge symmetry. Neutrino mass arises both at tree level as well as radiatively by the anomaly-free addition of one singlet fermion NR and two triplet fermions Σ1R, Σ2R with suitable Higgs scalars. The spontaneous gauge symmetry breaking is achieved in a way that results in a residual Z2 symmetry and hence provides a stable cold dark matter candidate. We study the possible dark matter candidates in this model by incorporating the constraints from cosmology as well as direct detection experiments. We discuss both low- and high-mass (from GeV to the TeV scale) regimes of fermionic and scalar dark matter candidates in the model. We show that scalar dark matter relic density, although not significantly affected by the presence or absence of annihilation into U(1)X gauge boson pairs, is however affected by choice of U(1)X gauge charges. We discuss the neutrino mass phenomenology and its compatibility with the allowed dark matter mass ranges and we also comment on the implications of the model on Higgs signatures at colliders including those related to the fourth fermion generation.
A topological semimetal model with f-wave symmetry in a non-Abelian triangular optical lattice
NASA Astrophysics Data System (ADS)
Li, Ling; Bai, Zhiming; Hao, Ningning; Liu, Guocai
2016-08-01
We demonstrate that an chiral f-wave topological semimetal can be induced in a non-Abelian triangular optical lattice. We show that the f-wave symmetry topological semimetal is characterized by the topological invariant, i.e., the winding number W, with W=3 and is different from the semimetal with W=1 and 2 which have the p-wave and d-wave symmetry, respectively.
Non-Abelian twisted kinks in chiral Gross-Neveu model with isospin
NASA Astrophysics Data System (ADS)
Thies, Michael
2016-04-01
The two-dimensional, massless Gross-Neveu model with Nc colors and SU(2) isospin is studied analytically in the large Nc limit. The chiral SU (2 )L×SU (2 )R symmetry is broken spontaneously in the vacuum. Twisted kinks connecting two arbitrary points on the vacuum manifold S3 are constructed, and their properties are explored. The phase diagram as a function of temperature and baryon and isospin chemical potential is discussed, with special emphasis on inhomogeneous phases. The preferred form of the condensate is a product of the real kink crystal and the chiral spiral. Kink-kink scattering is solved, using the general solution of the multicomponent Bogoliubov-de Gennes equation recently presented by Takahashi.
Classical dynamics of the Abelian Higgs model from the critical point and beyond
NASA Astrophysics Data System (ADS)
Katsimiga, G. C.; Diakonos, F. K.; Maintas, X. N.
2015-09-01
We present two different families of solutions of the U(1)-Higgs model in a (1 + 1) dimensional setting leading to a localization of the gauge field. First we consider a uniform background (the usual vacuum), which corresponds to the fully higgsed-superconducting phase. Then we study the case of a non-uniform background in the form of a domain wall which could be relevantly close to the critical point of the associated spontaneous symmetry breaking. For both cases we obtain approximate analytical nodeless and nodal solutions for the gauge field resulting as bound states of an effective Pöschl-Teller potential created by the scalar field. The two scenaria differ only in the scale of the characteristic localization length. Numerical simulations confirm the validity of the obtained analytical solutions. Additionally we demonstrate how a kink may be used as a mediator driving the dynamics from the critical point and beyond.
Condensing Non-Abelian Quasiparticles
Hermanns, M.
2010-02-05
A most interesting feature of certain fractional quantum Hall states is that their quasiparticles obey non-Abelian fractional statistics. So far, candidate non-Abelian wave functions have been constructed from conformal blocks in cleverly chosen conformal field theories. In this work we present a hierarchy scheme by which we can construct daughter states by condensing non-Abelian quasiparticles (as opposed to quasiholes) in a parent state, and show that the daughters have a non-Abelian statistics that differs from the parent. In particular, we discuss the daughter of the bosonic, spin-polarized Moore-Read state at nu=4/3 as an explicit example.
Optical Abelian lattice gauge theories
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.
Dynamical non-Abelian two-form: BRST quantization
Lahiri, A.
1997-04-01
When an antisymmetric tensor potential is coupled to the field strength of a gauge field via a BANDF coupling and a kinetic term for B is included, the gauge field develops an effective mass. The theory can be made invariant under a non-Abelian vector gauge symmetry by introducing an auxiliary vector field. The covariant quantization of this theory requires ghosts for ghosts. The resultant theory including gauge fixing and ghost terms is BRST invariant by construction, and therefore unitary. The construction of the BRST-invariant action is given for both Abelian and non-Abelian models of mass generation. {copyright} {ital 1997} {ital The American Physical Society}
Symmetries of abelian orbifolds
NASA Astrophysics Data System (ADS)
Hanany, Amihay; Seong, Rak-Kyeong
2011-01-01
Using the Polya Enumeration Theorem, we count with particular attention to {{{{mathbb{C}^3}}} left/ {Γ } right.} up to {{{{mathbb{C}^6}}} left/ {Γ } right.} , abelian orbifolds in various dimensions which are invariant under cycles of the permutation group S D . This produces a collection of multiplicative sequences, one for each cycle in the Cycle Index of the permutation group. A multiplicative sequence is controlled by its values on prime numbers and their pure powers. Therefore, we pay particular attention to orbifolds of the form {{{{mathbb{C}^D}}} left/ {Γ } right.} where the order of Γ is p α. We propose a generalization of these sequences for any D and any p.
Generalized symmetries of an 𝓝 = 1 supersymmetric Boiti-Leon-Manna-Pempinelli system
NASA Astrophysics Data System (ADS)
Wang, Jian-Yong; Tang, Xiao-Yan; Liang, Zu-Feng; Lou, Sen-Yue
2015-05-01
The formal series symmetry approach (FSSA), a quite powerful and straightforward method to establish infinitely many generalized symmetries of classical integrable systems, has been successfully extended in the supersymmetric framework to explore series of infinitely many generalized symmetries for supersymmetric systems. Taking the 𝒩 = 1 supersymmetric Boiti-Leon-Manna-Pempinelli system as a concrete example, it is shown that the application of the extended FSSA to this supersymmetric system leads to a set of infinitely many generalized symmetries with an arbitrary function f (t). Some interesting special cases of symmetry algebras are presented, including a limit case f (t) = 1 related to the commutativity of higher order generalized symmetries. Project supported by the National Natural Science Foundation of China (Grant Nos. 11275123, 11175092, 11475052, and 11435005), the Shanghai Knowledge Service Platform for Trustworthy Internet of Things, China (Grant No. ZF1213), and the Talent Fund and K CWong Magna Fund in Ningbo University, China.
Non-Abelian family symmetries as portals to dark matter
NASA Astrophysics Data System (ADS)
de Medeiros Varzielas, I.; Fischer, O.
2016-01-01
Non-Abelian family symmetries offer a very promising explanation for the flavour structure in the Standard Model and its extensions. We explore the possibility that dark matter consists in fermions that transform under a family symmetry, such that the visible and dark sector are linked by the familons - Standard Model gauge singlet scalars, responsible for spontaneously breaking the family symmetry. We study three representative models with non-Abelian family symmetries that have been shown capable to explain the masses and mixing of the Standard Model fermions.
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…
Non-Abelian Anyons and Interferometry
NASA Astrophysics Data System (ADS)
Bonderson, Parsa Hassan
This thesis is primarily a study of the measurement theory of non-Abelian anyons through interference experiments. We give an introduction to the theory of anyon models, providing all the formalism necessary to apply standard quantum measurement theory to such systems. This formalism is then applied to give a detailed analysis of a Mach-Zehnder interferometer for arbitrary anyon models. In this treatment, we find that the collapse behavior exhibited by a target anyon in a superposition of states is determined by the monodromy of the probe anyons with the target. Such measurements may also be used to gain knowledge that would help to properly identify the anyon model describing an unknown system. The techniques used and results obtained from this model interferometer have general applicability, and we use them to also describe the interferometry measurements in a two point-contact interferometer proposed for non-Abelian fractional quantum Hall states. Additionally, we give the complete description of a number of important examples of anyon models, as well as their corresponding quantities that are relevant for interferometry. Finally, we give a partial classification of anyon models with small numbers of particle types.
Hamedi, Azadeh; Farjadian, Shirin; Karami, Mohammad Reza
2015-10-01
Taranjebin manna is a substance produced by Poophilus nebulosus Leth. (Aphrophoridae) larva that feed from host plant Alhagi maurorum (Leguminosae). In Persian ethnomedicine, it is used as an antipyretic, antiviral, antimicrobial, demulcent, and adaptogen. But it is contraindicated in acute fever and some infections. This controversy might be due to its immunomodulatory properties. This study evaluated immunomodulatory properties of Taranjebin and its macromolecules. Taranjebin solution was prepared as described in traditional literature. After dialysis and precipitation, the macromolecules were isolated on DEAE Sephadex A-25. The cytotoxic/proliferative properties of Taranjebin and its isolated macromolecules on human Jurkat E6.1 cells were investigated (15.62-1000 μg/mL) using WST-1 reagent. Three of 4 isolated acidic polysaccharides inhibited the proliferation of Jurkat cells in a dose-dependent manner at concentrations higher than 31.25 μg/mL (IC50 range of 44.81-147.97 μg/mL). The crude aqueous Taranjebin solution had proliferative effects. These results indicate the immunomodulatory properties of Taranjebin. PMID:25868568
Inverse avalanches on Abelian sandpiles
Chau, H.F. Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois 61801-3080 )
1994-11-01
A simple and computationally efficient way of finding inverse avalanches for Abelian sandpiles, called the inverse particle addition operator, is presented. In addition, the method is shown to be optimal in the sense that it requires the minimum amount of computation among methods of the same kind. The method is also conceptually succinct because avalanche and inverse avalanche are placed in the same footing.
Directed Abelian sandpile with multiple downward neighbors.
Dhar, D; Pruessner, G; Expert, P; Christensen, K; Zachariou, N
2016-04-01
We study the directed Abelian sandpile model on a square lattice, with K downward neighbors per site, K>2. The K=3 case is solved exactly, which extends the earlier known solution for the K=2 case. For K>2, the avalanche clusters can have holes and side branches and are thus qualitatively different from the K=2 case where avalanche clusters are compact. However, we find that the critical exponents for K>2 are identical with those for the K=2 case, and the large-scale structure of the avalanches for K>2 tends to the K=2 case. PMID:27176254
Directed Abelian sandpile with multiple downward neighbors
NASA Astrophysics Data System (ADS)
Dhar, D.; Pruessner, G.; Expert, P.; Christensen, K.; Zachariou, N.
2016-04-01
We study the directed Abelian sandpile model on a square lattice, with K downward neighbors per site, K >2 . The K =3 case is solved exactly, which extends the earlier known solution for the K =2 case. For K >2 , the avalanche clusters can have holes and side branches and are thus qualitatively different from the K =2 case where avalanche clusters are compact. However, we find that the critical exponents for K >2 are identical with those for the K =2 case, and the large-scale structure of the avalanches for K >2 tends to the K =2 case.
Non-Abelian dynamics in the resonant decay of the Higgs after inflation
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.
Non-Abelian bosonic currents in cosmic strings
Lilley, Marc; Di Marco, Fabrizio; Martin, Jerome; Peter, Patrick
2010-07-15
A non-Abelian generalization of the neutral Witten current-carrying string model is discussed in which the bosonic current carrier belongs to a two-dimensional representation of SU(2). We find that the current-carrying solutions can be of three different kinds: either the current spans a U(1) subgroup, and in which case one is left with an Abelian current-carrying string, or the three currents are all lightlike, traveling in the same direction (only left or right movers). The third, genuinely non-Abelian situation, cannot be handled within a cylindrically symmetric framework, but can be shown to depend on all possible string Lorentz invariant quantities that can be constructed out of the phase gradients.
Non-Abelian quantum holonomy of hydrogenlike atoms
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.
Pertermann, D.; Ranft, J.
1986-09-15
We introduce a simplicial pseudorandom version of lattice gauge theory. In this formulation it is possible to interpolate continuously between a regular simplicial lattice and a pseudorandom lattice. Using this method we study a simple three-dimensional Abelian lattice gauge theory. Calculating average plaquette expectation values, we find an extremum of the action for our regular simplicial lattice. Such a behavior was found in analytical studies in one and two dimensions.
Breaking an Abelian gauge symmetry near a black hole horizon
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.
Non-Abelian strings in supersymmetric Yang-Mills
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.
Majorana meets Coxeter: Non-Abelian Majorana fermions and non-Abelian statistics
Yasui, Shigehiro; Itakura, Kazunori; Nitta, Muneto
2011-04-01
We discuss statistics of vortices having zero-energy non-Abelian Majorana fermions inside them. Considering the system of multiple non-Abelian vortices, we derive a non-Abelian statistics that differs from the previously derived non-Abelian statistics. The non-Abelian statistics presented here is given by a tensor product of two different groups, namely the non-Abelian statistics obeyed by the Abelian Majorana fermions and the Coxeter group. The Coxeter group is a symmetric group related to the symmetry of polytopes in a high-dimensional space. As the simplest example, we consider the case in which a vortex contains three Majorana fermions that are mixed with each other under the SO(3) transformations. We concretely present the representation of the Coxeter group in our case and its geometrical expressions in the high-dimensional Hilbert space constructed from non-Abelian Majorana fermions.
Non-Abelian SU(2) Lattice Gauge Theories in Superconducting Circuits.
Mezzacapo, A; Rico, E; Sabín, C; Egusquiza, I L; Lamata, L; Solano, E
2015-12-11
We propose a digital quantum simulator of non-Abelian pure-gauge models with a superconducting circuit setup. Within the framework of quantum link models, we build a minimal instance of a pure SU(2) gauge theory, using triangular plaquettes involving geometric frustration. This realization is the least demanding, in terms of quantum simulation resources, of a non-Abelian gauge dynamics. We present two superconducting architectures that can host the quantum simulation, estimating the requirements needed to run possible experiments. The proposal establishes a path to the experimental simulation of non-Abelian physics with solid-state quantum platforms. PMID:26705616
Geometry and energy of non-Abelian vortices
Manton, Nicholas S.; Rink, Norman A.
2011-04-15
We study pure Yang-Mills theory on {Sigma}xS{sup 2}, where {Sigma} is a compact Riemann surface, and invariance is assumed under rotations of S{sup 2}. It is well known that the self-duality equations in this setup reduce to vortex equations on {Sigma}. If the Yang-Mills gauge group is SU(2), the Bogomolny vortex equations of the Abelian Higgs model are obtained. For larger gauge groups, one generally finds vortex equations involving several matrix-valued Higgs fields. Here we focus on Yang-Mills theory with gauge group SU(N)/Z{sub N} and a special reduction which yields only one non-Abelian Higgs field. One of the new features of this reduction is the fact that while the instanton number of the theory in four dimensions is generally fractional with denominator N, we still obtain an integral vortex number in the reduced theory. We clarify the relation between these two topological charges at a bundle geometric level. Another striking feature is the emergence of nontrivial lower and upper bounds for the energy of the reduced theory on {Sigma}. These bounds are proportional to the area of {Sigma}. We give special solutions of the theory on {Sigma} by embedding solutions of the Abelian Higgs model into the non-Abelian theory, and we relate our work to the language of quiver bundles, which has recently proved fruitful in the study of dimensional reduction of Yang-Mills theory.
Non-Abelian vortices and non-Abelian statistics
Lo, H.; Preskill, J. )
1993-11-15
We study the interactions of non-Abelian vortices in two spatial dimensions. These interactions have novel features, because the Aharonov-Bohm effect enables a pair of vortices to exchange quantum numbers. The cross section for vortex-vortex scattering is typically a multivalued function of the scattering angle. There can be an exchange contribution to the vortex-vortex scattering amplitude that adds coherently with the direct amplitude, even if the two vortices have distinct quantum numbers. Thus two vortices can be indistinguishable'' even though they are not the same.
Abelian and non-abelian D-brane effective actions
NASA Astrophysics Data System (ADS)
Koerber, P.
2004-09-01
In this Ph.D. thesis, accepted at the Vrije Universiteit Brussel, we review and elaborate on a method to find the D-brane effective action, based on BPS equations. Firstly, both for the Yang-Mills action and the Born-Infeld action it is shown that these configurations are indeed BPS, i.e. solutions to these equations saturate a Bogomolny bound and leave some supersymmetry unbroken. Next, we use the BPS equations as a tool to construct the D-brane effective action and require that (a deformation of) these equations should still imply the equations of motion in more general cases. In the abelian case we managed to calculate all order in four-derivative corrections to the effective action and the BPS equations while in the non-abelian case we obtained the effective action up to order 4. Furthermore, we discuss a check based on the spectrum of strings stretching between intersecting branes. Finally, this Ph.D. thesis also discusses the construction of a boundary superspace which would be the first step to use the method of Weyl invariance in N = 2 superspace in order to again construct the D-brane effective action. A more detailed summary of each section can be found in the introduction.
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
NASA Astrophysics Data System (ADS)
Ortín, Tomás; Ramírez, Pedro F.
2016-09-01
We construct a supersymmetric black ring solution of SU (2) N = 1, d = 5 Super-Einstein-Yang-Mills (SEYM) theory by adding a distorted BPST instanton to an Abelian black ring solution of the same theory. The change cannot be observed from spatial infinity: neither the mass, nor the angular momenta or the values of the scalars at infinity differ from those of the Abelian ring. The entropy is, however, sensitive to the presence of the non-Abelian instanton, and it is smaller than that of the Abelian ring, in analogy to what happens in the supersymmetric colored black holes recently constructed in the same theory and in N = 2, d = 4 SEYM. By taking the limit in which the two angular momenta become equal we derive a non-Abelian generalization of the BMPV rotating black-hole solution.
Identifying non-Abelian topological order through minimal entangled states.
Zhu, W; Gong, S S; Haldane, F D M; Sheng, D N
2014-03-01
The topological order is encoded in the pattern of long-range quantum entanglements, which cannot be measured by any local observable. Here we perform an exact diagonalization study to establish the non-Abelian topological order for topological band models through entanglement entropy measurement. We focus on the quasiparticle statistics of the non-Abelian Moore-Read and Read-Rezayi states on the lattice models with bosonic particles. We identify multiple independent minimal entangled states (MESs) in the ground state manifold on a torus. The extracted modular S matrix from MESs faithfully demonstrates the Ising anyon or Fibonacci quasiparticle statistics, including the quasiparticle quantum dimensions and the fusion rules for such systems. These findings unambiguously demonstrate the topological nature of the quantum states for these flatband models without using the knowledge of model wave functions. PMID:24655269
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
Abelian link invariants and homology
Guadagnini, Enore; Mancarella, Francesco
2010-06-15
We consider the link invariants defined by the quantum Chern-Simons field theory with compact gauge group U(1) in a closed oriented 3-manifold M. The relation of the Abelian link invariants with the homology group of the complement of the links is discussed. We prove that, when M is a homology sphere or when a link--in a generic manifold M--is homologically trivial, the associated observables coincide with the observables of the sphere S{sup 3}. Finally, we show that the U(1) Reshetikhin-Turaev surgery invariant of the manifold M is not a function of the homology group only, nor a function of the homotopy type of M alone.
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.
An Exact Chiral Spin Liquid with Non-Abelian Anyons
Yao, Hong
2010-04-06
We establish the existence of a chiral spin liquid (CSL) as the exact ground state of the Kitaev model on a decorated honeycomb lattice, which is obtained by replacing each site in the familiar honeycomb lattice with a triangle. The CSL state spontaneously breaks time reversal symmetry but preserves other symmetries. There are two topologically distinct CSLs separated by a quantum critical point. Interestingly, vortex excitations in the topologically nontrivial (Chern number {+-}1) CSL obey non-Abelian statistics.
NASA Astrophysics Data System (ADS)
Khan, Mayukh; Teo, Jeffrey; Hughes, Taylor
2014-03-01
We consider bosonic abelian Fractional Quantum Hall (FQH) and Fractional Quantum Spin Hall (FQSH) states with edge theories drawn from the ADE Kac Moody algebras at level 1 . This set of systems have `anyonic' symmetries that leave braiding and fusion invariant Remarkably, the group of anyonic symmetries for this class of models is isomorphic to the symmetries of the Dynkin diagrams of the particular ADE Lie Algebra under consideration. The triality symmetry of the Dynkin diagram of so(8) leads to the largest anyonic symmetry group S3 (the permutation group on 3 elements). Each element of the anyonic symmetry group corresponds to a distinct way of gapping out the edge (i.e., each element corresponds to a Lagrangian subgroup). Junctions between two distinct gapped edges host non abelian twist defects with quantum dimensions (> 1). In the case of so(8) we have more exotic twist defects with non-abelian fusion. We acknowledge support from the U.S. Department of Energy, Division of Materials Sciences under Award No. DE-FG02- 07ER46453 (MK, TLH) and the Simons Foundation (JT).
Abelian 3-form gauge theory: Superfield approach
NASA Astrophysics Data System (ADS)
Malik, R. P.
2012-09-01
We discuss a D-dimensional Abelian 3-form gauge theory within the framework of Bonora-Tonin's superfield formalism and derive the off-shell nilpotent and absolutely anticommuting Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for this theory. To pay our homage to Victor I. Ogievetsky (1928-1996), who was one of the inventors of Abelian 2-form (antisymmetric tensor) gauge field, we go a step further and discuss the above D-dimensional Abelian 3-form gauge theory within the framework of BRST formalism and establish that the existence of the (anti-)BRST invariant Curci-Ferrari (CF) type of restrictions is the hallmark of any arbitrary p-form gauge theory (discussed within the framework of BRST formalism).
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.
Non-Abelian Braiding of Light.
Iadecola, Thomas; Schuster, Thomas; Chamon, Claudio
2016-08-12
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. PMID:27563965
Veneziano amplitudes, spin chains and Abelian reduction of QCD
NASA Astrophysics Data System (ADS)
Kholodenko, Arkady
2009-05-01
Although QCD can be treated perturbatively in the high energy limit, lower energies require uses of nonperturbative methods such as ADS/CFT and/or Abelian reduction. These methods are not equivalent. While the first is restricted to supersymmetric Yang-Mills model with number of colors going to infinity, the second is not restricted by requirements of supersymmetry and is designed to work in the physically realistic limit of a finite number of colors. In this paper we provide arguments in favor of the Abelian reduction methods. This is achieved by further developing results of our recent works re-analyzing Veneziano and Veneziano-like amplitudes and the models associated with these amplitudes. It is shown, that the obtained new partition function for these amplitudes can be mapped exactly into that for the Polychronakos-Frahm (P-F) spin chain model recoverable from the Richardon-Gaudin (R-G) XXX spin chain model originally designed for treatments of the BCS-type superconductivity. Because of this, it is demonstrated that the obtained mapping is compatible with the method of Abelian reduction. The R-G model is recovered from the asymptotic (WKB-type) solutions of the rational Knizhnik-Zamolodchikov (K-Z) equation. Linear independence of these solutions is controlled by determinants whose explicit form (up to a constant) coincides with Veneziano (or Veneziano-like) amplitudes. In the simplest case, the determinantal conditions coincide with those discovered by Kummer in the 19th century. Kummer's results admit physical interpretation by relating determinantal formula(s) to Veneziano-like amplitudes. Furthermore, these amplitudes can be interpreted as Poisson-Dirichlet distributions playing a central role in the stochastic theory of random coagulation-fragmentation processes. Such an interpretation is complementary to that known for the Lund model widely used for the description of coagulation-fragmentation processes in QCD.
Multiflavor QCD* on R_3 * S_1: Studying Transition From Abelian to Non-Abelian Confinement
Shifman, M.; Unsal, M.; /SLAC /Stanford U., Phys. Dept.
2009-03-31
The center-stabilized multiflavor QCD* theories formulated on R{sub 3} x S{sub 1} exhibit both Abelian and non-Abelian confinement as a function of the S{sub 1} radius, similar to the Seiberg-Witten theory as a function of the mass deformation parameter. For sufficiently small number of flavors and small r(S{sub 1}), we show occurrence of a mass gap in gauge fluctuations, and linear confinement. This is a regime of confinement without continuous chiral symmetry breaking ({chi}SB). Unlike one-flavor theories where there is no phase transition in r(S{sub 1}), the multiflavor theories possess a single phase transition associated with breaking of the continuous {chi}S. We conjecture that the scale of the {chi}SB is parametrically tied up with the scale of Abelian to non-Abelian confinement transition.
Necessity of an energy barrier for self-correction of Abelian quantum doubles
NASA Astrophysics Data System (ADS)
Kómár, Anna; Landon-Cardinal, Olivier; Temme, Kristan
2016-05-01
We rigorously establish an Arrhenius law for the mixing time of quantum doubles based on any Abelian group Zd. We have made the concept of the energy barrier therein mathematically well defined; it is related to the minimum energy cost the environment has to provide to the system in order to produce a generalized Pauli error, maximized for any generalized Pauli errors, not only logical operators. We evaluate this generalized energy barrier in Abelian quantum double models and find it to be a constant independent of system size. Thus, we rule out the possibility of entropic protection for this broad group of models.
The existence of self-dual vortices in a non-Abelian {Phi}{sup 2} Chern-Simons theory
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}.
Dyonic String-Like Solution in a Non-Abelian Gauge Theory with Two Potentials
NASA Astrophysics Data System (ADS)
Tripathi, Buddhi Vallabh; Nandan, Hemwati; Purohit, K. D.
2016-04-01
Axially symmetric dyon solutions of a non-Abelian gauge theory model with two potentials are sought. While seeking axially symmetric (flux tube like solutions) for the model, we stumbled upon an exact solution which represents an infinite string-like dyonic configuration with cylindrical symmetry.
Constraint Structure and Quantization of a Non-Abelian Gauge Theory by Means of Dirac Brackets
NASA Astrophysics Data System (ADS)
Bracken, Paul
An SO(3) non-Abelian gauge theory is introduced. The Hamiltonian density is determined and the constraint structure of the model is derived. The first-class constraints are obtained and gauge-fixing constraints are introduced into the model. Finally, using the constraints, the Dirac brackets can be determined and a canonical quantization is found using Dirac's procedure.
Collective States of D(D3) Non-Abelian Anyons
NASA Astrophysics Data System (ADS)
Finch, P. E.; Frahm, H.
2013-11-01
We study an exactly solvable model of non-Abelian anyons symmetric under the quantum double of the dihedral group D3 on a one-dimensional lattice. Bethe ansatz methods are employed to compute the ground states of this model in different regions of the parameter space. The finite size spectrum is studied and the corresponding low energy field theories are identified.
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.
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.
Canonical non-Abelian dual transformations in supersymmetric field theories
Curtright, T.; Zachos, C.
1995-07-15
A generating functional {ital F} is found for a canonical non-Abelian dual transformation which maps the supersymmetric chiral O(4) {sigma} model to an equivalent supersymmetric extension of the dual {sigma} model. This {ital F} produces a mapping between the classical phase spaces of the two theories in which the bosonic (coordinate) fields transform nonlocally, the fermions undergo a local tangent space chiral rotation, and all currents (fermionic and bosonic) mix locally. Purely bosonic curvature-free currents of the chiral model become a {ital symphysis} of purely bosonic and fermion bilinear currents of the dual theory. The corresponding transformation functional {ital T} which relates wave functions in the two quantum theories is argued to be {ital exactly} given by {ital T}=exp({ital iF}).
Critical string from non-Abelian vortex in four dimensions
NASA Astrophysics Data System (ADS)
Shifman, M.; Yung, A.
2015-11-01
In a class of non-Abelian solitonic vortex strings supported in certain N = 2 super-Yang-Mills theories we search for the vortex which can behave as a critical fundamental string. We use the Polchinski-Strominger criterion of the ultraviolet completeness. We identify an appropriate four-dimensional bulk theory: it has the U (2) gauge group, the Fayet-Iliopoulos term and four flavor hypermultiplets. It supports semilocal vortices with the world-sheet theory for orientational (size) moduli described by the weighted CP (2 , 2) model. The latter is superconformal. Its target space is six-dimensional. The overall Virasoro central charge is critical. We show that the world-sheet theory on the vortex supported in this bulk model is the bona fide critical string.
Mass generation for non-Abelian antisymmetric tensor fields in a three-dimensional space-time
Medeiros, D. M.; Landim, R. R.; Almeida, C. A. S.
2001-06-15
Starting from a recently proposed Abelian topological model in 2+1 dimensions, which involve the Kalb-Ramond two form field, we study a non-Abelian generalization of the model. An obstruction for the generalization is detected. However, we show that the goal is achieved if we introduce a vectorial auxiliary field. Consequently, a model is proposed, exhibiting a non-Abelian topological mass generation mechanism in D=3, that provides mass for the Kalb-Ramond field. The covariant quantization of this model requires ghosts for ghosts. Therefore, in order to quantize the theory, we construct a complete set of Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST equations using the horizontality condition.
On abelian group actions and Galois quantizations
NASA Astrophysics Data System (ADS)
Huru, H. L.; Lychagin, V. V.
2013-08-01
Quantizations of actions of finite abelian groups G are explicitly described by elements in the tensor square of the group algebra of G. Over algebraically closed fields of characteristic 0 these are in one to one correspondence with the second cohomology group of the dual of G. With certain adjustments this result is applied to group actions over any field of characteristic 0. In particular we consider the quantizations of Galois extensions, which are quantized by "deforming" the multiplication. For the splitting fields of products of quadratic polynomials this produces quantized Galois extensions that all are Clifford type algebras.
Non abelian hydrodynamics and heavy ion collisions
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.
Abelian BF theory and Turaev-Viro invariant
NASA Astrophysics Data System (ADS)
Mathieu, P.; Thuillier, F.
2016-02-01
The U(1) BF quantum field theory is revisited in the light of Deligne-Beilinson cohomology. We show how the U(1) Chern-Simons partition function is related to the BF one and how the latter on its turn coincides with an abelian Turaev-Viro invariant. Significant differences compared to the non-abelian case are highlighted.
On Geometrical Interpretation of Non-Abelian Flat Direction Constraints
NASA Astrophysics Data System (ADS)
Cleaver, G. B.; Nanopoulos, D. V.; Perkins, J. T.; Walker, J. W.
In order to produce a low-energy effective field theory from a string model, it is necessary to specify a vacuum state. In order that this vacuum be supersymmetric, it is well known that all field expectation values must be along so-called flat directions, leaving the F- and D-terms of the scalar potential to be zero. The situation becomes particularly interesting when one attempts to realize such directions while assigning vacuum expectation values to fields transforming under non-Abelian representations of the gauge group. Since the expectation value is now shared among multiple components of a field, satisfaction of flatness becomes an inherently geometrical problem in the group space. Furthermore, the possibility emerges that a single seemingly dangerous F-term might experience a self-cancellation among its components. The hope exists that the geometric language can provide an intuitive and immediate recognition of when the D and F conditions are simultaneously compatible, as well as a powerful tool for their comprehensive classification. This is the avenue explored in this paper, and applied to the cases of SU(2) and SO(2N), relevant respectively to previous attempts at reproducing the MSSM and the flipped SU(5) GUT. Geometrical interpretation of non-Abelian flat directions finds application to M-theory through the recent conjecture of equivalence between D-term strings and wrapped D-branes of Type II theory.1 Knowledge of the geometry of the flat direction "landscape" of a D-term string model could yield information about the dual brane model. It is hoped that the techniques encountered will be of benefit in extending the viability of the quasirealistic phenomenologies already developed.
Non-abelian symmetries in tensor networks: A quantum symmetry space approach
Weichselbaum, Andreas
2012-12-15
A general framework for non-abelian symmetries is presented for matrix-product and tensor-network states in the presence of well-defined orthonormal local as well as effective basis sets. The two crucial ingredients, the Clebsch-Gordan algebra for multiplet spaces as well as the Wigner-Eckart theorem for operators, are accounted for in a natural, well-organized, and computationally straightforward way. The unifying tensor-representation for quantum symmetry spaces, dubbed QSpace, is particularly suitable to deal with standard renormalization group algorithms such as the numerical renormalization group (NRG), the density matrix renormalization group (DMRG), or also more general tensor networks such as the multi-scale entanglement renormalization ansatz (MERA). In this paper, the focus is on the application of the non-abelian framework within the NRG. A detailed analysis is presented for a fully screened spin- 3/2 three-channel Anderson impurity model in the presence of conservation of total spin, particle-hole symmetry, and SU(3) channel symmetry. The same system is analyzed using several alternative symmetry scenarios based on combinations of U(1){sub charge}, SU(2){sub spin}, SU(2){sub charge}, SU(3){sub channel}, as well as the enveloping symplectic Sp(6) symmetry. These are compared in detail, including their respective dramatic gain in numerical efficiency. In the Appendix, finally, an extensive introduction to non-abelian symmetries is given for practical applications, together with simple self-contained numerical procedures to obtain Clebsch-Gordan coefficients and irreducible operators sets. The resulting QSpace tensors can deal with any set of abelian symmetries together with arbitrary non-abelian symmetries with compact, i.e. finite-dimensional, semi-simple Lie algebras. - Highlights: Black-Right-Pointing-Pointer We introduce a transparent framework for non-abelian symmetries in tensor networks. Black-Right-Pointing-Pointer The framework was successfully
Neutrino masses and non-abelian horizontal symmetries
NASA Astrophysics Data System (ADS)
Antonelli, V.; Caravaglios, F.; Ferrari, R.; Picariello, M.
2002-12-01
Recently neutrino experiments have made very significant progresses and our knowledge of neutrino masses and mixing has considerably improved. In a model-independent Monte Carlo approach, we have examined a very large class of textures, in the context of non-abelian horizontal symmetries; we have found that neutrino data select only those charged lepton matrices with left-right asymmetric texture. The large atmospheric mixing angle needs m23≃m33. This result, if combined with similar recent findings for the quark sector in the B oscillations, can be interpreted as a hint for SU(5) unification. In the neutrino sector strict neutrino anarchy is disfavored by data, and at least a factor 2 of suppression in the first row and column of the neutrino Majorana mass matrix is required.
Vortex operator and BKT transition in Abelian duality
NASA Astrophysics Data System (ADS)
Chern, Tong
2016-04-01
We give a new simple derivation for the sine-Gordon description of Berezinskii-Kosterlitz-Thouless (BKT) phase transition. Our derivation is simpler than traditional derivations. Besides, our derivation is a continuous field theoretic derivation by using path integration, different from the traditional derivations which are based on lattice theory or based on Coulomb gas model. Our new derivation relies on Abelian duality of two dimensional quantum field theory. By utilizing this duality in path integration, we find that the vortex configurations are naturally mapped to exponential operators in dual description. Since these operators are the vortex operators that can create vortices, the sine-Gordon description then naturally follows. Our method may be useful for the investigation to the BKT physics of superconductors.
Abelian Hidden Sectors at a GeV
Morrissey, David E.; Poland, David; Zurek, Kathryn; /Fermilab /Michigan U.
2009-04-16
We discuss mechanisms for naturally generating GeV-scale hidden sectors in the context of weak-scale supersymmetry. Such low mass scales can arise when hidden sectors are more weakly coupled to supersymmetry breaking than the visible sector, as happens when supersymmetry breaking is communicated to the visible sector by gauge interactions under which the hidden sector is uncharged, or if the hidden sector is sequestered from gravity-mediated supersymmetry breaking. We study these mechanisms in detail in the context of gauge and gaugino mediation, and present specific models of Abelian GeV-scale hidden sectors. In particular, we discuss kinetic mixing of a U(1){sub x} gauge force with hypercharge, singlets or bi-fundamentals which couple to both sectors, and additional loop effects. Finally, we investigate the possible relevance of such sectors for dark matter phenomenology, as well as for low- and high-energy collider searches.
Non-Abelian topological spin liquids from arrays of quantum wires or spin chains
NASA Astrophysics Data System (ADS)
Huang, Po-Hao; Chen, Jyong-Hao; Gomes, Pedro R. S.; Neupert, Titus; Chamon, Claudio; Mudry, Christopher
2016-05-01
We construct two-dimensional non-Abelian topologically ordered states by strongly coupling arrays of one-dimensional quantum wires via interactions. In our scheme, all charge degrees of freedom are gapped, so the construction can use either quantum wires or quantum spin chains as building blocks, with the same end result. The construction gaps the degrees of freedom in the bulk, while leaving decoupled states at the edges that are described by conformal field theories (CFT) in (1 +1 ) -dimensional space and time. We consider both the cases where time-reversal symmetry (TRS) is present or absent. When TRS is absent, the edge states are chiral and stable. We prescribe, in particular, how to arrive at all the edge states described by the unitary CFT minimal models with central charges c <1 . These non-Abelian spin liquid states have vanishing quantum Hall conductivities, but nonzero thermal ones. When TRS is present, we describe scenarios where the bulk state can be a non-Abelian, nonchiral, and gapped quantum spin liquid, or a gapless one. In the former case, we find that the edge states are also gapped. The paper provides a brief review of non-Abelian bosonization and affine current algebras, with the purpose of being self-contained. To illustrate the methods in a warm-up exercise, we recover the tenfold way classification of two-dimensional noninteracting topological insulators using the Majorana representation that naturally arises within non-Abelian bosonization. Within this scheme, the classification reduces to counting the number of null singular values of a mass matrix, with gapless edge modes present when left and right null eigenvectors exist.
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.
Particle coupled to a heat bath in non-Abelian gauge potentials
NASA Astrophysics Data System (ADS)
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.
NASA Astrophysics Data System (ADS)
Schröck, Mario; Vogt, Hannes
2016-01-01
On lattice gauge field configurations with 2 +1 dynamical quark flavors, we investigate the momentum space quark and gluon propagators in the combined maximally Abelian plus U (1 )3×U (1 )8 Landau gauge. We extract the gluon fields from the lattice link variables and study the diagonal and off-diagonal gluon propagators. We find that the infrared region of the transverse diagonal gluon propagator is strongly enhanced compared to the off-diagonal propagator. The Dirac operator from the Asqtad action is inverted on the diagonal and off-diagonal gluon backgrounds separately. In agreement with the hypothesis of infrared Abelian dominance, we find that the off-diagonal gluon background hardly gives rise to any nontrivial quark dynamics while the quark propagator from the diagonal gluon background closely resembles its Landau gauge counterpart.
Non-Abelian quantum error correction
NASA Astrophysics Data System (ADS)
Feng, Weibo
A quantum computer is a proposed device which would be capable of initializing, coherently manipulating, and measuring quantum states with sufficient accuracy to carry out new kinds of computations. In the standard scenario, a quantum computer is built out of quantum bits, or qubits, two-level quantum systems which replace the ordinary classical bits of a classical computer. Quantum computation is then carried out by applying quantum gates, the quantum equivalent of Boolean logic gates, to these qubits. The most fundamental barrier to building a quantum computer is the inevitable errors which occur when carrying out quantum gates and the loss of quantum coherence of the qubits due to their coupling to the environment (decoherence). Remarkably, it has been shown that in a quantum computer such errors and decoherence can be actively fought using what is known as quantum error correction. A closely related proposal for fighting errors and decoherence in a quantum computer is to build the computer out of so-called topologically ordered states of matter. These are states of matter which allow for the storage and manipulation of quantum states with a built in protection from error and decoherence. The excitations of these states are non-Abelian anyons, particle-like excitations which satisfy non-Abelian statistics, meaning that when two excitations are interchanged the result is not the usual +1 and -1 associated with identical Bosons or Fermions, but rather a unitary operation which acts on a multidimensional Hilbert space. It is therefore possible to envision computing with these anyons by braiding their world-lines in 2+1-dimensional spacetime. In this Dissertation we present explicit procedures for a scheme which lives at the intersection of these two approaches. In this scheme we envision a functioning ``conventional" quantum computer consisting of an array of qubits and the ability to carry out quantum gates on these qubits. We then give explicit quantum circuits
Topological invariants measured for Abelian and non-Abelian monopole fields
NASA Astrophysics Data System (ADS)
Sugawa, Seiji; Salces Carcoba, Francisco; Perry, Abigail; Yue, Yuchen; Putra, Andika; Spielman, Ian
2016-05-01
Understanding the topological nature of physical systems is an important topic in contemporary physics, ranging from condensed matter to high energy. In this talk, I will present experiments measuring the 1st and 2nd Chern number in a four-level quantum system both with degenerate and non-degenerate energies. We engineered the system's Hamiltonian by coupling hyperfine ground states of rubidium-87 Bose-Einstein condensates with rf and microwave fields. We non-adiabatically drove the system and measured the linear response to obtain the local (non-Abelian) Berry curvatures. Then, the Chern numbers were evaluated on (hyper-)spherical manifolds in parameter space. We obtain Chern numbers close to unity for both the 1st and the 2nd Chern numbers. The non-zero Chern number can be interpreted as monopole residing inside the manifold. For our system, the monopoles correspond to a Dirac monopole for non-degenerate spectra and a Yang monopole for our degenerate case. We also show how the dynamical evolution under non-Abelian gauge field emerged in degenerate quantum system is different from non-degenerate case by showing path-dependent acquisition of non-Abelian geometric phase and Wilson loops.
Topological quantum liquids with quaternion non-Abelian statistics.
Xu, Cenke; Ludwig, Andreas W W
2012-01-27
Noncollinear magnetic order is typically characterized by a tetrad ground state manifold (GSM) of three perpendicular vectors or nematic directors. We study three types of tetrad orders in two spatial dimensions, whose GSMs are SO(3) = S(3)/Z(2), S(3)/Z(4), and S(3)/Q(8), respectively. Q(8) denotes the non-Abelian quaternion group with eight elements. We demonstrate that after quantum disordering these three types of tetrad orders, the systems enter fully gapped liquid phases described by Z(2), Z(4), and non-Abelian quaternion gauge field theories, respectively. The latter case realizes Kitaev's non-Abelian toric code in terms of a rather simple spin-1 SU(2) quantum magnet. This non-Abelian topological phase possesses a 22-fold ground state degeneracy on the torus arising from the 22 representations of the Drinfeld double of Q(8). PMID:22400884
The non-abelian tensor multiplet in loop space
NASA Astrophysics Data System (ADS)
Gustavsson, Andreas
2006-01-01
We introduce a non-abelian tensor multiplet directly in the loop space associated with flat six-dimensional Miskowski space-time, and derive the supersymmetry variations for on-shell Script N = (2,0) supersymmetry.
Universal Reconnection of Non-Abelian Cosmic Strings
Eto, Minoru; Hashimoto, Koji; Marmorini, Giacomo; Nitta, Muneto; Ohashi, Keisuke; Vinci, Walter
2007-03-02
We show that local and semilocal strings in Abelian and non-Abelian gauge theories with critical couplings always reconnect classically in collision, by using moduli space approximation. The moduli matrix formalism explicitly identifies a well-defined set of the vortex moduli parameters. Our analysis of generic geodesic motion in terms of those shows right-angle scattering in head-on collision of two vortices, which is known to give the reconnection of the strings.
Universal reconnection of non-Abelian cosmic strings.
Eto, Minoru; Hashimoto, Koji; Marmorini, Giacomo; Nitta, Muneto; Ohashi, Keisuke; Vinci, Walter
2007-03-01
We show that local and semilocal strings in Abelian and non-Abelian gauge theories with critical couplings always reconnect classically in collision, by using moduli space approximation. The moduli matrix formalism explicitly identifies a well-defined set of the vortex moduli parameters. Our analysis of generic geodesic motion in terms of those shows right-angle scattering in head-on collision of two vortices, which is known to give the reconnection of the strings. PMID:17359147
Higher Genus Abelian Functions Associated with Cyclic Trigonal Curves
NASA Astrophysics Data System (ADS)
England, Matthew
2010-03-01
We develop the theory of Abelian functions associated with cyclic trigonal curves by considering two new cases. We investigate curves of genus six and seven and consider whether it is the trigonal nature or the genus which dictates certain areas of the theory. We present solutions to the Jacobi inversion problem, sets of relations between the Abelian function, links to the Boussinesq equation and a new addition formula.
Multiflavor QCD∗ on R3 ×S1: Studying transition from Abelian to non-Abelian confinement
NASA Astrophysics Data System (ADS)
Shifman, M.; Ünsal, M.
2009-11-01
The center-stabilized multiflavor QCD∗ theories formulated on R3 ×S1 exhibit both Abelian and non-Abelian confinement as a function of the S1 radius, similar to the Seiberg-Witten theory as a function of the mass deformation parameter. For sufficiently small number of flavors and small r (S1), we show occurrence of a mass gap in gauge fluctuations, and linear confinement. This is a regime of confinement without continuous chiral symmetry breaking (χSB). Unlike one-flavor theories where there is no phase transition in r (S1), the multiflavor theories possess a single phase transition associated with breaking of the continuous χS. We conjecture that the scale of the χSB is parametrically tied up with the scale of Abelian to non-Abelian confinement transition.
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.
Plasma analogy and non-Abelian statistics for Ising-type quantum Hall states
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.
Black holes and Abelian symmetry breaking
NASA Astrophysics Data System (ADS)
Chagoya, Javier; Niz, Gustavo; Tasinato, Gianmassimo
2016-09-01
Black hole configurations offer insights on the nonlinear aspects of gravitational theories, and can suggest testable predictions for modifications of General Relativity. In this work, we examine exact black hole configurations in vector–tensor theories, originally proposed to explain dark energy by breaking the Abelian symmetry with a non-minimal coupling of the vector to gravity. We are able to evade the no-go theorems by Bekenstein on the existence of regular black holes in vector–tensor theories with Proca mass terms, and exhibit regular black hole solutions with a profile for the longitudinal vector polarisation, characterised by an additional charge. We analytically find the most general static, spherically symmetric black hole solutions with and without a cosmological constant, and study in some detail their features, such as how the geometry depends on the vector charges. We also include angular momentum, and find solutions describing slowly-rotating black holes. Finally, we extend some of these solutions to higher dimensions.
Energy-momentum correlations for Abelian Higgs cosmic strings
NASA Astrophysics Data System (ADS)
Daverio, David; Hindmarsh, Mark; Kunz, Martin; Lizarraga, Joanes; Urrestilla, Jon
2016-04-01
We report on the energy-momentum correlators obtained with recent numerical simulations of the Abelian Higgs model, essential for the computation of cosmic microwave background and matter perturbations of cosmic strings. Due to significant improvements both in raw computing power and in our parallel simulation framework, the dynamical range of the simulations has increased fourfold both in space and time, and for the first time we are able to simulate strings with a constant physical width in both the radiation and matter eras. The new simulations improve the accuracy of the measurements of the correlation functions at the horizon scale and confirm the shape around the peak. The normalization is slightly higher in the high wave-number tails, due to a small increase in the string density. We study, for the first time, the behavior of the correlators across cosmological transitions and discover that the correlation functions evolve adiabatically; i.e., the network adapts quickly to changes in the expansion rate. We propose a new method for constructing source functions for Einstein-Boltzmann integrators, comparing it with two other methods previously used. The new method is more consistent, easier to implement, and significantly more accurate.
NASA Astrophysics Data System (ADS)
Pogrebkov, A. K.
2016-06-01
We show that the non-Abelian Hirota difference equation is directly related to a commutator identity on an associative algebra. Evolutions generated by similarity transformations of elements of this algebra lead to a linear difference equation. We develop a special dressing procedure that results in an integrable non-Abelian Hirota difference equation and propose two regular reduction procedures that lead to a set of known equations, Abelian or non-Abelian, and also to some new integrable equations.
The Hilbert scheme of points for supersingular abelian surfaces
NASA Astrophysics Data System (ADS)
Schröer, Stefan
2009-04-01
We study the geometry of Hilbert schemes of points on abelian surfaces and Beauville’s generalized Kummer varieties in positive characteristics. The main result is that, in characteristic two, the addition map from the Hilbert scheme of two points to the abelian surface is a quasifibration such that all fibers are nonsmooth. In particular, the corresponding generalized Kummer surface is nonsmooth, and minimally elliptic singularities occur in the supersingular case. We unravel the structure of the singularities in dependence of p-rank and a-number of the abelian surface. To do so, we establish a McKay Correspondence for Artin’s wild involutions on surfaces. Along the line, we find examples of canonical singularities that are not rational singularities.
Correlation-induced non-Abelian quantum holonomies
NASA Astrophysics Data System (ADS)
Johansson, Markus; Ericsson, Marie; Singh, Kuldip; Sjöqvist, Erik; Williamson, Mark S.
2011-04-01
In the context of two-particle interferometry, we construct a parallel transport condition that is based on the maximization of coincidence intensity with respect to local unitary operations on one of the subsystems. The dependence on correlation is investigated and it is found that the holonomy group is generally non-Abelian, but Abelian for uncorrelated systems. It is found that our framework contains the Lévay geometric phase (2004 J. Phys. A: Math. Gen. 37 1821) in the case of two-qubit systems undergoing local SU(2) evolutions.
Ward-Takahashi identities for Abelian chiral gauge theories
NASA Astrophysics Data System (ADS)
de Lima, Ana Paula Cardoso Rodrigues; Dias, Sebastião Alves
2016-04-01
By considering a general Abelian chiral gauge theory, we investigate the behavior of anomalous Ward-Takahashi (WT) identities concerning their prediction for the usual relationship between the vertex and two-point fermion functions. Using gauge anomaly vanishing results, we show that the usual (in the nonanomalous case) WT identity connecting the vertex and two-point fermion 1PI functions is modified for Abelian chiral gauge theories. The modification, however, implies a relation between fermion and charge renormalization constants that can be important in a future study of renormalization of such theories.
Fibonacci anyons from Abelian bilayer quantum Hall states.
Vaezi, Abolhassan; Barkeshli, Maissam
2014-12-01
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. PMID:25526149
Deligne-Beilinson cohomology and Abelian link invariants: Torsion case
Thuillier, F.
2009-12-15
For the Abelian Chern-Simons field theory, we consider the quantum functional integration over the Deligne-Beilinson cohomology classes and present an explicit path-integral nonperturbative computation of the Chern-Simons link invariants in SO(3){approx_equal}RP{sup 3}, a toy example of a 3-manifold with torsion.
Quantization of higher abelian gauge theory in generalized differential cohomology
NASA Astrophysics Data System (ADS)
Szabo, R.
We review and elaborate on some aspects of the quantization of certain classes of higher abelian gauge theories using techniques of generalized differential cohomology. Particular emphasis is placed on the examples of generalized Maxwell theory and Cheeger-Simons cohomology, and of Ramond-Ramond fields in Type II superstring theory and differential K-theory.
Probing Non-Abelian Statistics with Quasiparticle Interferometry
Bonderson, Parsa; Shtengel, Kirill; Slingerland, J.K.
2006-07-07
We examine interferometric experiments in systems that exhibit non-Abelian braiding statistics, expressing outcomes in terms of the modular S-matrix. In particular, this result applies to fractional quantum Hall interferometry, and we give a detailed treatment of the Read-Rezayi states, providing explicit predictions for the recently observed {nu}=12/5 plateau.
Infinite-randomness fixed points for chains of non-Abelian quasiparticles.
Bonesteel, N E; Yang, Kun
2007-10-01
One-dimensional chains of non-Abelian quasiparticles described by SU(2)k Chern-Simons-Witten theory can enter random singlet phases analogous to that of a random chain of ordinary spin-1/2 particles (corresponding to k-->infinity). For k=2 this phase provides a random singlet description of the infinite-randomness fixed point of the critical transverse field Ising model. The entanglement entropy of a region of size L in these phases scales as S(L) approximately lnd/3 log(2)L for large L, where d is the quantum dimension of the particles. PMID:17930652
Gauge invariance of color confinement due to the dual Meissner effect caused by Abelian monopoles
Suzuki, Tsuneo; Hasegawa, Masayasu; Ishiguro, Katsuya; Koma, Yoshiaki; Sekido, Toru
2009-09-01
The mechanism of non-Abelian color confinement is studied in SU(2) lattice gauge theory in terms of the Abelian fields and monopoles extracted from non-Abelian link variables without adopting gauge fixing. First, the static quark-antiquark potential and force are computed with the Abelian and monopole Polyakov loop correlators, and the resulting string tensions are found to be identical to the non-Abelian string tension. These potentials also show the scaling behavior with respect to the change of lattice spacing. Second, the profile of the color-electric field between a quark and an antiquark is investigated with the Abelian and monopole Wilson loops. The color-electric field is squeezed into a flux tube due to monopole supercurrent with the same Abelian color direction. The parameters corresponding to the penetration and coherence lengths show the scaling behavior, and the ratio of these lengths, i.e., the Ginzburg-Landau parameter, indicates that the vacuum type is near the border of the type 1 and type 2 (dual) superconductors. These results are summarized in which the Abelian fundamental charge defined in an arbitrary color direction is confined inside a hadronic state by the dual Meissner effect. As the color-neutral state in any Abelian color direction corresponds to the physical color-singlet state, this effect explains non-Abelian color confinement and supports the existence of a gauge-invariant mechanism of color confinement due to the dual Meissner effect caused by Abelian monopoles.
NASA Astrophysics Data System (ADS)
Goldman, N.; Gerbier, F.; Lewenstein, M.
2013-07-01
We describe a scheme to engineer non-Abelian gauge potentials on a square optical lattice using laser-induced transitions. We emphasize the case of two-electron atoms, where the electronic ground state g is laser-coupled to a metastable state e within a state-dependent optical lattice. In this scheme, the alternating pattern of lattice sites hosting g and e states depicts a chequerboard structure, allowing for laser-assisted tunnelling along both spatial directions. In this configuration, the nuclear spin of the atoms can be viewed as a ‘flavour’ quantum number undergoing non-Abelian tunnelling along nearest-neighbour links. We show that this technique can be useful to simulate the equivalent of the Haldane quantum Hall model using cold atoms trapped in square optical lattices, offering an interesting route to realize Chern insulators. The emblematic Haldane model is particularly suited to investigate the physics of topological insulators, but requires, in its original form, complex hopping terms beyond nearest-neighbouring sites. In general, this drawback inhibits a direct realization with cold atoms, using standard laser-induced tunnelling techniques. We demonstrate that a simple mapping allows us to express this model in terms of matrix hopping operators that are defined on a standard square lattice. This mapping is investigated for two models that lead to anomalous quantum Hall phases. We discuss the practical implementation of such models, exploiting laser-induced tunnelling methods applied to the chequerboard optical lattice.
Heterotic non-Abelian string of a finite length
NASA Astrophysics Data System (ADS)
Monin, S.; Shifman, M.; Yung, A.
2016-06-01
We consider non-Abelian strings in N =2 supersymmetric quantum chromodynamics (QCD) with the U (N ) gauge group and Nf=N quark flavors deformed by a mass term for the adjoint matter. This deformation breaks N =2 supersymmetry down to N =1 . Dynamics of orientational zero modes on the string world sheet are described then by C P (N -1 ) model with N =(0 ,2 ) supersymmetry. We study the string of a finite length L assuming compactification on a cylinder (periodic boundary conditions). The world-sheet theory is solved in the large-N approximation. At N =∞ we find a rich phase structure in the (L ,u ) plane where u is a deformation parameter. At large L and intermediate u we find a phase with broken Z2 N symmetry, N vacua and a mass gap. At large values of L and u still larger we have the Z2 N-symmetric phase with a single vacuum and massless fermions. In both phases N =(0 ,2 ) supersymmetry is spontaneously broken. We also observe a phase with would-be broken SU (N ) symmetry at small L (it is broken only for N =∞ ). In the latter phase the mass gap vanishes and the vacuum energy is zero in the leading 1 /N approximation. We expect that at large but finite N corrections O (1 /N ) will break N =(0 ,2 ) supersymmetry. Simultaneously, the phase transitions will become rapid crossovers. Finally we discuss how the observed rich phase structure matches the N =(2 ,2 ) limit in which the world-sheet theory has a single phase with the mass gap independent of L .
Competing Abelian and non-Abelian topological orders in ν =1 /3 +1 /3 quantum Hall bilayers
NASA Astrophysics Data System (ADS)
Geraedts, Scott; Zaletel, Michael P.; Papić, Zlatko; Mong, Roger S. K.
2015-05-01
Bilayer quantum Hall systems, realized either in two separated wells or in the lowest two subbands of a wide quantum well, provide an experimentally realizable way to tune between competing quantum orders at the same filling fraction. Using newly developed density matrix renormalization group techniques combined with exact diagonalization, we return to the problem of quantum Hall bilayers at filling ν =1 /3 +1 /3 . We first consider the Coulomb interaction at bilayer separation d , bilayer tunneling energy ΔSAS, and individual layer width w , where we find a phase diagram which includes three competing Abelian phases: a bilayer Laughlin phase (two nearly decoupled ν =1 /3 layers), a bilayer spin-singlet phase, and a bilayer symmetric phase. We also study the order of the transitions between these phases. A variety of non-Abelian phases has also been proposed for these systems. While absent in the simplest phase diagram, by slightly modifying the interlayer repulsion we find a robust non-Abelian phase which we identify as the "interlayer-Pfaffian" phase. In addition to non-Abelian statistics similar to the Moore-Read state, it exhibits a novel form of bilayer-spin charge separation. Our results suggest that ν =1 /3 +1 /3 systems merit further experimental study.
Abelian gauge symmetries and proton decay in global F-theory GUTs
Grimm, Thomas W.; Weigand, Timo
2010-10-15
The existence of Abelian gauge symmetries in four-dimensional F-theory compactifications depends on the global geometry of the internal Calabi-Yau four-fold and has important phenomenological consequences. We study conceptual and phenomenological aspects of such U(1) symmetries along the Coulomb and the Higgs branch. As one application we examine Abelian gauge factors arising after a certain global restriction of the Tate model that goes beyond a local spectral cover analysis. In SU(5) grand unified theory (GUT) models this mechanism enforces a global U(1){sub X} symmetry that prevents dimension-4 proton decay and allows for an identification of candidate right-handed neutrinos. We invoke a detailed account of the singularities of Calabi-Yau four-folds and their mirror duals starting from an underlying E{sub 8} and E{sub 7}xU(1) enhanced Tate model. The global resolutions and deformations of these singularities can be used as the appropriate framework to analyze F-theory GUT models.
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
Dynamical breakdown of Abelian gauge chiral symmetry by strong Yukawa interactions
Benes, Petr; Brauner, Tomas; Hosek, Jiri
2007-03-01
We consider a model with anomaly-free Abelian gauge axial-vector symmetry, which is intended to mimic the standard electroweak gauge chiral SU(2){sub L}xU(1){sub Y} theory. Within this model we demonstrate: (1) Strong Yukawa interactions between massless fermion fields and a massive scalar field carrying the axial charge generate dynamically the fermion and boson proper self-energies, which are ultraviolet-finite and chirally noninvariant. (2) Solutions of the underlying Schwinger-Dyson equations found numerically exhibit a huge amplification of the fermion mass ratios as a response to mild changes of the ratios of the Yukawa couplings. (3) The 'would-be' Nambu-Goldstone boson is a composite of both the fermion and scalar fields, and it gives rise to the mass of the axial-vector gauge boson. (4) Spontaneous breakdown of the gauge symmetry further manifests by mass splitting of the complex scalar and by new symmetry-breaking vertices, generated at one loop. In particular, we work out in detail the cubic vertex of the Abelian gauge boson.
Non-Abelian Effects on D-Branes
Russo, Jorge G.
2008-07-28
We review different non-Abelian configurations of D-branes. We then extend the Myers dielectric effect to configurations with angular momentum. The resulting time-dependent N D0-brane bound states can be interpreted as describing rotating fuzzy ellipsoids. A similar solution exists also in the presence of a RR magnetic field, that we study in detail. We show that, for any finite N, above a certain critical angular momentum it is energetically more favorable for the bound state system to dissociate into an Abelian configuration of N D0-branes moving independently. We further study D-string configurations representing fuzzy funnels deformed by the magnetic field and by the rotational motion.
Braiding non-Abelian quasiholes in fractional quantum Hall states.
Wu, Yang-Le; Estienne, B; Regnault, N; Bernevig, B Andrei
2014-09-12
Quasiholes in certain fractional quantum Hall states are promising candidates for the experimental realization of non-Abelian anyons. They are assumed to be localized excitations, and to display non-Abelian statistics when sufficiently separated, but these properties have not been explicitly demonstrated except for the Moore-Read state. In this work, we apply the newly developed matrix product state technique to examine these exotic excitations. For the Moore-Read and the Z_{3} Read-Rezayi states, we estimate the quasihole radii, and determine the correlation lengths associated with the exponential convergence of the braiding statistics. We provide the first microscopic verification for the Fibonacci nature of the Z_{3} Read-Rezayi quasiholes. We also present evidence for the failure of plasma screening in the nonunitary Gaffnian wave function. PMID:25259996
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.
NASA Astrophysics Data System (ADS)
Zhu, W.; Gong, S. S.; Haldane, F. D. M.; Sheng, D. N.
2015-10-01
The non-Abelian topological order has attracted a lot of attention for its fundamental importance and exciting prospect of topological quantum computation. However, explicit demonstration or identification of the non-Abelian states and the associated statistics in a microscopic model is very challenging. Here, based on a density-matrix renormalization-group calculation, we provide a complete characterization of the universal properties of the bosonic Moore-Read state on a Haldane honeycomb lattice model at filling number ν =1 for larger systems, including both the edge spectrum and the bulk anyonic quasiparticle (QP) statistics. We first demonstrate that there are three degenerating ground states for each of which there is a definite anyonic flux threading through the cylinder. We identify the nontrivial countings for the entanglement spectrum in accordance with the corresponding conformal field theory. Through simulating a flux-inserting experiment, it is found that two of the Abelian ground states can be adiabatically connected, whereas the ground state in the Ising anyon sector evolves back to itself, which reveals the fusion rules between different QPs in real space. Furthermore, we calculate the modular matrices S and U , which contain all the information for the anyonic QPs, such as quantum dimensions, fusion rule, and topological spins.
Linear resistivity from non-abelian black holes
NASA Astrophysics Data System (ADS)
Herzog, Christopher P.; Huang, Kuo-Wei; Vaz, Ricardo
2014-11-01
Starting with the holographic p-wave superconductor, we show how to obtain a finite DC conductivity through a non-abelian gauge transformation. The translational symmetry is preserved. We obtain phenomenological similarities with high temperature cuprate superconductors. Our results suggest that a lattice or impurities are not essential to produce a finite DC resistivity with a linear temperature dependence. An analogous field theory calculation for free fermions, presented in the appendix, indicates our results may be a special feature of strong interactions.
Non-Abelian anomalies on a curved space with torsion
Cognola, G.; Giacconi, P.
1989-05-15
Using path-integral methods and /zeta/-function regularization a nonperturbative derivation of non-Abelian-covariant and consistent anomalies on a curved space with torsion is given. All terms depending on torsion, that one has in the expression of the consistent anomaly, can be eliminated by adding suitable counterterms to the Lagrangian density. In this way, the well-known result of Bardeen is recovered. The so-called ''covariant anomaly'' will be discussed too.
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.
Non-Abelian discrete gauge symmetries in F-theory
NASA Astrophysics Data System (ADS)
Grimm, Thomas W.; Pugh, Tom G.; Regalado, Diego
2016-02-01
The presence of non-Abelian discrete gauge symmetries in four-dimensional F-theory compactifications is investigated. Such symmetries are shown to arise from seven-brane configurations in genuine F-theory settings without a weak string coupling description. Gauge fields on mutually non-local seven-branes are argued to gauge both R-R and NS-NS two-form bulk axions. The gauging is completed into a generalisation of the Heisenberg group with either additional seven-brane gauge fields or R-R bulk gauge fields. The former case relies on having seven-brane fluxes, while the latter case requires torsion cohomology and is analysed in detail through the M-theory dual. Remarkably, the M-theory reduction yields an Abelian theory that becomes non-Abelian when translated into the correct duality frame to perform the F-theory limit. The reduction shows that the gauge coupling function depends on the gauged scalars and transforms non-trivially as required for the groups encountered. This field dependence agrees with the expectations for the kinetic mixing of seven-branes and is unchanged if the gaugings are absent.
Universal attractor in a highly occupied non-Abelian plasma
NASA Astrophysics Data System (ADS)
Berges, J.; Boguslavski, K.; Schlichting, S.; Venugopalan, R.
2014-06-01
We study the thermalization process in highly occupied non-Abelian plasmas at weak coupling. The nonequilibrium dynamics of such systems is classical in nature and can be simulated with real-time lattice gauge theory techniques. We provide a detailed discussion of this framework and elaborate on the results reported in J. Berges, K. Boguslavski, S. Schlichting, and R. Venugopalan, Phys. Rev. D 89, 074011 (2014), 10.1103/PhysRevD.89.074011 along with novel findings. We demonstrate the emergence of universal attractor solutions, which govern the nonequilibrium evolution on large time scales both for nonexpanding and expanding non-Abelian plasmas. The turbulent attractor for a nonexpanding plasma drives the system close to thermal equilibrium on a time scale t ˜Q-1αs-7/4. The attractor solution for an expanding non-Abelian plasma leads to a strongly interacting albeit highly anisotropic system at the transition to the low-occupancy or quantum regime. This evolution in the classical regime is, within the uncertainties of our simulations, consistent with the "bottom up" thermalization scenario [R. Baier, A. H. Mueller, D. Schiff, and D. T. Son, Phys. Lett. B 502, 51 (2001), 10.1016/S0370-2693(01)00191-5]. While the focus of this paper is to understand the nonequilibrium dynamics in weak coupling asymptotics, we also discuss the relevance of our results for larger couplings in the early time dynamics of heavy ion collision experiments.
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.
Simulation of non-Abelian lattice gauge fields with a single-component gas
NASA Astrophysics Data System (ADS)
Kosior, Arkadiusz; Sacha, Krzysztof
2014-07-01
We show that non-Abelian lattice gauge fields can be simulated with a single-component ultra-cold atomic gas in an optical-lattice potential. An optical lattice can be viewed as a Bravais lattice with a N-point basis. An atom located at different points of the basis can be considered as a particle in different internal states. The appropriate engineering of tunneling amplitudes of atoms in an optical lattice allows one to realize U(N) gauge potentials and control a mass of particles that experience such non-Abelian gauge fields. We provide and analyze a concrete example of an optical-lattice configuration that allows for simulation of a static U(2) gauge model with a constant Wilson loop and an adjustable mass of particles. In particular, we observe that the non-zero mass creates large conductive gaps in the energy spectrum, which could be important in the experimental detection of the transverse Hall conductivity.
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.
Lectures on Non-Abelian Bosonization
NASA Astrophysics Data System (ADS)
Tsvelik, A. M.
The following sections are included: * Introduction * Kac-Moody algebra * Conformal embedding. Sugawara Hamiltonian * SU(N)×SU(M) model * From the fermionic to WZNW model * The perturbed SUk(2) WZNW model * Correlation functions and Quasi Long Range order * Generalization from SU(2) to SU(N) * A model with Sp(2N) symmetry * Solution for the special case gcdw = gsc * Attraction in the orbital channel. Competing orders. Emergent integrability. ZN parafermions. * Parafermion zero modes * Conclusions and Acknowledgements * Appendix A. TBA equations for the Sp1(2N) model * Appendix B. Bosonization of of Z4 parafermions * References
Non-Abelian Aharonov-Bohm effect with the time-dependent gauge fields
NASA Astrophysics Data System (ADS)
Hosseini Mansoori, Seyed Ali; Mirza, Behrouz
2016-04-01
We investigate the non-Abelian Aharonov-Bohm (AB) effect for time-dependent gauge fields. We prove that the non-Abelian AB phase shift related to time-dependent gauge fields, in which the electric and magnetic fields are written in the adjoint representation of SU (N) generators, vanishes up to the first order expansion of the phase factor. Therefore, the flux quantization in a superconductor ring does not appear in the time-dependent Abelian or non-Abelian AB effect.
Development aid: manna or myth?
Horton, R
2000-09-23
In Ethiopia, obstetricians from Australia and New Zealand set up in 1975 the Addis Ababa Fistula Hospital to cater to women with fistula who were being turned away from local clinics. This kind of development assistance seems an ideal to be replicated--humane, skilled, practical, a mix of charitable and government aid, meeting an urgent clinical need, and enabling new knowledge to be passed on to locally trained doctors. However, the Fistula Hospital raises many troubling issues about its sustainability in a politically and economically unstable environment. It is important to recognize that the needs of Third World societies are completely different from their Western counterparts. Part of the problem lies in the unequal power relationship, availability of research funding, trained scientists, information, and equipment. Moreover, the highjacking of clinical and research agendas by Western organizations causes profound insult to the poor countries. Overall, it is noted that research is a significant means of achieving a sustainable health infrastructure. It is essential that development be viewed as a respectful dialogue and not the colonization of the imagination of other societies. Development, in this formulation, is not only development as freedom from deprivation and oppression but also the development of a common horizon or perspective. PMID:11009134
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.
Fields in nonaffine bundles. IV. Harmonious non-Abelian currents in string defects
NASA Astrophysics Data System (ADS)
Carter, Brandon
2010-11-01
This article continues the study of the category of harmonious field models that was recently introduced as a kinetically nonlinear generalization of the well-known harmonic category of multiscalar fields over a supporting brane world sheet in a target space with a curved Riemannian metric. Like the perfectly harmonious case of which a familiar example is provided by ordinary barotropic perfect fluids, another important subcategory is the simply harmonious case, for which it is shown that as well as “wiggle” modes of the underlying brane world sheet, and sound type longitudinal modes, there will also be transverse shake modes that propagate at the speed of light. Models of this type are shown to arise from a non-Abelian generalization of the Witten mechanism for conducting string formation by ordinary scalar fields with a suitable quartic self-coupling term in the action.
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.
On spectral synthesis on zero-dimensional Abelian groups
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.
The non-Abelian gauge theory of matrix big bangs
NASA Astrophysics Data System (ADS)
O'Loughlin, Martin; Seri, Lorenzo
2010-07-01
We study at the classical and quantum mechanical level the time-dependent Yang-Mills theory that one obtains via the generalisation of discrete light-cone quantization to singular homogeneous plane waves. The non-Abelian nature of this theory is known to be important for physics near the singularity, at least as far as the number of degrees of freedom is concerned. We will show that the quartic interaction is always subleading as one approaches the singularity and that close enough to t = 0 the evolution is driven by the diverging tachyonic mass term. The evolution towards asymptotically flat space-time also reveals some surprising features.
Non-Abelian gauge invariance and the infrared approximation
Cho, H.h.; Fried, H.M.; Grandou, T.
1988-02-15
Two constructions are given of infrared approximations, defined by a nonlocal configuration-space restrictions, which preserve the local, non-Abelian gauge invariance of SU(N) two-dimensional QCD (QCD/sub 2/). These continuum infrared methods are used to estimate the quenched order parameter
Non-Abelian monopole in the parameter space of point-like interactions
NASA Astrophysics Data System (ADS)
Ohya, Satoshi
2014-12-01
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.
Explicit non-Abelian monopoles and instantons in SU(N) pure Yang-Mills theory
Popov, Alexander D.
2008-06-15
It is well known that there are no static non-Abelian monopole solutions in pure Yang-Mills theory on Minkowski space R{sup 3,1}. I show that such solutions exist in SU(N) gauge theory on the spaces R{sup 2}xS{sup 2} and RxS{sup 1}xS{sup 2} with Minkowski signature (-+++). In the temporal gauge they are solutions of pure Yang-Mills theory on TxS{sup 2}, where T is R or S{sup 1}. Namely, imposing SO(3) invariance and some reality conditions, I consistently reduce the Yang-Mills model on the above spaces to a non-Abelian analog of the {phi}{sup 4} kink model whose static solutions give SU(N) monopole (-antimonopole) configurations on the space R{sup 1,1}xS{sup 2} via the above-mentioned correspondence. These solutions can also be considered as instanton configurations of Yang-Mills theory in 2+1 dimensions. The kink model on RxS{sup 1} admits also periodic sphaleron-type solutions describing chains of n kink-antikink pairs spaced around the circle S{sup 1} with arbitrary n>0. They correspond to chains of n static monopole-antimonopole pairs on the space RxS{sup 1}xS{sup 2} which can also be interpreted as instanton configurations in 2+1 dimensional pure Yang-Mills theory at finite temperature (thermal time circle). I also describe similar solutions in Euclidean SU(N) gauge theory on S{sup 1}xS{sup 3} interpreted as chains of n instanton-anti-instanton pairs.
Non-Abelian gauge redundancy and entropic ambiguities
NASA Astrophysics Data System (ADS)
Balachandran, A. P.; de Queiroz, A. R.; Vaidya, S.
2015-04-01
The von Neumann entropy of a generic quantum state is not unique unless the state can be uniquely decomposed as a sum of extremal or pure states. Therefore one reaches the remarkable possibility that there may be many entropies for a given state. We show that this happens if the GNS representation (of the algebra of observables in some quantum state) is reducible, and some representations in the decomposition occur with non-trivial degeneracy. This ambiguity in entropy, which can occur at zero temperature, can often be traced to a gauge symmetry emergent from the non-trivial topological character of the configuration space of the underlying system. We also establish the analogue of an H-theorem for this entropy by showing that its evolution is Markovian, determined by a stochastic matrix. After demonstrating this entropy ambiguity for the simple example of the algebra of 2 × 2 matrices, we argue that the degeneracies in the GNS representation can be interpreted as an emergent broken gauge symmetry, and play an important role in the analysis of emergent entropy due to non-Abelian anomalies. We work out the simplest situation with such non-Abelian symmetry, that of an ethylene molecule.
On spectral synthesis on element-wise compact Abelian groups
NASA Astrophysics Data System (ADS)
Platonov, S. S.
2015-08-01
Let G be an arbitrary locally compact Abelian group and let C(G) be the space of all continuous complex-valued functions on G. A closed linear subspace \\mathscr H\\subseteq C(G) is referred to as an invariant subspace if it is invariant with respect to the shifts τ_y\\colon f(x)\\mapsto f(xy), y\\in G. By definition, an invariant subspace \\mathscr H\\subseteq C(G) admits strict spectral synthesis if \\mathscr H coincides with the closure in C(G) of the linear span of all characters of G belonging to \\mathscr H. We say that strict spectral synthesis holds in the space C(G) on G if every invariant subspace \\mathscr H\\subseteq C(G) admits strict spectral synthesis. An element x of a topological group G is said to be compact if x is contained in some compact subgroup of G. A group G is said to be element-wise compact if all elements of G are compact. The main result of the paper is the proof of the fact that strict spectral synthesis holds in C(G) for a locally compact Abelian group G if and only if G is element-wise compact. Bibliography: 14 titles.
Origin of Abelian gauge symmetries in heterotic/F-theory duality
NASA Astrophysics Data System (ADS)
Cvetič, Mirjam; Grassi, Antonella; Klevers, Denis; Poretschkin, Maximilian; Song, Peng
2016-04-01
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, we derive both the Calabi-Yau geometry as well as 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) × U(1)) structure group, spectral covers containing torsional sections that seem to give rise to bundles with SU( m) × Z_k structure group and bundles with purely non-Abelian structure groups having a centralizer in E8 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. 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 Stückelberg mechanism in the lower-dimensional effective theory. 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.
Quantum Hall effects in a non-Abelian honeycomb lattice
NASA Astrophysics Data System (ADS)
Li, Ling; Hao, Ningning; Liu, Guocai; Bai, Zhiming; Li, Zai-Dong; Chen, Shu; Liu, W. M.
2015-12-01
We study the tunable quantum Hall effects in a non-Abelian honeycomb optical lattice which is a multi-Dirac-point system. We find that the quantum Hall effects present different features with the change in relative strengths of several perturbations. Namely, the quantum spin Hall effect can be induced by gauge-field-dressed next-nearest-neighbor hopping, which, together with a Zeeman field, can induce the quantum anomalous Hall effect characterized by different Chern numbers. Furthermore, we find that the edge states of the multi-Dirac-point system represent very different features for different boundary geometries, in contrast with the generic two-Dirac-point system. Our study extends the borders of the field of quantum Hall effects in a honeycomb optical lattice with multivalley degrees of freedom.
Simulation of non-Abelian gauge theories with optical lattices.
Tagliacozzo, L; Celi, A; Orland, P; Mitchell, M W; Lewenstein, M
2013-01-01
Many phenomena occurring in strongly correlated quantum systems still await conclusive explanations. The absence of isolated free quarks in nature is an example. It is attributed to quark confinement, whose origin is not yet understood. The phase diagram for nuclear matter at general temperatures and densities, studied in heavy-ion collisions, is not settled. Finally, we have no definitive theory of high-temperature superconductivity. Though we have theories that could underlie such physics, we lack the tools to determine the experimental consequences of these theories. Quantum simulators may provide such tools. Here we show how to engineer quantum simulators of non-Abelian lattice gauge theories. The systems we consider have several applications: they can be used to mimic quark confinement or to study dimer and valence-bond states (which may be relevant for high-temperature superconductors). PMID:24162080
Simulation of non-Abelian gauge theories with optical lattices
NASA Astrophysics Data System (ADS)
Tagliacozzo, L.; Celi, A.; Orland, P.; Mitchell, M. W.; Lewenstein, M.
2013-10-01
Many phenomena occurring in strongly correlated quantum systems still await conclusive explanations. The absence of isolated free quarks in nature is an example. It is attributed to quark confinement, whose origin is not yet understood. The phase diagram for nuclear matter at general temperatures and densities, studied in heavy-ion collisions, is not settled. Finally, we have no definitive theory of high-temperature superconductivity. Though we have theories that could underlie such physics, we lack the tools to determine the experimental consequences of these theories. Quantum simulators may provide such tools. Here we show how to engineer quantum simulators of non-Abelian lattice gauge theories. The systems we consider have several applications: they can be used to mimic quark confinement or to study dimer and valence-bond states (which may be relevant for high-temperature superconductors).
On formulae for the class number of real Abelian fields
NASA Astrophysics Data System (ADS)
Kuz'min, L. V.
1996-08-01
For a given real Abelian field k and a given prime natural number \\ell we obtain an index formula for the order of the group \\operatorname{Cl}(k)_{\\ell,\\varphi}, where \\operatorname{Cl}(k)_{\\ell} is the \\ell-component of the class group of k \\operatorname{Cl}(k)_{\\ell,\\varphi} denotes the \\varphi-component of \\operatorname{Cl}(k)_\\ell corresponding to a {\\mathbf Q}_\\ell-irreducible character \\varphi of the Galois group G(k/{\\mathbf Q}) that is trivial on the Sylow \\ell-subgroup of G(k/{\\mathbf Q}). This result generalizes a conjecture of Gras. The proofs rely on the "main conjecture" of Iwasawa theory.
Non-Abelian gerbes and enhanced Leibniz algebras
NASA Astrophysics Data System (ADS)
Strobl, Thomas
2016-07-01
We present the most general gauge-invariant action functional for coupled 1- and 2-form gauge fields with kinetic terms in generic dimensions, i.e., dropping eventual contributions that can be added in particular space-time dimensions only such as higher Chern-Simons terms. After appropriate field redefinitions it coincides with a truncation of the Samtleben-Szegin-Wimmer action. In the process one sees explicitly how the existence of a gauge-invariant functional enforces that the most general semistrict Lie 2-algebra describing the bundle of a non-Abelian gerbe gets reduced to a very particular structure, which, after the field redefinition, can be identified with the one of an enhanced Leibniz algebra. This is the first step towards a systematic construction of such functionals for higher gauge theories, with kinetic terms for a tower of gauge fields up to some highest form degree p , solved here for p =2 .
Non-Abelian gauge field theory in scale relativity
NASA Astrophysics Data System (ADS)
Nottale, Laurent; Célérier, Marie-Noëlle; Lehner, Thierry
2006-03-01
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.
Beyond parafermions: Defects and zero-modes in non-Abelian phases
NASA Astrophysics Data System (ADS)
Lindner, Netanel; Berg, Erez; Stern, Ady
Non-Abelian topological phases of matter can be utilized to encode and manipulate quantum information in a non-local manner, such that it is protected from imperfections in the implemented protocols and from interactions with the environment. The condition that the non-Abelian statistics of the anyons supports a computationally universal set of gates sets a very stringent requirement which is not met by many topological phases. We consider the possibility to enrich the possible topological operations supported by a non-Abelian topological phase by introducing defects into the system. We show that such defects bind zero modes which form a unique algebra that goes beyond the algebra of parafermions which describes defects in Abelian phases. For the case of a bi-layer containing Ising anyons, we show that by coupling zero modes one can obtain a set of topological operations that implements a universal set of gates.
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.
Collective states of non-Abelian quasiparticles in a magnetic field
NASA Astrophysics Data System (ADS)
Levin, Michael; Halperin, Bertrand I.
2009-05-01
Motivated by the physics of the Moore-Read ν=1/2 state away from half filling, we investigate collective states of non-Abelian e/4 quasiparticles in a magnetic field. We consider two types of collective states: incompressible liquids and Wigner crystals. In the incompressible liquid case, we construct a natural series of states which can be thought of as a non-Abelian generalization of the Laughlin states. These states are associated with a series of hierarchical states derived from the Moore-Read state—the simplest of which occur at filling fraction 8/17 and 7/13. Interestingly, we find that the hierarchical states are Abelian even though their parent state is non-Abelian. In the Wigner crystal case, we construct two candidate states. We find that they, too, are Abelian—in agreement with previous analysis.
NASA Astrophysics Data System (ADS)
Mross, David F.; Essin, Andrew; Alicea, Jason; Stern, Ady
2016-01-01
We show that boundaries of 3D weak topological insulators can become gapped by strong interactions while preserving all symmetries, leading to Abelian surface topological order. The anomalous nature of weak topological insulator surfaces manifests itself in a nontrivial action of symmetries on the quasiparticles; most strikingly, translations change the anyon types in a manner impossible in strictly 2D systems with the same symmetry. As a further consequence, screw dislocations form non-Abelian defects that trap Z4 parafermion zero modes.
A non-perturbative argument for the non-abelian Higgs mechanism
De Palma, G.; Strocchi, F.
2013-09-15
The evasion of massless Goldstone bosons by the non-abelian Higgs mechanism is proved by a non-perturbative argument in the local BRST gauge. -- Highlights: •The perturbative explanation of the Higgs mechanism (HM) is not under mathematical control. •We offer a non-perturbative proof of the absence of Goldstone bosons from the non-abelian HM. •Our non-perturbative proof in the BRST gauge avoids a mean field ansatz and expansion.
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.
Harada–Tsutsui gauge recovery procedure: From Abelian gauge anomalies to the Stueckelberg mechanism
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.
NASA Astrophysics Data System (ADS)
Robertson, Christopher; Worth, Graham A.
2015-10-01
The vibronic coupling Hamiltonian is a standard model used to describe the potential energy surfaces of systems in which non-adiabatic coupling is a key feature. This includes Jahn-Teller and Renner-Teller systems. The model approximates diabatic potential energy functions as polynomials expanded about a point of high symmetry. One must ensure the model Hamiltonian belongs to the totally symmetric irreducible representation of this point group. Here, a simple approach is presented to generate functions that form a basis for totally symmetric irreducible representations of non-Abelian groups and apply it to D∞h (2D) and O (3D). For the O group, the use of a well known basis-generating operator is also required. The functions generated for D∞h are then used to construct a ten state, four coordinate model of acetylene. The calculated absorption spectrum is compared to the experimental spectrum to serve as a validation of the approach.
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.
Fast non-Abelian geometric gates via transitionless quantum driving
Zhang, J.; Kyaw, Thi Ha; Tong, D. M.; Sjöqvist, Erik; Kwek, Leong-Chuan
2015-01-01
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. PMID:26687580
Fast non-Abelian geometric gates via transitionless quantum driving
NASA Astrophysics Data System (ADS)
Zhang, J.; Kyaw, Thi Ha; Tong, D. M.; Sjöqvist, Erik; Kwek, Leong-Chuan
2015-12-01
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.
Non-Abelian statistics of Luttinger holes in quantum wells
NASA Astrophysics Data System (ADS)
Simion, George; Lyanda-Geller, Yuli
2015-03-01
Non-Abelian quasiparticle excitations represent a key element of topologically protected quantum computing. Such exotic states appear in fractional quantum Hall (FQH) effect as eigenstates of N-body interaction potential. These potentials can be obtained by renormalization of electron-electron interactions in the presence of Landau level (LL) mixing. The properties of valence band holes makes them fundamentally different from electrons. In the presence of magnetic field, low-lying states do not exhibit fan-like diagram and several of the levels cross. Variation of magnetic field in the vicinity of level crossings serves as a knob that tunes LL mixing and enhances the 3-body interaction. 1 / 2 filling factor FQH is a state that was not observed in electron liquid, but has been observed for holes. The properties of the two dimensional charged quantum hole liquid in the presence of magnetic field are studied using the spherical geometry. The properties of the novel 1 / 2 state are discussed. Research was supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Award DE-SC0010544.
Topologically Massive Non-Abelian Theory:. Superfield Approach
NASA Astrophysics Data System (ADS)
Krishna, S.; Shukla, A.; Malik, R. P.
We apply the well-established techniques of geometrical superfield approach to Becchi-Rouet-Stora-Tyutin (BRST) formalism in the context of four (3+1)-dimensional (4D) dynamical non-Abelian 2-form gauge theory by exploiting its inherent "scalar" and "vector" gauge symmetry transformations and derive the corresponding off-shell nilpotent and absolutely anticommuting BRST and anti-BRST symmetry transformations. Our approach leads to the derivation of three (anti-)BRST invariant Curci-Ferrari (CF)-type restrictions that are found to be responsible for the absolute anticommutativity of the BRST and anti-BRST symmetry transformations. We derive the coupled Lagrangian densities that respect the (anti-)BRST symmetry transformations corresponding to the "vector" gauge transformations. We also capture the (anti-)BRST invariance of the CF-type restrictions and coupled Lagrangian densities within the framework of our superfield approach. We obtain, furthermore, the off-shell nilpotent (anti-)BRST symmetry transformations when the (anti-)BRST symmetry transformations corresponding to the "scalar" and "vector" gauge symmetries are merged together. These off-shell nilpotent "merged" (anti-)BRST symmetry transformations are, however, found to be non-anticommuting in nature.
Fast non-Abelian geometric gates via transitionless quantum driving.
Zhang, J; Kyaw, Thi Ha; Tong, D M; Sjöqvist, Erik; Kwek, Leong-Chuan
2015-01-01
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. PMID:26687580
Symmetric solitonic excitations of the (1 + 1)-dimensional Abelian-Higgs classical vacuum.
Diakonos, F K; Katsimiga, G C; Maintas, X N; Tsagkarakis, C E
2015-02-01
We study the classical dynamics of the Abelian-Higgs model in (1 + 1) space-time dimensions for the case of strongly broken gauge symmetry. In this limit the wells of the potential are almost harmonic and sufficiently deep, presenting a scenario far from the associated critical point. Using a multiscale perturbation expansion, the equations of motion for the fields are reduced to a system of coupled nonlinear Schrödinger equations. Exact solutions of the latter are used to obtain approximate analytical solutions for the full dynamics of both the gauge and Higgs field in the form of oscillons and oscillating kinks. Numerical simulations of the exact dynamics verify the validity of these solutions. We explore their persistence for a wide range of the model's single parameter, which is the ratio of the Higgs mass (m(H)) to the gauge-field mass (m(A)). We show that only oscillons oscillating symmetrically with respect to the "classical vacuum," for both the gauge and the Higgs field, are long lived. Furthermore, plane waves and oscillating kinks are shown to decay into oscillon-like patterns, due to the modulation instability mechanism. PMID:25768621
Dynamical symmetry breaking, gauge fields, and stability in four-Fermi, non-abelian interactions
Portney, M.N.
1983-01-01
The Nambu model of dynamical breaking of global symmetry is extended to the case of non-abelian SU(N) models. The possible patterns of symmetry breaking are investigated, and the masses of the composite spinless particles are found. Corresponding to each broken generator, this composite is the massless Goldstone boson. When the global symmetries are made local by the addition of gauge fields, the composite pseudoscalar Goldstone bosons disappear and the axial gauge fields become massive. This is analogous to the Higgs mechanism, but without the introduction of fundamental scalar fields. The composite scalar Goldstone bosons remain in the theory, and the vector gauge fields are still massless. This is in agreement with the charge conjugation argument. The stability of the possible solutions is discussed using several criteria. It is concluded that in theories with zero bare mass, if a nontrivial solution exists, the completely symmetric massive solution is realized. If the bare mass is symmetric and non-zero, asymmetric solutions may be found, with corresponding scalar Goldstone composites. These violate the persistent mass condition of Preskill and Weinberg.
Universal topological quantum computation from a superconductor/Abelian quantum Hall heterostructure
NASA Astrophysics Data System (ADS)
Mong, Roger
2014-03-01
Non-Abelian anyons promise to reveal spectacular features of quantum mechanics that could ultimately provide the foundation for a decoherence-free quantum computer. A key breakthrough in the pursuit of these exotic particles originated from Read and Green's observation that the Moore-Read quantum Hall state and a (relatively simple) two-dimensional p + ip superconductor both support so-called Ising non-Abelian anyons. Here we establish a similar correspondence between the Z3 Read-Rezayi quantum Hall state and a novel two-dimensional superconductor in which charge- 2 e Cooper pairs are built from fractionalized quasiparticles. In particular, both phases harbor Fibonacci anyons that--unlike Ising anyons--allow for universal topological quantum computation solely through braiding. Using a variant of Teo and Kane's construction of non-Abelian phases from weakly coupled chains, we provide a blueprint for such a superconductor using Abelian quantum Hall states interlaced with an array of superconducting islands. These results imply that one can, in principle, combine well-understood and widely available phases of matter to realize non-Abelian anyons with universal braid statistics.
Universal Topological Quantum Computation from a Superconductor-Abelian Quantum Hall Heterostructure
NASA Astrophysics Data System (ADS)
Mong, Roger S. K.; Clarke, David J.; Alicea, Jason; Lindner, Netanel H.; Fendley, Paul; Nayak, Chetan; Oreg, Yuval; Stern, Ady; Berg, Erez; Shtengel, Kirill; Fisher, Matthew P. A.
2014-01-01
Non-Abelian anyons promise to reveal spectacular features of quantum mechanics that could ultimately provide the foundation for a decoherence-free quantum computer. A key breakthrough in the pursuit of these exotic particles originated from Read and Green's observation that the Moore-Read quantum Hall state and a (relatively simple) two-dimensional p+ip superconductor both support so-called Ising non-Abelian anyons. Here, we establish a similar correspondence between the Z3 Read-Rezayi quantum Hall state and a novel two-dimensional superconductor in which charge-2e Cooper pairs are built from fractionalized quasiparticles. In particular, both phases harbor Fibonacci anyons that—unlike Ising anyons—allow for universal topological quantum computation solely through braiding. Using a variant of Teo and Kane's construction of non-Abelian phases from weakly coupled chains, we provide a blueprint for such a superconductor using Abelian quantum Hall states interlaced with an array of superconducting islands. Fibonacci anyons appear as neutral deconfined particles that lead to a twofold ground-state degeneracy on a torus. In contrast to a p+ip superconductor, vortices do not yield additional particle types, yet depending on nonuniversal energetics can serve as a trap for Fibonacci anyons. These results imply that one can, in principle, combine well-understood and widely available phases of matter to realize non-Abelian anyons with universal braid statistics. Numerous future directions are discussed, including speculations on alternative realizations with fewer experimental requirements.
Bilayer quantum Hall phase transitions and the orbifold non-Abelian fractional quantum Hall states
Barkeshli, Maissam; Wen Xiaogang
2011-09-15
We study continuous quantum phase transitions that can occur in bilayer fractional quantum Hall (FQH) systems as the interlayer tunneling and interlayer repulsion are tuned. We introduce a slave-particle gauge theory description of a series of continuous transitions from the (ppq) Abelian bilayer states to a set of non-Abelian FQH states, which we dub orbifold FQH states, of which the Z{sub 4} parafermion (Read-Rezayi) state is a special case. This provides an example in which Z{sub 2} electron fractionalization leads to non-Abelian topological phases. The naive ''ideal'' wave functions and ideal Hamiltonians associated with these orbifold states do not in general correspond to incompressible phases but, instead, lie at a nearby critical point. We discuss this unusual situation from the perspective of the pattern-of-zeros/vertex algebra frameworks and discuss implications for the conceptual foundations of these approaches. Due to the proximity in the phase diagram of these non-Abelian states to the (ppq) bilayer states, they may be experimentally relevant, both as candidates for describing the plateaus in single-layer systems at filling fractions 8/3 and 12/5 and as a way to tune to non-Abelian states in double-layer or wide quantum wells.
Non-abelian dynamics in first-order cosmological phase transitions
Johnson, Mikkel B.; Kisslinger, Leonard S.; Henley, Ernest M.; Hwang, P. W-Y.; Stevens, T.
2004-01-01
Bubble collisions in cosmological phase transitions are explored, taking the non-abelian character of the gauge fields into account. Both the QCD and electroweak phase transitions are considered. Numerical solutions of the field equations in several limits are presented. The investigations reported in this talk have been motivated by an interest in studying cosmological phase transitions quantitatively, taking the non-abelian character of the gauge fields into account. Ultimately, we hope to identify observable consequences of cosmological phase transitions. First-order phase transitions proceed by nucleation of bubbles of the broken phase in the background of the symmetric phase. Bubble collisions are of special interest, as they may lead to observable effects such as correlations in the cosmic microwave background (CMB) or as seeds of galactic and extra-galactic magnetic fields. The quantum chromodynamic (QCD) and the electroweak (EW) phase transitions are both candidates of interest in these respects. The Lagrangian driving both the QCD and the EW phase transitions are essentially known and make it possible to approach the physics of the phase transitions from first principles. However, a difficulty to making reliable predictions is that the fundamental guage fields in both these instances are non-abelian: the gluon field in QCD and the W and Z fields in the EW case. The quantitative role of non-abelian fields in cosmological phase transitions is poorly known and difficult to calculate due to the nonlinearities arising from the non-abelian character of the gauge fields.
Studying critical string emerging from non-Abelian vortex in four dimensions
NASA Astrophysics Data System (ADS)
Koroteev, P.; Shifman, M.; Yung, A.
2016-08-01
Recently a special vortex string was found [5] in a class of soliton vortices supported in four-dimensional Yang-Mills theories that under certain conditions can become infinitely thin and can be interpreted as a critical ten-dimensional string. The appropriate bulk Yang-Mills theory has the U (2) gauge group and the Fayet-Iliopoulos term. It supports semilocal non-Abelian vortices with the world-sheet theory for orientational and size moduli described by the weighted CP (2 , 2) model. The full target space is R4 ×Y6 where Y6 is a non-compact Calabi-Yau space. We study the above vortex string from the standpoint of string theory, focusing on the massless states in four dimensions. In the generic case all massless modes are non-normalizable, hence, no massless gravitons or vector fields are predicted in the physical spectrum. However, at the selfdual point (at strong coupling) weighted CP (2 , 2) admits deformation of the complex structure, resulting in a single massless hypermultiplet in the bulk. We interpret it as a composite "baryon."
On Geometrical Interpretation of Non-Abelian D and F-Flat Direction Constraints
NASA Astrophysics Data System (ADS)
Walker, Joel; Cleaver, Gerald; Nanopoulos, Dimitri; Perkins, John
2004-10-01
In order to produce a low energy effective field theory from a string model, it is necessary to specify a vacuum state. In order that this vacuum be supersymmetric, it is well known that all field expectation values must be along so-called flat directions, leaving the F- and D-terms of the scalar potential to be zero. The situation becomes particularly interesting when one attempts to realize such directions while assigning VEVS to fields transforming under non-Abelian representations of the gauge group. Since the expectation value is now shared among multiple components of a field, satisfaction of flatness becomes an inherently geometrical problem in the group space. Furthermore, the possibility emerges that a single seemingly dangerous F-term might experience a self-cancellation among its components. The hope exists that the geometric language can provide an intuitive and immediate recognition of when the D and F conditions are simultaneously compatible, as well as a powerful tool for their comprehensive classification. This is the avenue explored in this study, and applied to the cases of SU(2) and SO(2N), relevant respectively to previous attempts at reproducing the MSSM and the flipped SU(5) GUT. It is hoped that the techniques encountered will be of benefit in extending the viability of the quasi-realistic phenomenologies already developed.
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
Controlling and probing non-abelian emergent gauge potentials in spinor Bose-Fermi mixtures
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
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).
Electric-magnetic dualities in non-abelian and non-commutative gauge theories
NASA Astrophysics Data System (ADS)
Ho, Jun-Kai; Ma, Chen-Te
2016-08-01
Electric-magnetic dualities are equivalence between strong and weak coupling constants. A standard example is the exchange of electric and magnetic fields in an abelian gauge theory. We show three methods to perform electric-magnetic dualities in the case of the non-commutative U (1) gauge theory. The first method is to use covariant field strengths to be the electric and magnetic fields. We find an invariant form of an equation of motion after performing the electric-magnetic duality. The second method is to use the Seiberg-Witten map to rewrite the non-commutative U (1) gauge theory in terms of abelian field strength. The third method is to use the large Neveu Schwarz-Neveu Schwarz (NS-NS) background limit (non-commutativity parameter only has one degree of freedom) to consider the non-commutative U (1) gauge theory or D3-brane. In this limit, we introduce or dualize a new one-form gauge potential to get a D3-brane in a large Ramond-Ramond (R-R) background via field redefinition. We also use perturbation to study the equivalence between two D3-brane theories. Comparison of these methods in the non-commutative U (1) gauge theory gives different physical implications. The comparison reflects the differences between the non-abelian and non-commutative gauge theories in the electric-magnetic dualities. For a complete study, we also extend our studies to the simplest abelian and non-abelian p-form gauge theories, and a non-commutative theory with the non-abelian structure.
Cold Atoms in Non-Abelian Gauge Potentials: From the Hofstadter Moth to Lattice Gauge Theory
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.
Momentum subtraction scheme renormalization group functions in the maximal Abelian gauge
NASA Astrophysics Data System (ADS)
Bell, J. M.; Gracey, J. A.
2013-10-01
The one-loop 3-point vertex functions of QCD in the maximal Abelian gauge are evaluated at the fully symmetric point at one loop. As a consequence the theory is renormalized in the various momentum subtraction schemes, which are defined by the trivalent vertices, as well as in the MS¯ scheme. From these the two-loop renormalization group functions in the momentum schemes are derived using the one-loop conversion functions. In parallel we repeat the analysis for the Curci-Ferrari gauge, which corresponds to the maximal Abelian gauge in a specific limit. The relation between the Λ parameters in different schemes is also provided.
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.
Kauffman knot polynomials in classical abelian Chern-Simons field theory
Liu Xin
2010-12-15
Kauffman knot polynomial invariants are discovered in classical abelian Chern-Simons field theory. A topological invariant t{sup I(L)} is constructed for a link L, where I is the abelian Chern-Simons action and t a formal constant. For oriented knotted vortex lines, t{sup I} satisfies the skein relations of the Kauffman R-polynomial; for un-oriented knotted lines, t{sup I} satisfies the skein relations of the Kauffman bracket polynomial. As an example the bracket polynomials of trefoil knots are computed, and the Jones polynomial is constructed from the bracket polynomial.
NASA Astrophysics Data System (ADS)
Liu, YiMin; Liu, RongWan
2014-12-01
A potentially practical scheme is proposed to realize optical quantum simulation of artificial Abelian gauge field in a scalable architecture consisting of cold atomic ensembles with optical cavities. In the present model, the collective excitations of cold atomic ensembles can be converted to the bosonic modes within the low-excitation limit, where the structure of two-dimension (2D) square plaquette enables the polaritons to move like a charged particle subjected to an external magnetic field. We find that the energy spectrum of this hybrid system exhibits a shape of Hofstadter buttery. Our work provides a different perspective to the quantum simulation of condensed matter and many-body physics in the context of cavity quantum electrodynamics. The experimental feasibility are justified using the existing techniques.
Experimental evidence for non-Abelian gauge potentials in twisted graphene bilayers
NASA Astrophysics Data System (ADS)
Yin, Long-Jing; Qiao, Jia-Bin; Zuo, Wei-Jie; Li, Wen-Tian; He, Lin
2015-08-01
Non-Abelian gauge potentials are quite relevant in subatomic physics, but they are relatively rare in a condensed matter context. Here we report the experimental evidence for non-Abelian gauge potentials in twisted graphene bilayers by scanning tunneling microscopy and spectroscopy. At a magic twisted angle, θ ≈(1.11±0.05 ) ∘ , a pronounced sharp peak, which arises from the nondispersive flat bands at the charge neutrality point, is observed in the tunneling density of states due to the action of the non-Abelian gauge fields. Moreover, we observe confined electronic states in the twisted bilayer, as manifested by regularly spaced tunneling peaks with energy spacing δ E ≈vF/D ≈70 meV (here vF is the Fermi velocity of graphene and D is the period of the moiré patterns). This indicates that the non-Abelian gauge potentials in twisted graphene bilayers confine low-energy electrons into a triangular array of quantum dots following the modulation of the moiré patterns. Our results also directly demonstrate that the Fermi velocity in twisted bilayers can be tuned from about 106m /s to zero by simply reducing the twisted angle of about 2∘.
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.
Non-abelian dark matter solutions for Galactic gamma-ray excess and Perseus 3.5 keV X-ray line
Cheung, Kingman; Huang, Wei-Chih; Tsai, Yue-Lin Sming
2015-05-26
We attempt to explain simultaneously the Galactic center gamma-ray excess and the 3.5 keV X-ray line from the Perseus cluster based on a class of non-abelian SU(2) DM models, in which the dark matter and an excited state comprise a “dark” SU(2) doublet. The non-abelian group kinetically mixes with the standard model gauge group via dimensions-5 operators. The dark matter particles annihilate into standard model fermions, followed by fragmentation and bremsstrahlung, and thus producing a continuous spectrum of gamma-rays. On the other hand, the dark matter particles can annihilate into a pair of excited states, each of which decays back into the dark matter particle and an X-ray photon, which has an energy equal to the mass difference between the dark matter and the excited state, which is set to be 3.5 keV. The large hierarchy between the required X-ray and γ-ray annihilation cross-sections can be achieved by a very small kinetic mixing between the SM and dark sector, which effectively suppresses the annihilation into the standard model fermions but not into the excited state.
NASA Astrophysics Data System (ADS)
Hong, Xiaochun; Xie, Shaolong; Chen, Longwei
In this study, we determine the associated number of zeros for Abelian integrals in four classes of quadratic reversible centers of genus one. Based on the results of [Li et al., 2002b],, we prove that the upper bounds of the associated number of zeros for Abelian integrals with orbits formed by conics, cubics, quartics, and sextics, under polynomial perturbations of arbitrary degree n, depend linearly on n.
Study of the zero modes of the Faddeev–Popov operator in the maximal Abelian gauge
Capri, M.A.L. Guimaraes, M.S. Lemes, V.E.R. Sorella, S.P. Tedesco, D.G.
2014-05-15
A study of the zero modes of the Faddeev–Popov operator in the maximal Abelian gauge is presented in the case of the gauge group SU(2) and for different Euclidean space–time dimensions. Explicit examples of classes of normalizable zero modes and corresponding gauge field configurations are constructed by taking into account two boundary conditions, namely: (i) the finite Euclidean Yang–Mills action, (ii) the finite Hilbert norm. -- Highlights: •We study the zero modes of the Faddeev–Popov operator in the maximal Abelian gauge. •For d=2 we obtain solutions with finite action but not finite Hilbert norm. •For d=3,4 we obtain solutions with finite action and finite Hilbert norm. •These results can be compared with those previously obtained in the Landau gauge.
a Note on the - Invariant Lagrangian Densities for the Free Abelian 2-FORM Gauge Theory
NASA Astrophysics Data System (ADS)
Gupta, Saurabh; Malik, R. P.
We show that the previously known off-shell nilpotent (s(a)b2 = 0) and absolutely anticommuting (sb sab + sab sb = 0) Becchi-Rouet-Stora-Tyutin (BRST) transformations (sb) and anti-BRST transformations (sab) are the symmetry transformations of the appropriate Lagrangian densities of a four (3+1)-dimensional (4D) free Abelian 2-form gauge theory which do not explicitly incorporate a very specific constrained field condition through a Lagrange multiplier 4D vector field. The above condition, which is the analogue of the Curci-Ferrari restriction of the non-Abelian 1-form gauge theory, emerges from the Euler-Lagrange equations of motion of our present theory and ensures the absolute anticommutativity of the transformations s(a)b. Thus, the coupled Lagrangian densities, proposed in our present investigation, are aesthetically more appealing and more economical.
Bulk-Edge Correspondence in 2+1-Dimensional Abelian Topological Phases
NASA Astrophysics Data System (ADS)
Plamadeala, Eugeniu; Cheng, Meng; Mulligan, Michael; Nayak, Chetan; Cano, Jennifer; Yard, Jon
2014-03-01
The same bulk two-dimensional topological phase can have multiple distinct, fully-chiral edge phases. We show that this can occur in the integer quantum Hall and Abelian fractional quantum Hall states. We give a general criterion for the existence of multiple distinct chiral edge phases for the same bulk phase and discuss experimental consequences. We show that fermionic systems can have edge phases with only bosonic low-energy excitations and discuss a fermionic generalization of the relation between bulk topological spins and the central charge. The latter follows from our demonstration that every fermionic topological phase can be represented as a bosonic topological phase, together with some number of filled Landau levels. Our analysis shows that every Abelian topological phase can be decomposed into a tensor product of theories associated with prime numbers p in which every quasiparticle has a topological spin that is a pn-th root of unity for some n.
Non-Abelian vortices on a cylinder: Duality between vortices and walls
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.
Topological phase transitions on a triangular optical lattice with non-Abelian gauge fields
NASA Astrophysics Data System (ADS)
Iskin, M.
2016-03-01
We study the mean-field BCS-BEC evolution of a uniform Fermi gas on a single-band triangular lattice and construct its ground-state phase diagrams, showing a wealth of topological quantum phase transitions between gapped and gapless superfluids that are induced by the interplay of an out-of-plane Zeeman field and a generic non-Abelian gauge field.
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.
Computer-assisted techniques for the verification of the Chebyshev property of Abelian integrals
NASA Astrophysics Data System (ADS)
Figueras, Jordi-Lluís; Tucker, Warwick; Villadelprat, Jordi
We develop techniques for the verification of the Chebyshev property of Abelian integrals. These techniques are a combination of theoretical results, analysis of asymptotic behavior of Wronskians, and rigorous computations based on interval arithmetic. We apply this approach to tackle a conjecture formulated by Dumortier and Roussarie in [F. Dumortier, R. Roussarie, Birth of canard cycles, Discrete Contin. Dyn. Syst. 2 (2009) 723-781], which we are able to prove for q≤2.
Entanglement of Vortex Lattices for Ultracold Bose Gases in a Non-Abelian Gauge Potential
NASA Astrophysics Data System (ADS)
Cheng, Szu-Cheng; Jiang, T. F.; Jheng, Shih-Da; Atomic; Molecular Physics Team; Atomic; Molecular Physics Team
We develop a theory, referred to as the von Neumann lattice in a higher Landau level, for vortex lattices labelled by an integral number of flux quantums per unit cell in a higher Landau level. Using this lattice theory, we study the vortex lattice states of a pseudospin-1/2 ultracold Bose gas with contact interactions in a non-Abelian gauge potential. In addition to a uniform magnetic field, the Bose gas is also subjected to a non-Abelian gauge field, which creates an effect of the spin-orbit coupling to lift the spin degeneracy of the Landau levels. Because of interactions from the spin-orbit coupling, there are new degenerate points of the single particle spectrum due to the crossings of two Landau levels at certain coupling strengths. We show that interactions from the spin-orbit coupling force the nature and structure of the vortex lattice changing dramatically if the strength of the non-Abelian gauge field is increasing. We also find that the ground state of the vortex lattice at a degenerate point exhibits strong correlation and entanglement involving vortex lattices from different Landau levels. This entangled state builds the connection between two phases of vortex lattices during the first order phase transition of the adiabatic evolution.
Non-Abelian black holes in D=5 maximal gauged supergravity
Cvetic, M.; Lue, H.; Pope, C. N.
2010-02-15
We investigate static non-Abelian black hole solutions of anti-de Sitter (AdS) Einstein-Yang-Mills-dilaton gravity, which is obtained as a consistent truncation of five-dimensional maximal gauged supergravity. If the dilaton is (consistently) set to zero, the remaining equations of motion, with a spherically-symmetric ansatz, may be derived from a superpotential. The associated first-order equations admit an explicit solution supported by a non-Abelian SU(2) gauge potential, which has a logarithmically growing mass term. In an extremal limit the horizon geometry becomes AdS{sub 2}xS{sup 3}. If the dilaton is also excited, the equations of motion cannot easily be solved explicitly, but we obtain the asymptotic form of the more general non-Abelian black holes in this case. An alternative consistent truncation, in which the Yang-Mills fields are set to zero, also admits a description in terms of a superpotential. This allows us to construct explicit wormhole solutions (neutral spherically-symmetric domain walls). These solutions may be generalized to dimensions other than five.
Application of abelian holonomy formalism to the elementary theory of numbers
NASA Astrophysics Data System (ADS)
Abe, Yasuhiro
2012-05-01
We consider an abelian holonomy operator in two-dimensional conformal field theory with zero-mode contributions. The analysis is made possible by use of a geometric-quantization scheme for abelian Chern-Simons theory on S1 × S1 × R. We find that a purely zero-mode part of the holonomy operator can be expressed in terms of Riemann's zeta function. We also show that a generalization of linking numbers can be obtained in terms of the vacuum expectation values of the zero-mode holonomy operators. Inspired by mathematical analogies between linking numbers and Legendre symbols, we then apply these results to a space of Fp = Z/pZ, where p is an odd prime number. This enables us to calculate "scattering amplitudes" of identical odd primes in the holonomy formalism. In this framework, the Riemann hypothesis can be interpreted by means of a physically obvious fact, i.e., there is no notion of "scattering" for a single-particle system. Abelian gauge theories described by the zero-mode holonomy operators will be useful for studies on quantum aspects of topology and number theory.
Manna in winter: indigenous Americans and blueberries
Technology Transfer Automated Retrieval System (TEKTRAN)
More than 35 species of blueberries (Vaccinium L.) and huckleberries (Vaccinium and Gaylussacia Kunth.) are indigenous to North America. The indigenous North American Peoples, wise in the ways of survival, recognized the quality of these edible fruits and revered these plants. Beyond food needs, the...
Non-abelian gauge extensions for B-decay anomalies
NASA Astrophysics Data System (ADS)
Boucenna, Sofiane M.; Celis, Alejandro; Fuentes-Martín, Javier; Vicente, Avelino; Virto, Javier
2016-09-01
We study the generic features of minimal gauge extensions of the Standard Model in view of recent hints of lepton-flavor non-universality in semi-leptonic b → sℓ+ℓ- and b → cℓν decays. We classify the possible models according to the symmetry-breaking pattern and the source of flavor non-universality. We find that in viable models the SU (2) L factor is embedded non-trivially in the extended gauge group, and that gauge couplings should be universal, hinting to the presence of new degrees of freedom sourcing non-universality. Finally, we provide an explicit model that can explain the B-decay anomalies in a coherent way and confront it with the relevant phenomenological constraints.
Magnetic-field-tuned Aharonov-Bohm oscillations and evidence for non-Abelian anyons at ν = 5/2.
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. PMID:24237543
Properties of a consistent Lorentz-violating Abelian gauge theory
Alexandre, J.; Vergou, A.
2011-06-15
A Lorentz-violating modification of massless QED is proposed, with higher-order space derivatives for the photon field. The fermion dynamical mass generation is studied with the Schwinger-Dyson approach. Perturbative properties of the model are calculated at one-loop and discussed at higher-order loops, showing the consistency of the model. We explain that there is no contradiction with the definition of the speed of light c, although fermions see an effective light cone, with a maximum speed smaller than c.
Chaos, scaling and existence of a continuum limit in classical non-Abelian lattice gauge theory
Nielsen, H.B.; Rugh, H.H.; Rugh, S.E.
1996-12-31
We discuss space-time chaos and scaling properties for classical non-Abelian gauge fields discretized on a spatial lattice. We emphasize that there is a {open_quote}no go{close_quotes} for simulating the original continuum classical gauge fields over a long time span since there is a never ending dynamical cascading towards the ultraviolet. We note that the temporal chaotic properties of the original continuum gauge fields and the lattice gauge system have entirely different scaling properties thereby emphasizing that they are entirely different dynamical systems which have only very little in common. Considered as a statistical system in its own right the lattice gauge system in a situation where it has reached equilibrium comes closest to what could be termed a {open_quotes}continuum limit{close_quotes} in the limit of very small energies (weak non-linearities). We discuss the lattice system both in the limit for small energies and in the limit of high energies where we show that there is a saturation of the temporal chaos as a pure lattice artifact. Our discussion focuses not only on the temporal correlations but to a large extent also on the spatial correlations in the lattice system. We argue that various conclusions of physics have been based on monitoring the non-Abelian lattice system in regimes where the fields are correlated over few lattice units only. This is further evidenced by comparison with results for Abelian lattice gauge theory. How the real time simulations of the classical lattice gauge theory may reach contact with the real time evolution of (semi-classical aspects of) the quantum gauge theory (e.g. Q.C.D.) is left an important question to be further examined.
Understanding the physics of a possible non-Abelian fractional quantum hall effect state.
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.
Bulk-edge correspondence in (2 + 1)-dimensional Abelian topological phases
NASA Astrophysics Data System (ADS)
Cano, Jennifer; Cheng, Meng; Mulligan, Michael; Nayak, Chetan; Plamadeala, Eugeniu; Yard, Jon
2014-03-01
The same bulk two-dimensional topological phase can have multiple distinct, fully chiral edge phases. We show that this can occur in the integer quantum Hall states at ν =8 and 12, with experimentally testable consequences. We show that this can occur in Abelian fractional quantum Hall states as well, with the simplest examples being at ν =8/7,12/11,8/15,16/5. We give a general criterion for the existence of multiple distinct chiral edge phases for the same bulk phase and discuss experimental consequences. Edge phases correspond to lattices while bulk phases correspond to genera of lattices. Since there are typically multiple lattices in a genus, the bulk-edge correspondence is typically one-to-many; there are usually many stable fully chiral edge phases corresponding to the same bulk. We explain these correspondences using the theory of integral quadratic forms. We show that fermionic systems can have edge phases with only bosonic low-energy excitations and discuss a fermionic generalization of the relation between bulk topological spins and the central charge. The latter follows from our demonstration that every fermionic topological phase can be represented as a bosonic topological phase, together with some number of filled Landau levels. Our analysis shows that every Abelian topological phase can be decomposed into a tensor product of theories associated with prime numbers p in which every quasiparticle has a topological spin that is a pnth root of unity for some n. It also leads to a simple demonstration that all Abelian topological phases can be represented by U(1)N Chern-Simons theory parameterized by a K matrix.
Role of nonlocal probes of thermalization for a strongly interacting non-Abelian plasma
NASA Astrophysics Data System (ADS)
Bellantuono, L.; Colangelo, P.; De Fazio, F.; Giannuzzi, F.; Nicotri, S.
2016-07-01
The thermalization process of an out-of-equilibrium boost-invariant strongly interacting non-Abelian plasma is investigated using a holographic method. Boundary sourcing, a distortion of the boundary metric, is employed to drive the system far from equilibrium. Thermalization is analyzed in the fully dynamical system through nonlocal probes: the equal-time two-point correlation function of large conformal dimension operators in the boundary theory, and Wilson loops of different shapes. A dependence of the thermalization time on the size of the probes is found, which can be compared to the result of local observables: the onset of thermalization is first observed at short distances.
Probing Non-Abelian Statistics of Majorana Fermions in Ultracold Atomic Superfluid
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.
Mimetic discretization of the Abelian Chern-Simons theory and link invariants
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.
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.
Non-Abelian Berry-s phase effects and optical pumping of atoms
Segert, J.
1987-11-01
We predict experimentally verifiable manifestations of non-Abelian Berry's phase effects for atoms in external collinear electric and magnetic fields. The field strengths are arranged so as to cause accidental degeneracy between atomic states. The relevant theoretical results, which have been presented in detail elsewhere, are summarized and explained. We propose an experiment using optically pumped metastable multiplets of Pb/sup 208/ in an atomic beam apparatus to test these predictions. We estimate required experimental parameters, and conclude that the proposed experiment can realistically be performed. copyright 1987 Academic Press, Inc.
NASA Astrophysics Data System (ADS)
Borgh, Magnus O.; Ruostekoski, Janne
2016-05-01
We demonstrate that multiple interaction-dependent defect core structures as well as dynamics of non-Abelian vortices can be realized in the biaxial nematic (BN) phase of a spin-2 atomic Bose-Einstein condensate (BEC). An experimentally simple protocol may be used to break degeneracy with the uniaxial nematic phase. We show that a discrete spin-space symmetry in the core may be reflected in a breaking of its spatial symmetry. The discrete symmetry of the BN order parameter leads to non-commuting vortex charges. We numerically simulate reconnection of non-Abelian vortices, demonstrating formation of the obligatory rung vortex. In addition to atomic BECs, non-Abelian vortices are theorized in, e.g., liquid crystals and cosmic strings. Our results suggest the BN spin-2 BEC as a prime candidate for their realization. We acknowledge financial support from the EPSRC.
Quantum phase transition of ultracold bosons in the presence of a non-Abelian synthetic gauge field
Grass, T.; Saha, K.; Sengupta, K.; Lewenstein, M.
2011-11-15
We study the Mott phases and the superfluid-insulator transition of two-component ultracold bosons on a square optical lattice in the presence of a non-Abelian synthetic gauge field, which renders a SU(2)-hopping matrix for the bosons. Using a resummed hopping expansion, we calculate the excitation spectra in the Mott insulating phases and demonstrate that the superfluid-insulator phase boundary displays a nonmonotonic dependence on the gauge-field strength. We also compute the momentum distribution of the bosons in the presence of the non-Abelian field and show that they develop peaks at nonzero momenta as the superfluid-insulator transition point is approached from the Mott side. Finally, we study the superfluid phases near the transition and discuss the induced spatial pattern of the superfluid density due to the presence of the non-Abelian gauge potential.
Non-abelian binding energies from the lightcone bootstrap
NASA Astrophysics Data System (ADS)
Li, Daliang; Meltzer, David; Poland, David
2016-02-01
We analytically study the lightcone limit of the conformal bootstrap for 4-point functions containing scalars charged under global symmetries. We show the existence of large spin double-twist operators in various representations of the global symmetry group. We then compute their anomalous dimensions in terms of the central charge C T , current central charge C J , and the OPE coefficients of low dimension scalars. In AdS, these results correspond to the binding energy of two-particle states arising from the exchange of gravitons, gauge bosons, and light scalar fields. Using unitarity and crossing symmetry, we show that gravity is universal and attractive among different types of two-particle states, while the gauge binding energy can have either sign as determined by the representation of the two-particle state, with universal ratios fixed by the symmetry group. We apply our results to 4D {N}=1 SQCD and the 3D O( N) vector models. We also show that in a unitary CFT, if the current central charge C J stays finite when the global symmetry group becomes infinitely large, such as the N → ∞ limit of the O( N) vector model, then the theory must contain an infinite number of higher spin currents.
Stability of domain walls coupled to Abelian gauge fields
George, Damien P.; Volkas, Raymond R.
2005-11-15
Rozowsky, Volkas and Wali [J. Rozowsky, R. Volkas, and K. Wali, Phys. Lett. B 580, 249 (2004).] recently found interesting numerical solutions to the field equations for a gauged U(1)xU(1) scalar field model. Their solutions describe a reflection-symmetric domain wall with scalar fields and coupled gauge configurations that interpolate between constant magnetic fields on one side of the wall and exponentially decaying ones on the other side. This corresponds physically to an infinite sheet of supercurrent confined to the domain wall with a linearly rising gauge potential on one side and Meissner suppression on the other. While it was shown that these static solutions satisfied the field equations, their stability was left unresolved. In this paper, we analyze the normal modes of perturbations of the static solutions to demonstrate their perturbative stability.
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.
Experimental realization of non-abelian geometric gates with a superconducting three-level system
NASA Astrophysics Data System (ADS)
Abdumalikov, Abdufarrukh; Fink, J. M.; Juliusson, K.; Pechal, M.; Berger, S.; Wallraff, A.; Filipp, S.
2013-03-01
Geometric gates hold promise to provide the building blocks for robust quantum computation. In our experiments, we use a superconducting three-level system (transmon) to realize non-adiabatic non-abelian geometric gates. As computational basis we choose the ground and second excited states, while the first excited state acts as an ancilla state. The gates are realized by applying two resonant drives between the transmon levels. During the geometric gate ration of the amplitudes of the two drive tone is kept constant. Different gates are obtained for different ratio of the drive tones. We implement a Hadamard, a NOT and a phase gates with the fidelities of 95 % , 98 % , and 97 % as determined by full process tomography and maximum likelihood methods. We explicitly show the non-abelian nature of gates by applying two non-commuting gates in alternating order. The demonstrated holonomic gates are not exclusive to superconducting quantum devices, but can also be applied to other three level systems with similar energy level structure.
A solenoidal synthetic field and the non-Abelian Aharonov-Bohm effects in neutral atoms
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
Fermion structure of non-Abelian vortices in high density QCD
Yasui, Shigehiro; Itakura, Kazunori; Nitta, Muneto
2010-05-15
We study the internal structure of a non-Abelian vortex in color superconductivity with respect to quark degrees of freedom. Stable non-Abelian vortices appear in the color-flavor-locked phase whose symmetry SU(3){sub c+L+R} is further broken to SU(2){sub c+L+R} x U(1){sub c+L+R} at the vortex cores. Microscopic structure of vortices at scales shorter than the coherence length can be analyzed by the Bogoliubov-de Gennes equation (rather than the Ginzburg-Landau equation). We obtain quark spectra from the Bogoliubov-de Gennes equation by treating the diquark gap having the vortex configuration as a background field. We find that there are massless modes (zero modes) well-localized around a vortex, in the triplet and singlet states of the unbroken symmetry SU(2){sub c+L+R} x U(1){sub c+L+R}. The velocities v{sub i} of the massless modes (i=t, s for triplet and singlet) change at finite chemical potential {mu}{ne}0, and decrease as {mu} becomes large. Therefore, low energy excitations in the vicinity of the vortices are effectively described by 1+1 dimensional massless fermions whose velocities are reduced v{sub i}<1.
Non-Abelian states in Fractional Quantum Hall effect in charge carrier hole systems
NASA Astrophysics Data System (ADS)
Simion, George; Lyanda-Geller, Yuli
Quasiparticle excitations obeying non-Abelian statistics represent the key element of topological quantum computing. Crossing of levels and strong coupling between angular momentum and orbital motion, described by Luttinger Hamiltonian, make properties of charge carrier holes different from those of electrons. Peculiarities of hole spectrum in magnetic field provide an opportunity for controlling Landau level mixing in charge carier hole systems. In order to describe Fractional Quantum Hall effect for holes, we propose a method to map hole spectrum and wavefunctions using a spherical shell. We investigate the experimentally observed ν = 1 / 2 state in spherical geometry. Haldane pseudopotentials are computed and the effect of Landau level mixing is evaluated. Exact diagonalization of Coulomb interaction in systems with eight to fourteen holes is performed. We determine that the ground state superposition with Abelian 331 state is very small and the overlap with Moore-Read state is significant. The quasihole and quasielectron excitations are discussed. Research was supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Award DE-SC0010544.
Non-abelian fractional quantum hall effect for fault-resistant topological quantum computation.
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.
A solenoidal synthetic field and the non-Abelian Aharonov-Bohm effects in neutral atoms.
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
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.
Maximal Abelian subalgebras of pseudoeuclidean real Lie algebras and their application in physics
NASA Astrophysics Data System (ADS)
Thomova, Zora
1998-12-01
We construct the conjugacy classes of maximal abelian subalgebras (MASAs) of the real pseudoeuclidean Lie algebras e(p, q) under the conjugation by the corresponding pseudoeuclidean Lie groups E(p, q). The algebra e( p, q) is a semi-direct sum of the pseudoorthogonal algebra o(p, q) and the abelian ideal of translations T(p + q). We use this particular structure to construct first the splitting MASAs, which are themselves direct sums of subalgebras of o(p, q) and T(p + q). Splitting MASAs give rise to the nonsplitting MASAs of e(p, q). The results for q = 0, 1 and 2 are entirely explicit. MASAs of e(p, 0) and e( p, 1) are used to construct conformally nonequivalent coordinate systems in which the wave equation and Hamilton-Jacobi equations allow the separation of variables. As an application of subgroup classification we perform symmetry reduction for two nonlinear partial differential equations. The method of symmetry reduction is used to obtain analytical solutions of the Landau-Lifshitz and a nonlinear diffusion equations. The symmetry group is found for both equations and all two-dimensional subgroups are classified. These are used to reduce both equations to ordinary differential equations, which are solved in terms of elliptic functions.
NASA Astrophysics Data System (ADS)
Kazakov, Alexander; Kolkovsky, V.; Adamus, Z.; Karczewski, G.; Wojtowicz, T.; Rokhinson, Leonid
2015-03-01
Several experiments detected signatures of Majorana fermions in nanowires, and the focus of current research is shifting toward systems where non-Abelian statistics of excitations can be demonstrated. To achieve this goal we are developing a new platform where non-Abelian excitations can be created and manipulated in a two-dimensional plane, with support for Majorana and higher order non-Abelian excitations. The system is based on CdTe quantum wells non-uniformly doped with paramagnetic impurities, which result in a complicate field-dependence of Zeeman splitting. A unique property of the system is that at high fields we can form a quantum Hall ferromagnet with gate-controllable spin polarization. Helical 1D edge channels formed along the edges of electrostatic gates may support generalized non-Abelian excitations in the fractional qunatum Hall regime, and Majorana and parafermion excitations in the presence of induced superconductivity. We will present results on the gate control of s-d exchange in specially designed heterostructures, demonstrate gate control of spin polarization at filling factor ν = 2 , and show spatial separation of quantum Hall states with different spin polarization using lithographically defined gates.
Topological phase transitions with non-Abelian gauge potentials on square lattices
NASA Astrophysics Data System (ADS)
Chen, Yao-Hua; Li, Jian; Ting, C. S.
2013-11-01
We investigate the topological phase transition on interacting square lattices via the non-Abelian potential by employing the real-space cellular dynamical mean-field theory combining with the continuous-time Monte Carlo method. For a weak on-site Hubbard interaction, a topological band insulating state with a pair of gapless edge states is induced by a next-nearest-neighbor hopping. A phase transition from the metallic phase to the Mott insulating phase is observed when the interaction is increased. These two phases can be distinguished by detecting whether a bulk gap in the K-dependent spectral function exists. The whole phase diagrams as functions of the interaction, next-nearest-neighbor hopping energy, and temperature are presented. The experimental setup to observe these new interesting phase transitions is also discussed.
Non-Abelian evolution of electromagnetic waves in a weakly anisotropic inhomogeneous medium
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.
NASA Astrophysics Data System (ADS)
Gupta, S.; Kumar, R.; Malik, R. P.
2010-11-01
We demonstrate the existence of the nilpotent and absolutely anticommuting Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for the four (3+1)-dimensional (4D) topologically massive Abelian U(1) gauge theory that is described by the coupled Lagrangian densities (which incorporate the celebrated ( B∧ F) term). The absolute anticommutativity of the (anti-) BRST symmetry transformations is ensured by the existence of a Curci-Ferrari type restriction that emerges from the superfield formalism as well as from the equations of motion which are derived from the above coupled Lagrangian densities. We show the invariance of the action from the point of view of the symmetry considerations as well as superfield formulation. We discuss, furthermore, the topological term within the framework of superfield formalism and provide the geometrical meaning of its invariance under the (anti-)BRST symmetry transformations.
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.
Transverse momentum diffusion and collisional jet energy loss in non-Abelian plasmas
Schenke, Bjoern; Strickland, Michael; Dumitru, Adrian; Nara, Yasushi; Greiner, Carsten
2009-03-15
We consider momentum broadening and energy loss of high-momentum partons in a hot non-Abelian plasma due to collisions. We solve the coupled system of Wong-Yang-Mills equations on a lattice in real time, including binary hard elastic collisions among the partons. The collision kernel is constructed such that the total collisional energy loss and momentum broadening are lattice-spacing independent. We find that the transport coefficient q corresponding to transverse momentum broadening receives sizable contributions from a power-law tail in the p{sub perpendicular} distribution of high-momentum partons. We establish the scaling of q and of dE/dx with density, temperature, and energy in the weak-coupling regime. We also estimate the nuclear modification factor R{sub AA} due to elastic energy loss of a jet in a classical Yang-Mills field.
Collective Non-Abelian Instabilities in a Melting Color Glass Condensate
Romatschke, Paul; Venugopalan, Raju
2006-02-17
We present first results for (3+1)D simulations of SU(2) Yang-Mills equations for matter expanding into the vacuum after a heavy ion collision. Violations of boost invariance cause a non-Abelian Weibel instability leading soft modes to grow with proper time {tau} as exp({gamma}{radical}(g{sup 2}{mu}{tau})), where g{sup 2}{mu} is a scale arising from the saturation of gluons in the nuclear wave function. The scale for the growth rate {gamma} is set by a plasmon mass, defined as {omega}{sub pl}={kappa}{sub 0}{radical}(g{sup 2}{mu}/{tau}), generated dynamically in the collision. We compare the numerical ratio {gamma}/{kappa}{sub 0} to the corresponding value predicted by the hard thermal loop formalism for anisotropic plasmas.
Non-Abelian chiral instabilities at high temperature on the lattice
NASA Astrophysics Data System (ADS)
Akamatsu, Yukinao; Rothkopf, Alexander; Yamamoto, Naoki
2016-03-01
We report on an exploratory lattice study on the phenomenon of chiral instabilities in non-Abelian gauge theories at high temperature. It is based on a recently constructed anomalous Langevin-type effective theory of classical soft gauge fields in the presence of a chiral number density n 5 = n R - n L. Evaluated in thermal equilibrium using classical lattice techniques it reveals that the fluctuating soft fields indeed exhibit a rapid energy increase at early times and we observe a clear dependence of the diffusion rate of topological charge (sphaleron rate) on the the initial n 5, relevant in both early universe baryogenesis and relativistic heavy-ion collisions. The topological charge furthermore shows a drift among distinct vacuum sectors, roughly proportional to the initial n 5 and in turn the chiral imbalance is monotonously reduced as required by helicity conservation.
Robustness of non-Abelian holonomic quantum gates against parametric noise
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)].
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.
C*-Algebras Associated with Endomorphisms and Polymorphisms of Compact Abelian Groups
NASA Astrophysics Data System (ADS)
Cuntz, Joachim; Vershik, Anatoly
2013-07-01
A surjective endomorphism or, more generally, a polymorphism in the sense of Schmidt and Vershik [Erg Th Dyn Sys 28(2):633-642, 2008], of a compact abelian group H induces a transformation of L 2( H). We study the C*-algebra generated by this operator together with the algebra of continuous functions C( H) which acts as multiplication operators on L 2( H). Under a natural condition on the endo- or polymorphism, this algebra is simple and can be described by generators and relations. In the case of an endomorphism it is always purely infinite, while for a polymorphism in the class we consider, it is either purely infinite or has a unique trace. We prove a formula allowing to determine the K-theory of these algebras and use it to compute the K-groups in a number of interesting examples.
On the effective character of a non-abelian DBI action
NASA Astrophysics Data System (ADS)
Osorio, M. A. R.; Suárez, M.
2001-03-01
We study the way Lorentz covariance can be reconstructed from Matrix Theory as a IMF description of M-theory. The problem is actually related to the interplay between a non-abelian Dirac-Born-Infeld action and Super-Yang-Mills as its generalized non-relativistic approximation. All this physics shows up by means of an analysis of the asymptotic expansion of the Bessel functions Kν that profusely appear in the computations of amplitudes at finite temperature and solitonic calculations. We hope this might help to better understand the issue of getting a Lorentz covariant formulation in relation with the /N-->+∞ limit. There are also some computations that could be of some interest in Relativistic Statistical Mechanics.
BCS-BEC crossover induced by a synthetic non-Abelian gauge field
NASA Astrophysics Data System (ADS)
Vyasanakere, Jayantha P.; Zhang, Shizhong; Shenoy, Vijay B.
2011-07-01
We investigate the ground state of interacting spin-(1)/(2) fermions in three dimensions at a finite density (ρ˜kF3) in the presence of a uniform non-Abelian gauge field. The gauge-field configuration (GFC) described by a vector λ≡(λx,λy,λz), whose magnitude λ determines the gauge coupling strength, generates a generalized Rashba spin-orbit interaction. For a weak attractive interaction in the singlet channel described by a small negative scattering length (kF|as|≲1), the ground state in the absence of the gauge field (λ=0) is a BCS (Bardeen-Cooper-Schrieffer) superfluid with large overlapping pairs. With increasing gauge-coupling strength, a non-Abelian gauge field engenders a crossover of this BCS ground state to a BEC (Bose-Einstein condensate) of bosons even with a weak attractive interaction that fails to produce a two-body bound state in free vacuum (λ=0). For large gauge couplings (λ/kF≫1), the BEC attained is a condensate of bosons whose properties are solely determined by the Rashba gauge field (and not by the scattering length so long as it is nonzero)—we call these bosons “rashbons.” In the absence of interactions (as=0-), the shape of the Fermi surface of the system undergoes a topological transition at a critical gauge coupling λT. For high-symmetry GFCs we show that the crossover from the BCS superfluid to the rashbon BEC occurs in the regime of λ near λT. In the context of cold atomic systems, these results make an interesting suggestion of obtaining BCS-BEC crossover through a route other than tuning the interaction between the fermions.
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.
BCS-BEC crossover induced by a synthetic non-Abelian gauge field
Vyasanakere, Jayantha P.; Shenoy, Vijay B.; Zhang Shizhong
2011-07-01
We investigate the ground state of interacting spin-(1/2) fermions in three dimensions at a finite density ({rho}{approx}k{sub F}{sup 3}) in the presence of a uniform non-Abelian gauge field. The gauge-field configuration (GFC) described by a vector {lambda}{identical_to}({lambda}{sub x},{lambda}{sub y},{lambda}{sub z}), whose magnitude {lambda} determines the gauge coupling strength, generates a generalized Rashba spin-orbit interaction. For a weak attractive interaction in the singlet channel described by a small negative scattering length (k{sub F}|a{sub s}| < or approx. 1), the ground state in the absence of the gauge field ({lambda}=0) is a BCS (Bardeen-Cooper-Schrieffer) superfluid with large overlapping pairs. With increasing gauge-coupling strength, a non-Abelian gauge field engenders a crossover of this BCS ground state to a BEC (Bose-Einstein condensate) of bosons even with a weak attractive interaction that fails to produce a two-body bound state in free vacuum ({lambda}=0). For large gauge couplings ({lambda}/k{sub F}>>1), the BEC attained is a condensate of bosons whose properties are solely determined by the Rashba gauge field (and not by the scattering length so long as it is nonzero)--we call these bosons ''rashbons.'' In the absence of interactions (a{sub s}=0{sup -}), the shape of the Fermi surface of the system undergoes a topological transition at a critical gauge coupling {lambda}{sub T}. For high-symmetry GFCs we show that the crossover from the BCS superfluid to the rashbon BEC occurs in the regime of {lambda} near {lambda}{sub T}. In the context of cold atomic systems, these results make an interesting suggestion of obtaining BCS-BEC crossover through a route other than tuning the interaction between the fermions.
Non-Abelian clouds around Reissner-Nordström black holes: The existence line
NASA Astrophysics Data System (ADS)
Radu, Eugen; Tchrakian, D. H.; Yang, Yisong
2016-06-01
A known feature of electrically charged Reissner-Nordström-anti-de Sitter planar black holes is that they can become unstable when considered as solutions of Einstein-Yang-Mills theory. The mechanism for this is that the linearized Yang-Mills equations in the background of the Reissner-Nordström (RN) black holes possess a normalizable zero mode, resulting in non-Abelian (nA) magnetic clouds near the horizon. In this work we show that the same pattern may occur also for asymptotically flat RN black holes. Different from the anti-de Sitter case, in the Minkowskian background the prerequisites for the existence of the nA clouds are (i) a large enough gauge group, and (ii) the presence of some extra interaction terms in the matter Lagrangian. To illustrate this mechanism we present two specific examples, one in four- and the other in five-dimensional asymptotically flat spacetime. In the first case, we augment the usual S U (3 ) Yang-Mills Lagrangian with a higher-order (quartic) curvature term, while for the second one we add the Chern-Simons density to the S O (6 ) Yang-Mills system. In both cases, an Abelian gauge symmetry is spontaneously broken near a RN black hole horizon with the appearance of a condensate of nA gauge fields. In addition to these two examples, we review the corresponding picture for anti-de Sitter black holes. All these solutions are studied both analytically and numerically, existence proofs being provided for nA clouds in the background of RN black holes. The proofs use shooting techniques which are suggested by and in turn offer insights for our numerical methods. They indicate that, for a black hole of given mass, appropriate electric charge values are required to ensure the existence of solutions interpolating desired boundary behavior at the horizons and spatial infinity.
NASA Astrophysics Data System (ADS)
Ye, Peng; Gu, Zheng-Cheng
2016-05-01
Symmetry-protected topological phases (SPT) are short-range entangled gapped states protected by global symmetry. Nontrivial SPT phases cannot be adiabatically connected to the trivial disordered state (or atomic insulator) as long as certain global symmetry G is unbroken. At low energies, most of the two-dimensional SPTs with Abelian symmetry can be described by topological quantum field theory (TQFT) of the multicomponent Chern-Simons type. However, in contrast to the fractional quantum Hall effect where TQFT can give rise to interesting bulk anyons, TQFT for SPTs only supports trivial bulk excitations. The essential question in TQFT descriptions for SPTs is to understand how the global symmetry is implemented in the partition function. In this paper, we systematically study TQFT of three-dimensional SPTs with unitary Abelian symmetry (e.g., ZN1×ZN2×... ). In addition to the usual multicomponent B F topological term at level-1, we find that there are new topological terms with quantized coefficients (e.g., a1∧a2∧d a2 and a1∧a2∧a3∧a4 ) in TQFT actions, where a1,a2,... are 1-form U(1) gauge fields. These additional topological terms cannot be adiabatically turned off as long as G is unbroken. By investigating symmetry transformations for the TQFT partition function, we end up with the classification of SPTs that is consistent with the well-known group cohomology approach. We also discuss how to gauge the global symmetry and possible TQFT descriptions of Dijkgraaf-Witten gauge theory.
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.
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.
NASA Astrophysics Data System (ADS)
Markov, Yuri A.; Markova, Margaret A.; Shishmarev, Alexey A.
2010-10-01
Based on the most general principles of reality, gauge and reparametrization invariance, a problem of constructing the action describing dynamics of a classical color-charged particle interacting with background non-Abelian gauge and fermion fields is considered. The cases of the linear and quadratic dependence of a Lagrangian on background Grassmann fermion field are discussed. It is shown that in both cases in general there exists an infinite number of interaction terms, which should be included in the Lagrangian in question. Employing a simple iteration scheme, examples of the construction of the first few gauge-covariant currents and sources induced by a moving particle with non-Abelian charge are given. It is found that these quantities, by a suitable choice of parameters, exactly reproduce additional currents and sources previously obtained in Markov and Markova (2007 Nucl. Phys. A 784 443) on the basis of heuristic considerations.
Viennot, David
2010-10-15
We show that the holonomy of a connection defined on a principal composite bundle is related by a non-Abelian Stokes theorem to the composition of the holonomies associated with the connections of the component bundles of the composite. We apply this formalism to describe the non-Abelian geometric phase (when the geometric phase generator does not commute with the dynamical phase generator). We find then an assumption to obtain a new kind of separation between the dynamical and the geometric phases. We also apply this formalism to the gauge theory of gravity in the presence of a Dirac spinor field in order to decompose the holonomy of the Lorentz connection into holonomies of the linear connection and of the Cartan connection.
S-duality in SU(3) Yang-Mills theory with non-abelian unbroken gauge group
NASA Astrophysics Data System (ADS)
Schroers, B. J.; Bais, F. A.
1998-12-01
It is observed that the magnetic charges of classical monopole solutions in Yang-Mills-Higgs theory with non-abelian unbroken gauge group H are in one-to-one correspondence with coherent states of a dual or magnetic group H˜. In the spirit of the Goddard-Nuyts-Olive conjecture this observation is interpreted as evidence for a hidden magnetic symmetry of Yang-Mills theory. SU(3) Yang-Mills-Higgs theory with unbroken gauge group U(2) is studied in detail. The action of the magnetic group on semi-classical states is given explicitly. Investigations of dyonic excitations show that electric and magnetic symmetry are never manifest at the same time: Non-abelian magnetic charge obstructs the realisation of electric symmetry and vice-versa. On the basis of this fact the charge sectors in the theory are classified and their fusion rules are discussed. Non-abelian electric-magnetic duality is formulated as a map between charge sectors. Coherent states obey particularly simple fusion rules, and in the set of coherent states S-duality can be formulated as an SL(2, Z) mapping between sectors which leaves the fusion rules invariant.
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
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.
Index theorem and Majorana zero modes along a non-Abelian vortex in a color superconductor
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.
Non-Abelian vortices at weak and strong coupling in mass deformed ABJM theory
NASA Astrophysics Data System (ADS)
Auzzi, Roberto; Kumar, S. Prem
2009-10-01
We find half-BPS vortex solitons, at both weak and strong coupling, in the Script N = 6 supersymmetric mass deformation of ABJM theory with U(N) × U(N) gauge symmetry and Chern-Simons level k. The strong coupling gravity dual is obtained by performing a Bbb Zk quotient of the Script N = 8 supersymmetric eleven dimensional supergravity background of Lin, Lunin and Maldacena corresponding to the mass deformed M2-brane theory. At weak coupling, the BPS vortices preserving six supersymmetries are found in the Higgs vacuum of the theory where the gauge symmetry is broken to U(1) × U(1). The classical vortex solitons break a colour-flavour locked global symmetry resulting in non-Abelian internal orientational moduli and a CP1 moduli space of solutions. At strong coupling and large k, upon reduction to type IIA strings, the vortex moduli space and its action are computed by a probe D0-brane in the dual geometry. The mass of the D0-brane matches the classical vortex mass. However, the gravity picture exhibits a six dimensional moduli space of solutions, a section of which can be identified as the CP1 we find classically, along with a Dirac monopole connection of strength k. It is likely that the extra four dimensions in the moduli space are an artifact of the strong coupling limit and of the supergravity approximation.
Localizing gauge fields on a topological Abelian string and the Coulomb law
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.
Strong-weak coupling duality in non-abelian gauge theories
NASA Astrophysics Data System (ADS)
Ferrari, Frank
1997-05-01
This is a general introduction to electric-magnetic duality in non-abelian gauge theories. In chapter I, I review the general ideas which led in the late 70s to the idea of electric/magnetic duality in quantum field theory. In chapters II and III, I focus mainly on N=2 supersymmetric theories. I present the lagrangians and explain in more or less detail the non-renormalization theorems, rigid special geometry, supersymmetric instanton calculus, charge fractionization, the semiclassical theory of monopoles, duality in Maxwell theory and the famous Seiberg-Witten solution. I discuss various physical applications, as electric charge confinement, chiral symmetry breaking or non-trivial superconformal theories in four dimensions. In Section II.3 new material is presented, related to the computation of the eta invariant of certain Dirac operators coupled minimally to non-trivial monopole field configurations. I explain how these invariants can be obtained exactly by a one-loop calculation in a suitable N=2 supersymmetric gauge theory. This is an unexpected application of the holomorphy properties of N=2 supersymmetry, and constitutes a tremendous simplification of the usual computation. An expanded version of these new results will be published soon.
Quiver gauge theory of non-Abelian vortices and noncommutative instantons in higher dimensions
Popov, Alexander D.; Szabo, Richard J.
2006-01-15
We construct explicit Bogomolnyi, Prasad, Sommerfeld (BPS) and non-BPS solutions of the Yang-Mills equations on the noncommutative space R{sub {theta}}{sup 2n}xS{sup 2} which have manifest spherical symmetry. Using SU(2)-equivariant dimensional reduction techniques, we show that the solutions imply an equivalence between instantons on R{sub {theta}}{sup 2n}xS{sup 2} and non-Abelian vortices on R{sub {theta}}{sup 2n}, which can be interpreted as a blowing-up of a chain of D0-branes on R{sub {theta}}{sup 2n} into a chain of spherical D2-branes on R{sub {theta}}{sup 2n}xS{sup 2}. The low-energy dynamics of these configurations is described by a quiver gauge theory which can be formulated in terms of new geometrical objects generalizing superconnections. This formalism enables the explicit assignment of D0-brane charges in equivariant K-theory to the instanton solutions.
Non-Abelian Gauge Groups for Real and Complex Amended Maxwell's Equations
NASA Astrophysics Data System (ADS)
Rauscher, E. A.
2002-04-01
We have developed an eight dimensional complex Minkowski space M4, compiled of four real dimensions and four imaginary dimensions, which is constant with Lorentz invariance and analytic continuation in the complex plane(1). Complexification, of Maxwell's equations requires a non-Abelian gauge group, which amends the usual theory which utilizes the usual unimodular Weyl U1 group. We have examined the modification of gauge conditions using higher symmetry groups such as SU2, SUn and other groups such as the SL(2,c) double cover group of the rotational group SO(3,1). The mappability of the twistor algebra and the spinor calculus is analyzed in the context of the electromagnetic theory. Thus we are led to new and interesting physics involving extended metrical space constraints, the usual transverse and also longitudinal, non Hertzian electric and magnetic field solutions to Maxwell's equations, possibly leading to new communications systems and antennae theory, non-zero solutions to Ñ·B, and a possible finite but small rest mass of the photon. Comparison of our theoretical approach is made to the work of T.W. Barrett and H.F. Hermuth?s work on amended Maxwell's theories. (1) C. Ramon and E. A. Rauscher, Found. of Phys. 10, 661 (1980)
Lee, Sang Bub
2015-12-01
The absorbing phase transition of the modified conserved lattice gas (m-CLG) model was investigated in one dimension. The m-CLG model was modified from the conserved lattice gas (CLG) model in such a way that each active particle hops to one of the nearest-neighbor and next-nearest-neighbor empty sites. The order parameter exponent, the dynamic exponent, and the correlation length exponent were estimated from the power-law behavior and finite-size scaling of the active particle densities. The exponents were found to differ considerably from those of the ordinary CLG model and were also distinct from those of the Manna model, suggesting that next-nearest-neighbor hopping is a relevant factor that alters the critical behavior in the one-dimensional CLG model. PMID:26764627
Gluon propagators in maximally Abelian gauge in SU(3) lattice QCD
NASA Astrophysics Data System (ADS)
Gongyo, Shinya; Suganuma, Hideo
2013-04-01
In SU(3) lattice QCD, we study diagonal and off-diagonal gluon propagators in the maximally Abelian gauge with U(1)3×U(1)8 Landau gauge fixing. These propagators are studied both in the coordinate space and in the momentum space. The Monte Carlo simulation is performed on 164 at β=6.0 and 324 at β=5.8 and 6.0 at the quenched level. In the four-dimensional Euclidean space-time, the effective mass of diagonal gluons is estimated as Mdiag≃0.3GeV and that of off-diagonal gluons as Moff≃1GeV in the region of r=0.4-1.0fm. In the momentum space, the effective mass of diagonal gluons is estimated as Mdiag≃0.3GeV and that of off-diagonal gluons as Moff≃1GeV in the region of p<1.1GeV. The off-diagonal gluon propagator is relatively suppressed in the infrared region and seems to be finite at zero momentum, while the diagonal gluon propagator is enhanced. Furthermore, we also study the functional form of these propagators in momentum space. These propagators are well fitted by Z/(p2+m2)ν with fit parameters, Z, m, and ν in the region of p<3.0GeV. From the fit results and lattice calculations, all of the spectral functions of diagonal and off-diagonal gluons would have negative regions.
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
Triyanta; Zen, F. P.; Supardi; Wardaya, A. Y.
2010-12-23
Gauge theory, under the framework of quantum field theory, has successfully described three fundamental interactions: electromagnetic, weak, and strong interactions. Problems of describing the gravitational interaction in a similar manner has not been satisfied yet until now. Teleparallel gravity (TG) is one proposal describing gravitational field as a gauge field. This theory is quite new and it is equivalent to Einstein's general relativity. But as gravitational field in TG is expressed by torsion, rather than curvature, it gives an alternative framework for solving problems on gravity. This paper will present solution of the dynamical equation of abelian vector fields under the framework of TG in the Bianchi type I spacetime.
Gluon production from non-Abelian Weizsäcker-Williams fields in nucleus-nucleus collisions
NASA Astrophysics Data System (ADS)
Kovner, Alex; McLerran, Larry; Weigert, Heribert
1995-12-01
We consider the collisions of large nuclei using the theory of McLerran and Venugopalan. The two nuclei are ultrarelativistic and sources of non-Abelian Weizs¨acker-Williams fields. These sources are in the end averaged over all color orientations locally with a Gaussian weight. We show that there is a solution of the equations of motion for the two nucleus scattering problem where the fields are time and rapidity independent before the collision. After the collision the solution depends on proper time, but is independent of rapidity. We show how to extract the produced gluons from the classical evolution of the fields.
A non-Abelian SO(8) monopole as generalization of Dirac-Yang monopoles for a 9-dimensional space
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).
Hou, Chang-Yu; Chamon, Claudio
2006-10-01
We study a tunneling geometry defined by a single point-contact constriction that brings to close vicinity two points sitting at the same edge of a quantum Hall liquid, shortening the trip between the otherwise spatially separated points along the normal chiral edge path. This wormhole-like geometry allows for entrapping bulk quasiparticles between the edge path and the tunnel junction, possibly realizing a topologically protected qubit if the quasiparticles have non-Abelian statistics. We show how either noise or simpler voltage measurements along the edge can probe the non-Abelian nature of the trapped quasiparticles. PMID:17155280
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
NASA Astrophysics Data System (ADS)
Zhang, Yi; Vishwanath, Ashvin
2013-04-01
We use entanglement entropy signatures to establish non-Abelian topological order in projected Chern-insulator wave functions. The simplest instance is obtained by Gutzwiller projecting a filled band with Chern number C=2, whose wave function may also be viewed as the square of the Slater determinant of a band insulator. We demonstrate that this wave function is captured by the SU(2)2 Chern-Simons theory coupled to fermions. This is established most persuasively by calculating the modular S-matrix from the candidate ground-state wave functions, following a recent entanglement-entropy-based approach. This directly demonstrates the peculiar non-Abelian braiding statistics of Majorana fermion quasiparticles in this state. We also provide microscopic evidence for the field theoretic generalization, that the Nth power of a Chern number C Slater determinant realizes the topological order of the SU(N)C Chern-Simons theory coupled to fermions, by studying the SU(2)3 (Read-Rezayi-type state) and the SU(3)2 wave functions. An advantage of our projected Chern-insulator wave functions is the relative ease with which physical properties, such as entanglement entropy and modular S-matrix, can be numerically calculated using Monte Carlo techniques.
Fractional Quantum Hall States at ν =13 /5 and 12 /5 and Their Non-Abelian Nature
NASA Astrophysics Data System (ADS)
Zhu, W.; Gong, S. S.; Haldane, F. D. M.; Sheng, D. N.
2015-09-01
Topological quantum states with non-Abelian Fibonacci anyonic excitations are widely sought after for the exotic fundamental physics they would exhibit, and for universal quantum computing applications. The fractional quantum Hall (FQH) state at a filling factor of ν =12 /5 is a promising candidate; however, its precise nature is still under debate and no consensus has been achieved so far. Here, we investigate the nature of the FQH ν =13 /5 state and its particle-hole conjugate state at 12 /5 with the Coulomb interaction, and we address the issue of possible competing states. Based on a large-scale density-matrix renormalization group calculation in spherical geometry, we present evidence that the essential physics of the Coulomb ground state (GS) at ν =13 /5 and 12 /5 is captured by the k =3 parafermion Read-Rezayi state (RR3), including a robust excitation gap and the topological fingerprint from the entanglement spectrum and topological entanglement entropy. Furthermore, by considering the infinite-cylinder geometry (topologically equivalent to torus geometry), we expose the non-Abelian GS sector corresponding to a Fibonacci anyonic quasiparticle, which serves as a signature of the RR3 state at 13 /5 and 12 /5 filling numbers.
The Fractional Quantum Hall States at ν = 13 / 5 and 12 / 5 and their Non-Abelian Nature
NASA Astrophysics Data System (ADS)
Zhu, W.; Gong, S. S.; Sheng, D. N.
Topological quantum states with non-Abelian Fibonacci anyonic excitations are widely sought after for their exotic fundamental physics and potential applications in universal quantum computing. The fractional quantum Hall (FQH) state at filling factor ν = 12 / 5 is such a promising candidate, however, its precise nature is still under debate and no consensus has been achieved so far. Here, we investigate the nature of the FQH ν = 13 / 5 state and its particle-hole conjugate state at 12 / 5 with the Coulomb interaction, and address the issue of possible competing states. Based on a large-scale density-matrix renormalization group (DMRG) calculation in spherical geometry, we present evidence that the essential physics of the Coulomb ground state (GS) at ν = 13 / 5 and 12 / 5 is captured by the k = 3 parafermion Read-Rezayi state (RR3), including a robust excitation gap and the topological fingerprint from entanglement spectrum and topological entanglement entropy. Furthermore, by considering the infinite-cylinder geometry (topologically equivalent to torus geometry), we expose the non-Abelian GS sector corresponding to a Fibonacci anyonic quasiparticle, which serves as a signature of the RR3 state at 13 / 5 and 12 / 5 filling numbers. This work is supported by the DOE Grants No. DE-FG02-06ER46305, DE-SC0002140, and the NSF Grant No. DMR-1408560.
Fractional Quantum Hall States at ν=13/5 and 12/5 and Their Non-Abelian Nature.
Zhu, W; Gong, S S; Haldane, F D M; Sheng, D N
2015-09-18
Topological quantum states with non-Abelian Fibonacci anyonic excitations are widely sought after for the exotic fundamental physics they would exhibit, and for universal quantum computing applications. The fractional quantum Hall (FQH) state at a filling factor of ν=12/5 is a promising candidate; however, its precise nature is still under debate and no consensus has been achieved so far. Here, we investigate the nature of the FQH ν=13/5 state and its particle-hole conjugate state at 12/5 with the Coulomb interaction, and we address the issue of possible competing states. Based on a large-scale density-matrix renormalization group calculation in spherical geometry, we present evidence that the essential physics of the Coulomb ground state (GS) at ν=13/5 and 12/5 is captured by the k=3 parafermion Read-Rezayi state (RR_{3}), including a robust excitation gap and the topological fingerprint from the entanglement spectrum and topological entanglement entropy. Furthermore, by considering the infinite-cylinder geometry (topologically equivalent to torus geometry), we expose the non-Abelian GS sector corresponding to a Fibonacci anyonic quasiparticle, which serves as a signature of the RR_{3} state at 13/5 and 12/5 filling numbers. PMID:26431006
NASA Astrophysics Data System (ADS)
Zhang, Yi; Vishwanath, Ashvin
2013-03-01
We use entanglement entropy signatures to establish non-Abelian topological order in a new class of ground states, the projected Chern-insulator wave functions. The simplest instance is obtained by Gutzwiller projecting a filled band with Chern number C=2 which may also be viewed as the square of the band insulator Slater determinant. We demonstrate that this wave function is captured by the SU(2)2 Chern Simons theory coupled to fermions. In addition to the expected torus degeneracy and topological entanglement entropy, we also show that the modular S-matrix, extracted from entanglement entropy calculations, provides direct access to the peculiar non-Abelian braiding statistics of Majorana fermions in this state. We also provide microscopic evidence for the generalization (expected from the field theory), that the Nth power of a Chern number C Slater determinant realizes the topological order of the SU(N)C Chern Simons theory coupled to fermions, by studying the SU(2)3 and the SU(3)2 wave functions. An advantage of projected Chern insulator wave functions over lowest Landau level wave functions for the same phases is the relative ease with which physical properties, such as entanglement entropy, can be numerically calculated using Monte Carlo techniques.
Bound states of two spin-(1/2) fermions in a synthetic non-Abelian gauge field
Vyasanakere, Jayantha P.; Shenoy, Vijay B.
2011-03-01
We study the bound states of two spin-(1/2) fermions interacting via a contact attraction (characterized by a scattering length) in the singlet channel in three-dimensional space in presence of a uniform non-Abelian gauge field. The configuration of the gauge field that generates a Rashba-type spin-orbit interaction is described by three coupling parameters ({lambda}{sub x},{lambda}{sub y},{lambda}{sub z}). For a generic gauge field configuration, the critical scattering length required for the formation of a bound state is negative, i.e., shifts to the ''BCS side'' of the resonance. Interestingly, we find that there are special high-symmetry configurations (e.g., {lambda}{sub x}={lambda}{sub y}={lambda}{sub z}) for which there is a two-body bound state for anyscattering length however small and negative. Remarkably, the bound-state wave functions obtained for such configurations have nematic spin structure similar to those found in liquid {sup 3}He. Our results show that the BCS-BEC (Bose-Einstein condensation) crossover is drastically affected by the presence of a non-Abelian gauge field. We discuss possible experimental signatures of our findings both at high and low temperatures.
Implementing a topological quantum model using a cavity lattice
NASA Astrophysics Data System (ADS)
Xiang, ZeLiang; Yu, Ting; Zhang, WenXian; Hu, XueDong; You, JianQiang
2012-09-01
Kitaev model has both Abelian and non-Abelian anyonic excitations. It can act as a starting point for topological quantum computation. However, this model Hamiltonian is difficult to implement in natural condensed matter systems. Here we propose a quantum simulation scheme by constructing the Kitaev model Hamiltonian in a lattice of coupled cavities with embedded Λ-type three-level atoms. In this scheme, several parameters are tunable, for example, via external laser fields. Importantly, our scheme is based on currently existing technologies and it provides a feasible way of realizing the Kitaev model to explore topological excitations.
NASA Astrophysics Data System (ADS)
Willett, Robert; Manfra, Michael; Pfeiffer, Loren; Shtengel, Kirill; Nayak, Chetan
The excitations of charge e/4 at 5/2 filling factor are proposed to obey non-Abelian statistics. To test this, interferometry at fractional quantum Hall states can be performed that controllably braids edge currents around localized charges. We have conducted these measurements in a large number of interferometers of different sizes, also using multiple designs of high quality 2D electron heterostructures. We observe properties of the interference measurements at 5/2 that are specifically consistent with non-Abelian e/4. In particular, magnetic field sweeps around 5/2 show interference oscillations with frequency spectra that are consistent in detail with non-Abelian e/4 properties. Four frequency spectra peaks are observed corresponding to both e/4 and e/2 charges; importantly a rapid non-Abelian e/4 component is seen that is split due to beating between the two e/4 braiding processes. We review these results and their observation in a range of interferometer dimensions and in different heterostructure designs.
Supersymmetric F-theory GUT models
NASA Astrophysics Data System (ADS)
Chung, Yu-Chieh
F-theory is a twelve-dimensional geometric version of string theory and is believed to be a natural framework for GUT model building. The aim of this dissertation is to study how gauge theories realized by F-theory can accommodate GUT models. In this dissertation, we focus on local and semi-local GUT model building in F-theory. For local GUT models, we build SU(5) GUTs by using abelian U(1) fluxes via theSU6) gauge group. Doing so, we obtain non-minimal spectra of the MSSM with doublet-triplet splitting by switching on abelian U(1)2 fluxes. We also classify all supersymmetric U(1)2 fluxes by requiring an exotic-free bulk spectrum. For semi-local GUT models, we start with an E8 singularity and obtain lower rank gauge groups by unfolding the singularity governed by spectral covers. In this framework, the spectra can be calculated by the intersection numbers of spectral covers and matter curves. In particular, we useSU4) spectral covers and abelian U(1)X fluxes to build flippedSU5) models. We show that three-generation spectra of flippedSU5) models can be achieved by turning on suitable fluxes. To construct E6 GUTs, we consider SU3) spectral covers breaking E8 down to E6. Also three-generation extended MSSM can be obtained by using non-abelian SU2) x U(1)2 fluxes.
Assembling Fibonacci anyons from a Z3 parafermion lattice model
NASA Astrophysics Data System (ADS)
Stoudenmire, E. M.; Clarke, David J.; Mong, Roger S. K.; Alicea, Jason
2015-06-01
Recent concrete proposals suggest it is possible to engineer a two-dimensional bulk phase supporting non-Abelian Fibonacci anyons out of Abelian fractional quantum Hall systems. The low-energy degrees of freedom of such setups can be modeled as Z3 parafermions "hopping" on a two-dimensional lattice. We use the density matrix renormalization group to study a model of this type interpolating between the decoupled-chain, triangular-lattice, and square-lattice limits. The results show clear evidence of the Fibonacci phase over a wide region of the phase diagram, most notably including the isotropic triangular-lattice point. We also study the broader phase diagram of this model and show that elsewhere it supports an Abelian state with semionic excitations.
NASA Astrophysics Data System (ADS)
Eto, Minoru; Murakami, Yoshihide
2015-03-01
Dyonic non-Abelian local/semi-global vortex strings are studied in detail in supersymmetric/non-supersymmetric Yang-Mills-Higgs theories. While the BPS tension formula is known to be the same as that for the BPS dyonic instanton, we find that the non-BPS tension formula is approximated very well by the well-known tension formula of the BPS dyon. We show that this mysterious tension formula for the dyonic non-BPS vortex stings can be understood from the perspective of a low energy effective field theory. Furthermore, we propose an efficient method to obtain an effective theory of a single vortex string, which includes not only lower derivative terms but also all order derivative corrections by making use of the tension formula. We also find a novel dyonic vortex string whose internal orientation vectors rotate in time and spiral along the string axis.
NASA Astrophysics Data System (ADS)
Vyasanakere, Jayanth P.; Shenoy, Vijay B.
2013-03-01
A non-Abelian gauge field that induces a spin-orbit coupling on the motion of fermions engenders a BCS-BEC crossover even for weakly attracting fermions. The transition temperature at large spin-orbit coupling is known to be determined by the mass of the emergent boson - the rashbon. We obtain the transition temperature of the system as a function of the spin-orbit coupling by constructing and studying a Gaussian fluctuation (Nozieres-Schmitt-Rink) theory. These results will help guide the upcoming experiments on spin-orbit coupled fermions. In addition, this work suggests a route to enhance the transition temperature of a weakly attracting fermionic system by tuning the spin-orbit coupling. Work supported by CSIR, DST, DAE India
Galilo, Bogdan V.; Nedelko, Sergei N.
2011-11-01
The one-loop quark contribution to the QCD effective potential for the homogeneous Abelian gluon field in the presence of an external strong electromagnetic field is evaluated. The structure of extrema of the potential as a function of the angles between chromoelectric, chromomagnetic, and electromagnetic fields is analyzed. In this setup, the electromagnetic field is considered as an external one while the gluon field represents domain structured nonperturbative gluon configurations related to the QCD vacuum in the confinement phase. Two particularly interesting gluon configurations, (anti-)self-dual and crossed orthogonal chromomagnetic and chromoelectric fields, are discussed specifically. Within this simplified framework it is shown that the strong electromagnetic fields can play a catalyzing role for a deconfinement transition. At the qualitative level, the present consideration can be seen as a highly simplified study of an impact of the electromagnetic fields generated in relativistic heavy ion collisions on the strongly interacting hadronic matter.
NASA Astrophysics Data System (ADS)
Gao, Ya-Jun
2006-01-01
The so-called extended hyperbolic complex (EHC) function method is used to study further the stationary axisymmetric Einstein-Maxwell theory with p Abelian gauge fields (EM-p theory, for short). Two EHC structural Riemann-Hilbert (RH) transformations are constructed and are then shown to give an infinite-dimensional symmetry group of the EM-p theory. This symmetry group is verified to have the structure of semidirect product of Kac-Moody group SU(hat p+1,1) and Virasoro group. Moreover, the infinitesimal forms of these two RH transformations are calculated and found to give exactly the same infinitesimal transformations as in previous author's paper by a different scheme. This demonstrates that the results obtained in the present paper provide some exponentiations of all the infinitesimal symmetry transformations obtained before.
Lu Yuanming; Wang Ziqiang; Wen Xiaogang; Wang Zhenghan
2010-03-15
In the pattern-of-zeros approach to quantum Hall states, a set of data (n;m;S{sub a}|a=1,...,n;n,m,S{sub a} is n element of N) (called the pattern of zeros) is introduced to characterize a quantum Hall wave function. In this paper we find sufficient conditions on the pattern of zeros so that the data correspond to a valid wave function. Some times, a set of data (n;m;S{sub a}) corresponds to a unique quantum Hall state, while other times, a set of data corresponds to several different quantum Hall states. So in the latter cases, the pattern of zeros alone does not completely characterize the quantum Hall states. In this paper, we find that the following expanded set of data (n;m;S{sub a};c|a=1,...,n;n,m,S{sub a} is an element of N;c is an element of R) provides a more complete characterization of quantum Hall states. Each expanded set of data completely characterizes a unique quantum Hall state, at least for the examples discussed in this paper. The result is obtained by combining the pattern of zeros and Z{sub n} simple-current vertex algebra which describes a large class of Abelian and non-Abelian quantum Hall states PHI{sub Z{sub n}{sup sc}}. The more complete characterization in terms of (n;m;S{sub a};c) allows us to obtain more topological properties of those states, which include the central charge c of edge states, the scaling dimensions and the statistics of quasiparticle excitations.
Manna in winter: indigenous Americans, huckleberries, and blueberries
Technology Transfer Automated Retrieval System (TEKTRAN)
More than 35 species of blueberries (Vaccinium L.) and huckleberries (Vaccinium and Gaylussacia Kunth.) are indigenous to North America. The indigenous North American peoples, wise in the ways of survival, recognized the quality of these edible fruits and revered these plants. Beyond food needs, the...
School-Business Partnerships: Trojan Horse or Manna from Heaven?
ERIC Educational Resources Information Center
Burke, Michael A.
1986-01-01
Recent national initiatives have renewed interest in the development of cooperative programs involving participation by businesses in school activities. This article reviews potential problems and benefits in school-business partnerships and identifies six steps that must be followed if such partnerships are to be successful. (PGD)
A New Approach to Geoengineering: Manna From Heaven
NASA Astrophysics Data System (ADS)
Ellery, Alex
2015-04-01
Geo-engineering, although controversial, has become an emerging factor in coping with climate change. Although most are terrestrial-based technologies, I focus on a space-based approach implemented through a solar shield system. I present several new elements that essentially render the high-cost criticism moot. Of special relevance are two seemingly unrelated technologies - the Resource Prospector Mission (RPM) to the Moon in 2018 that shall implement a technology demonstration of simple material resource extraction from lunar regolith, and the emergence of multi-material 3D printing technology that promises unprecedented robotic manufacturing capabilities. My research group has begun theoretical and experimentation work in developing the concept of a 3D printed electric motor system from lunar-type resources. The electric motor underlies every universal mechanical machine. Together with 3D printed electronics, I submit that this would enable self-replicating machines to be realised. A detailed exposition on how this may be achieved will be outlined. Such self-replicating machines could construct the spacecraft required to implement a solar shield and solar power satellites in large numbers from lunar resources with the same underlying technologies at extremely low cost.
The Thirring-Wess model revisited: a functional integral approach
Belvedere, L.V. . E-mail: armflavio@if.uff.br
2005-06-01
We consider the Wess-Zumino-Witten theory to obtain the functional integral bosonization of the Thirring-Wess model with an arbitrary regularization parameter. Proceeding a systematic of decomposing the Bose field algebra into gauge-invariant- and gauge-non-invariant field subalgebras, we obtain the local decoupled quantum action. The generalized operator solutions for the equations of motion are reconstructed from the functional integral formalism. The isomorphism between the QED {sub 2} (QCD {sub 2}) with broken gauge symmetry by a regularization prescription and the Abelian (non-Abelian) Thirring-Wess model with a fixed bare mass for the meson field is established.
Lattice Defects in the Kitaev Honeycomb Model.
Brennan, John; Vala, Jiří
2016-05-19
The Kitaev honeycomb lattice system is an important model of topological materials whose phase diagram exhibits both abelian and non-abelian topological phases. The latter, a so-called Ising phase, is related to topological superconductors. Its quasiparticle excitations, which are formed by Majorana fermions attached to vortices, show non-abelian fractional statistics and are known as Ising anyons. We investigate dislocation defects in the Ising phase of the Kitaev honeycomb model. After introducing them to the system, we accordingly generalize our solution of this model to the situation with the defects. The important part of this effort is developing an appropriate Jordan-Wigner fermionization procedure. It is expected that the presence of defects manifests itself by the formation of fermionic zero-energy modes around the defect end points. We numerically confirm this expectation and further investigate properties of these modes. The computational potential of our technique is demonstrated for both diagonalization and dynamical simulations. The latter focuses on the process of fusion of the vortex zero-energy modes with the Majorana fermions attached to the defect. This process simulates fusion of non-abelian Ising anyons. PMID:26886150
More on ghosts in the Dvali-Gabadaze-Porrati model
Gorbunov, Dmitry; Sibiryakov, Sergei; Koyama, Kazuya
2006-02-15
It is shown by an explicit calculation that the excitations about the self-accelerating cosmological solution of the Dvali-Gabadaze-Porrati model contain a ghost mode. This raises serious doubts about viability of this solution. Our analysis reveals the similarity between the quadratic theory for the perturbations around the self-accelerating universe and an Abelian gauge model with two Stueckelberg fields.
Sharma, Sandeep
2015-01-14
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 C{sub 2} dimer in the cc-pVQZ basis set (with a frozen-core), corresponding to a Hilbert space dimension of 10{sup 12} many-body states. While our calculated energy lies within the 0.3 mE{sub h} 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 mE{sub h}, much more accurate than these previous estimates. Due to the additional efficiency afforded by the algorithm, the excitation energies (T{sub e}) of eight lowest lying excited states: a{sup 3}Π{sub u}, b{sup 3}Σ{sub g}{sup −}, A{sup 1}Π{sub u}, c{sup 3}Σ{sub u}{sup +}, B{sup 1}Δ{sub g}, B{sup ′1}Σ{sub g}{sup +}, d{sup 3}Π{sub g}, and C{sup 1}Π{sub g} 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 {sup 1}Σ{sub g}{sup +}, {sup 1}Σ{sub u}{sup +}, {sup 1}Σ{sub g}{sup −}, and {sup 1}Σ{sub u}{sup −}, to an estimated accuracy of 0.1 mE{sub h} of the exact result in this basis.
Universal Accretion Growth Using Sandpile Models
NASA Astrophysics Data System (ADS)
Datta, Srabani; McKie, Shane; Spencer, Ralph
2015-08-01
The Bak-Tang- Wiesenfeld (BTW) sandpile process is a model of a complex dynamical system with a large collection of particles or grains in a node that sheds load to their neighbours when they reach capacity. The cascades move around thesystem till it reaches stability with a critical point as an attractor. The BTW growth process shows self-organized criticality (SOC) with power-law distribution in cascade sizes having slope -5/3. This self-similarity of structureis synonymous with the fractal structure found in molecular clouds of Kolmogorov dimension 1.67 and by treating cascades as waves, scaling functions are found to be analogous to those observed for velocity structure functions influid turbulence. We apply the BTW sandpile model to study growth on a 2 dimensional rotating lattice in a magnetic field. In this paper, we show that this is a naturally occuring universal process giving rise to scale-freestructures with size limited only by the number of infalling grains. We also compare the BTW process with other sandpile models such as the Manna and Zhang processes. We find that the BTW sandpile model can be applied to a widerange of objects including molecular clouds, accretion disks and perhaps galaxies.
NASA Astrophysics Data System (ADS)
Gadella, M.; Mateos-Guilarte, J.; Muñoz-Castañeda, J. M.; Nieto, L. M.
2016-01-01
In this contribution to the study of one-dimensional point potentials, we prove that if we take the limit q\\to 0 on a potential of the type {v}0δ (y)+2{v}1{δ }\\prime (y)+{w}0δ (y-q)+2{w}1{δ }\\prime (y-q), we obtain a new point potential of the type {u}0δ (y)+2{u}1{δ }\\prime (y), when u 0 and u 1 are related to v 0, v 1, w 0 and w 1 by a law with the structure of a group. This is the Borel subgroup of {{SL}}2({{R}}). We also obtain the non-abelian addition law from the scattering data. The spectra of the Hamiltonian in the decoupling cases emerging in the study are also described in full. It is shown that for the {v}1=+/- 1, {w}1=+/- 1 values of the {δ }\\prime couplings the singular Kurasov matrices become equivalent to Dirichlet at one side of the point interaction and Robin boundary conditions at the other side.
NASA Astrophysics Data System (ADS)
Khan, Mayukh; Teo, Jeffrey; Hughes, Taylor
2015-03-01
Non-abelian anyons exhibit exotic braiding statistics which can be utilized to realize a universal topological quantum computer. In this work we focus on Fibonacci anyons which occur in Z3 Read Rezayi fractional quantum hall states. Traditionally they have been constructed using su(2)3 / u (1) coset theories. We introduce conformal field theories(CFTs) of exceptional and non-simply laced Lie Algebras at level 1, for example G2 ,F4 which host Fibonacci anyons. We realize these CFT's concretely on the 1d gapless edge of an anisotropic 2d system built out of coupled, interacting Luttinger wires. Interactions are introduced within a bundle of wires to fractionalize the original chiral bosons into different sectors. Next, we couple these sectors to get the desired topological phase in the bulk. The 2d bulk of the stack is gapped by backscattering terms between counterpropagating modes on different bundles. The emergence of this topological phase can be interpreted using techniques of anyon condensation . We also explicitly construct the Kac Moody algebra on the edge CFT using original bosonic degrees of freedom.We acknowledge support from NSF CAREER DMR-1351895(TH) and Simons Foundation (JT).
Lepton Flavour Violation and electron EDM in SUSY with a non-abelian flavour symmetry
Calibbi, Lorenzo
2008-11-23
We present the lepton sector phenomenology of a supersymmetric flavour model based on a SU(3) horizontal symmetry. This model successfully reproduces the observed fermion masses and mixings, without introducing unacceptably large SUSY sources of flavour and CP violation. We show that the model, which is at present weakly constrained, predicts the electron EDM and {mu}{yields}e,y to be within the final sensitivity of the currently running experiments, at least for SUSY masses within the reach of the LHC.
Inhomogeneous generalizations of Bianchi type VIh models with perfect fluid
NASA Astrophysics Data System (ADS)
Roy, S. R.; Prasad, A.
1991-07-01
Inhomogeneous universes admitting an Abelian G2 of isometry and filled with perfect fluid have been derived. These contain as special cases exact homogeneous universes of Bianchi type VIh. Many of these universes asymptotically tend to homogeneous Bianchi VIh universes. The models have been discussed for their physical and kinematical behaviors.
Confinement Driven by Scalar Field in 4d Non Abelian Gauge Theories
Chabab, Mohamed
2007-01-12
We review some of the most recent work on confinement in 4d gauge theories with a massive scalar field (dilaton). Emphasis is put on the derivation of confining analytical solutions to the Coulomb problem versus dilaton effective couplings to gauge terms. It is shown that these effective theories can be relevant to model quark confinement and may shed some light on confinement mechanism. Moreover, the study of interquark potential, derived from Dick Model, in the heavy meson sector proves that phenomenological investigation of tmechanism is more than justified and deserves more efforts.
The J1-J2 Heisenberg model on the triangular lattice
NASA Astrophysics Data System (ADS)
McCulloch, Ian; Saadatmand, Seyed; Powell, Ben
2015-03-01
We study the J1-J2 spin-1/2 Heisenberg model on triangular cylinders using non-abelian DMRG techniques. This model exhibits a rich phase diagram in the J1-J2 plane with a quasi-long-range 120° order, valence-bond crystal and columnar phases. ARC Centre for Engineered Quantum Systems.
Consequences of an Abelian Z' for neutrino oscillations and dark matter
NASA Astrophysics Data System (ADS)
Plestid, Ryan
2016-02-01
The Standard Model's accidental and anomaly-free currents, B -L , Le-Lμ, Le-Lτ, and Lμ-Lτ, could be indicative of a hidden gauge structure beyond the Standard Model. Additionally, neutrino masses can be generated by a dimension-5 operator that generically breaks all of these symmetries. It is therefore important to investigate the compatibility of a gauged U'(1 ) and neutrino phenomenology. We consider gauging each of the symmetries above with a minimal extended matter content. This includes the Z', an order parameter to break the U'(1 ), and three right-handed neutrinos. We find all but B -L require additional matter content to explain the measured neutrino oscillation parameters. We also discuss the compatibility of the measured neutrino textures with a nonthermal dark matter production mechanism involving the decay of the Z'. Finally, we present a parametric relation that implies that any sterile neutrino dark matter candidate should not be expected to contribute to neutrino masses beyond ten parts per million.
Topological flat band models with arbitrary Chern numbers
NASA Astrophysics Data System (ADS)
Yang, Shuo; Gu, Zheng-Cheng; Sun, Kai; Das Sarma, S.
2012-12-01
We report the theoretical discovery of a systematic scheme to produce topological flat bands (TFBs) with arbitrary Chern numbers. We find that generically a multiorbital high Chern number TFB model can be constructed by considering multilayer Chern number C=1 TFB models with enhanced translational symmetry. A series of models are presented as examples, including a two-band model on a triangular lattice with a Chern number C=3 and an N-band square lattice model with C=N for an arbitrary integer N. In all these models, the flatness ratio for the TFBs is larger than 30 and increases with increasing Chern number. In the presence of appropriate interparticle interactions, these models are likely to lead to the formation of Abelian and non-Abelian fractional Chern insulators. As a simple example, we test the C=2 model with hardcore bosons at 1/3 filling, and an intriguing fractional quantum Hall state is observed.
Holographic entropy and real-time dynamics of quarkonium dissociation in non-Abelian plasma
Iatrakis, Ioannis; Kharzeev, Dmitri E.
2016-04-26
The peak of the heavy quark pair entropy at the deconfinement transition, observed in lattice QCD, suggests that the transition is effectively driven by the increase of the entropy of bound states. The growth of the entropy with the interquark distance leads to the emergent entropic force that induces dissociation of quarkonium states. Since the quark-gluon plasma around the transition point is a strongly coupled system, we use the gauge-gravity duality to study the entropy of heavy quarkonium and the real-time dynamics of its dissociation. In particular, we employ the improved holographic QCD model as a dual description of largemore » Nc Yang-Mills theory. Studying the dynamics of the fundamental string between the quarks placed on the boundary, we find that the entropy peaks at the transition point. We also study the real-time dynamics of the system by considering the holographic string falling in the black hole horizon where it equilibrates. As a result, in the vicinity of the deconfinement transition, the dissociation time is found to be less than a fermi, suggesting that the entropic destruction is the dominant dissociation mechanism in this temperature region.« less
Holographic entropy and real-time dynamics of quarkonium dissociation in non-Abelian plasma
NASA Astrophysics Data System (ADS)
Iatrakis, Ioannis; Kharzeev, Dmitri E.
2016-04-01
The peak of the heavy quark pair entropy at the deconfinement transition, observed in lattice QCD, suggests that the transition is effectively driven by the increase of the entropy of bound states. The growth of the entropy with the interquark distance leads to the emergent entropic force that induces dissociation of quarkonium states. Since the quark-gluon plasma around the transition point is a strongly coupled system, we use the gauge-gravity duality to study the entropy of heavy quarkonium and the real-time dynamics of its dissociation. In particular, we employ the improved holographic QCD model as a dual description of large Nc Yang-Mills theory. Studying the dynamics of the fundamental string between the quarks placed on the boundary, we find that the entropy peaks at the transition point. We also study the real-time dynamics of the system by considering the holographic string falling in the black hole horizon where it equilibrates. In the vicinity of the deconfinement transition, the dissociation time is found to be less than a fermi, suggesting that the entropic destruction is the dominant dissociation mechanism in this temperature region.
Tushev, A V
2006-10-31
In the present paper certain methods are developed that enable one to study the properties of the controller of a prime faithful ideal I of the group algebra kA of an Abelian torsion-free group A of finite rank over a field k. The main idea is that the quotient ring kA/I by the given ideal I can be embedded as an integral domain k[A] into some field F and the group A becomes a subgroup of the multiplicative group of the field F. This allows one to apply certain results of field theory, such as Kummer's theory and the properties of the multiplicative groups of fields, to the study of the integral domain k[A]. In turn, the properties of the integral domain k[A]{approx_equal}kA/I depend essentially on the properties of the ideal I. In particular, by using these methods, an independent proof of the new version of Brookes's theorem on the controllers of prime ideals of the group algebra kA of an Abelian torsion-free group A of finite rank is obtained in the case where the field k has positive characteristic.
Projective ribbon permutation statistics: A remnant of non-Abelian braiding in higher dimensions
NASA Astrophysics Data System (ADS)
Freedman, Michael; Hastings, Matthew B.; Nayak, Chetan; Qi, Xiao-Liang; Walker, Kevin; Wang, Zhenghan
2011-03-01
In a recent paper, Teo and Kane [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.104.046401 104, 046401 (2010)] proposed a three-dimensional (3D) model in which the defects support Majorana fermion zero modes. They argued that exchanging and twisting these defects would implement a set R of unitary transformations on the zero-mode Hilbert space which is a “ghostly” recollection of the action of the braid group on Ising anyons in two dimensions. In this paper, we find the group T2n, which governs the statistics of these defects by analyzing the topology of the space K2n of configurations of 2n defects in a slowly spatially varying gapped free-fermion Hamiltonian: T2n≡π1(K2n). We find that the group T2n=Z×T2nr, where the “ribbon permutation group” T2nr is a mild enhancement of the permutation group S2n: T2nr≡Z2×E((Z2)2n⋊S2n). Here, E((Z2)2n⋊S2n) is the “even part” of (Z2)2n⋊S2n, namely, those elements for which the total parity of the element in (Z2)2n added to the parity of the permutation is even. Surprisingly, R is only a projective representation of T2n, a possibility proposed by Wilczek [e-print arXiv:hep-th/9806228]. Thus, Teo and Kane’s defects realize projective ribbon permutation statistics,” which we show to be consistent with locality. We extend this phenomenon to other dimensions, codimensions, and symmetry classes. We note that our analysis applies to 3D networks of quantum wires supporting Majorana fermions; thus, these networks are not required to be planar. Because it is an essential input for our calculation, we review the topological classification of gapped free-fermion systems and its relation to Bott periodicity.
Spin correlation and Majorana spectrum in chiral spin liquids in a decorated-honeycomb Kitaev model
NASA Astrophysics Data System (ADS)
Nasu, Joji; Motome, Yukitoshi
2016-02-01
Temperature evolution of the spin correlation and excitation spectrum is investigated for the Kitaev model defined on a decorated honeycomb lattice by using the quantum Monte Carlo simulation in the Majorana fermion representation. The ground state of this quantum spin model is given by two kinds of chiral spin liquids: one is topologically trivial with Abelian anyon excitations, and the other is topologically nontrivial with non-Abelian anyon excitations. While lowering temperature, the model exhibits several crossovers in the paramagnetic state, which originate from the fractionalization of quantum spins into Majorana fermions, in addition to a phase transition associated with time reversal symmetry breaking. We show that the spin correlation develops around the crossover temperatures, whereas it shows a slight change at the critical temperature, as in other Kitaev-type models. We also calculate the excitation spectrum in terms of Majorana fermions, and find that the excitation gap in the non-Abelian phase is fragile against thermal fluctuations of the Z2 fluxes, while that in the Abelian phase remains open.
ERIC Educational Resources Information Center
Kohl, Timothy
2012-01-01
A pair of elementary exercises, one from topology, the other from group theory are such that if one replaces three words in the topology problem, you get the group theory problem and vice-versa. This suggests connections between the two that are explored here.
Fixed-energy sandpiles belong generically to directed percolation.
Basu, Mahashweta; Basu, Urna; Bondyopadhyay, Sourish; Mohanty, P K; Hinrichsen, Haye
2012-07-01
Fixed-energy sandpiles with stochastic update rules are known to exhibit a nonequilibrium phase transition from an active phase into infinitely many absorbing states. Examples include the conserved Manna model, the conserved lattice gas, and the conserved threshold transfer process. It is believed that the transitions in these models belong to an autonomous universality class of nonequilibrium phase transitions, the so-called Manna class. Contrarily, the present numerical study of selected (1+1)-dimensional models in this class suggests that their critical behavior converges to directed percolation after very long time, questioning the existence of an independent Manna class. PMID:23031115
NASA Astrophysics Data System (ADS)
Dorey, Nick; Tong, David; Turner, Carl
2016-08-01
We study a U( N) gauged matrix quantum mechanics which, in the large N limit, is closely related to the chiral WZW conformal field theory. This manifests itself in two ways. First, we construct the left-moving Kac-Moody algebra from matrix degrees of freedom. Secondly, we compute the partition function of the matrix model in terms of Schur and Kostka polynomials and show that, in the large N limit, it coincides with the partition function of the WZW model. This same matrix model was recently shown to describe non-Abelian quantum Hall states and the relationship to the WZW model can be understood in this framework.
NASA Astrophysics Data System (ADS)
Aleshin, S. S.; Kazantsev, A. E.; Skoptsov, M. B.; Stepanyantz, K. V.
2016-05-01
We consider a general non-Abelian renormalizable {N} = 1 supersymmetric gauge theory, regularized by higher covariant derivatives without breaking the BRST invariance, and calculate one-loop divergences for a general form of higher derivative regulator and of the gauge fixing term. It is demonstrated that the momentum integrals giving the one-loop β-function are integrals of double total derivatives independently of a particular choice of the higher derivative term. Evaluating them we reproduce the well-known result for the one-loop β-function. Also we find that the three-point ghost vertices with a single line of the quantum gauge superfield are not renormalized in the considered approximation.
NASA Astrophysics Data System (ADS)
Wang, Juven C.; Wen, Xiao-Gang
2015-01-01
String and particle braiding statistics are examined in a class of topological orders described by discrete gauge theories with a gauge group G and a 4-cocycle twist ω4 of G 's cohomology group H4(G ,R /Z ) in three-dimensional space and one-dimensional time (3 +1 D ) . We establish the topological spin and the spin-statistics relation for the closed strings and their multistring braiding statistics. The 3 +1 D twisted gauge theory can be characterized by a representation of a modular transformation group, SL (3 ,Z ) . We express the SL (3 ,Z ) generators Sx y z and Tx y in terms of the gauge group G and the 4-cocycle ω4. As we compactify one of the spatial directions z into a compact circle with a gauge flux b inserted, we can use the generators Sx y and Tx y of an SL (2 ,Z ) subgroup to study the dimensional reduction of the 3D topological order C3 D to a direct sum of degenerate states of 2D topological orders Cb2 D in different flux b sectors: C3 D=⊕bCb2 D . The 2D topological orders Cb2 D are described by 2D gauge theories of the group G twisted by the 3-cocycle ω3 (b ), dimensionally reduced from the 4-cocycle ω4. We show that the SL (2 ,Z ) generators, Sx y and Tx y, fully encode a particular type of three-string braiding statistics with a pattern that is the connected sum of two Hopf links. With certain 4-cocycle twists, we discover that, by threading a third string through two-string unlink into a three-string Hopf-link configuration, Abelian two-string braiding statistics is promoted to non-Abelian three-string braiding statistics.
Urrestilla, Jon; Bevis, Neil; Hindmarsh, Mark; Kunz, Martin E-mail: n.bevis@imperial.ac.uk E-mail: martin.kunz@physics.unige.ch
2011-12-01
We present a significant update of the constraints on the Abelian Higgs cosmic string tension by cosmic microwave background (CMB) data, enabled both by the use of new high-resolution CMB data from suborbital experiments as well as the latest results of the WMAP satellite, and by improved predictions for the impact of Abelian Higgs cosmic strings on the CMB power spectra. The new cosmic string spectra [1] were improved especially for small angular scales, through the use of larger Abelian Higgs string simulations and careful extrapolation. If Abelian Higgs strings are present then we find improved bounds on their contribution to the CMB anisotropies, fd{sup AH} < 0.095, and on their tension, Gμ{sub AH} < 0.57 × 10{sup −6}, both at 95% confidence level using WMAP7 data; and fd{sup AH} < 0.048 and Gμ{sub AH} < 0.42 × 10{sup −6} using all the CMB data. We also find that using all the CMB data, a scale invariant initial perturbation spectrum, n{sub s} = 1, is now disfavoured at 2.4σ even if strings are present. A Bayesian model selection analysis no longer indicates a preference for strings.
Model Fractional Chern Insulators.
Behrmann, Jörg; Liu, Zhao; Bergholtz, Emil J
2016-05-27
We devise local lattice models whose ground states are model fractional Chern insulators-Abelian and non-Abelian topologically ordered states characterized by exact ground state degeneracies at any finite size and infinite entanglement gaps. Most saliently, we construct exact parent Hamiltonians for two distinct families of bosonic lattice generalizations of the Z_{k} parafermion quantum Hall states: (i) color-entangled fractional Chern insulators at band filling fractions ν=k/(C+1) and (ii) nematic states at ν=k/2, where C is the Chern number of the lowest band. In spite of a fluctuating Berry curvature, our construction is partially frustration free: the ground states reside entirely within the lowest band and exactly minimize a local (k+1) body repulsion term by term. In addition to providing the first known models hosting intriguing states such as higher Chern number generalizations of the Fibonacci anyon quantum Hall states, the remarkable stability and finite-size properties make our models particularly well suited for the study of novel phenomena involving, e.g., twist defects and proximity induced superconductivity, as well as being a guide for designing experiments. PMID:27284668
Model Fractional Chern Insulators
NASA Astrophysics Data System (ADS)
Behrmann, Jörg; Liu, Zhao; Bergholtz, Emil J.
2016-05-01
We devise local lattice models whose ground states are model fractional Chern insulators—Abelian and non-Abelian topologically ordered states characterized by exact ground state degeneracies at any finite size and infinite entanglement gaps. Most saliently, we construct exact parent Hamiltonians for two distinct families of bosonic lattice generalizations of the Zk parafermion quantum Hall states: (i) color-entangled fractional Chern insulators at band filling fractions ν =k /(C +1 ) and (ii) nematic states at ν =k /2 , where C is the Chern number of the lowest band. In spite of a fluctuating Berry curvature, our construction is partially frustration free: the ground states reside entirely within the lowest band and exactly minimize a local (k +1 ) body repulsion term by term. In addition to providing the first known models hosting intriguing states such as higher Chern number generalizations of the Fibonacci anyon quantum Hall states, the remarkable stability and finite-size properties make our models particularly well suited for the study of novel phenomena involving, e.g., twist defects and proximity induced superconductivity, as well as being a guide for designing experiments.
NASA Astrophysics Data System (ADS)
Pesando, Igor
2016-09-01
We consider the simplest possible setting of non-abelian twist fields which corresponds to SU (2) monodromies. We first review the theory of hypergeometric function and of the solutions of the most general Fuchsian second order equation with three singularities. Then we solve the problem of writing the general solution with prescribed U (2) monodromies. We use this result to compute the classical string solution corresponding to three D2 branes in R4. Despite the fact that the configuration is supersymmetric the classical string solution is not holomorphic. Using the equation of motion and not the KLT approach we give a very simple expression for the classical action of the string. We find that the classical action is not proportional to the area of the triangle determined by the branes intersection points since the solution is not holomorphic. Phenomenologically this means that the Yukawa couplings for these supersymmetric configurations on non-factorized tori are suppressed with respect to the factorized case.
Gauged WZW Models via Equivariant Cohomology
NASA Astrophysics Data System (ADS)
García-Compeán, Hugo; Paniagua, Pablo
The problem of finding a systematic computation of the gauge-invariant extension of WZW term by using equivariant cohomology is addressed. Witten's analysis for the two-dimensional case is extended to higher dimensions, in particular to four dimensions. It is shown that Cartan's model is used to find the anomaly cancellation condition while Weil's model is more appropriated to express the gauge-invariant extension of the WZW term. In the process we point out that both models are also useful to emphasize some nice relations with the Abelian anomaly.
Towards LHC physics with nonlocal Standard Model
NASA Astrophysics Data System (ADS)
Biswas, Tirthabir; Okada, Nobuchika
2015-09-01
We take a few steps towards constructing a string-inspired nonlocal extension of the Standard Model. We start by illustrating how quantum loop calculations can be performed in nonlocal scalar field theory. In particular, we show the potential to address the hierarchy problem in the nonlocal framework. Next, we construct a nonlocal abelian gauge model and derive modifications of the gauge interaction vertex and field propagators. We apply the modifications to a toy version of the nonlocal Standard Model and investigate collider phenomenology. We find the lower bound on the scale of nonlocality from the 8 TeV LHC data to be 2.5-3 TeV.
Line of critical points in 2+1 dimensions: quantum critical loop gases and non-Abelian gauge theory.
Freedman, Michael; Nayak, Chetan; Shtengel, Kirill
2005-04-15
In this Letter, we (1) construct a one-parameter family of lattice models of interacting spins; (2) obtain their exact ground states; (3) derive a statistical-mechanical analogy which relates their ground states to O(n) loop gases; (4) show that the models are critical for dmodels; (5) note that, for the special values d=2cos([pi/(k+2)], they are related to doubled level-k SU(2) Chern-Simons theory; (6) conjecture that they are in the universality class of a nonrelativistic SU(2) gauge theory; and (7) show that its one-loop beta function vanishes for all values of the coupling constant, implying that it is also on a critical line. PMID:15904103
Quantum structure of the non-Abelian Weizsäcker-Williams field for a very large nucleus
NASA Astrophysics Data System (ADS)
Kovchegov, Yuri V.
1997-05-01
We consider the McLerran-Venugopalan model for calculation of the small-x part of the gluon distribution function for a very large ultrarelativistic nucleus at weak coupling. We construct the Feynman diagrams which correspond to the classical Weizsäcker-Williams field found previously [Yu. V. Kovchegov, Phys. Rev. D 54, 5463 (1996)] as a solution of the classical equations of motion for the gluon field in the light-cone gauge. Analyzing these diagrams we obtain a limit for the McLerran-Venugopalan model. We show that as long as this limit is not violated a classical field can be used for the calculation of scattering amplitudes.
Quantum structure of the non-Abelian Weizs{umlt a}cker-Williams field for a very large nucleus
Kovchegov, Y.V.
1997-05-01
We consider the McLerran-Venugopalan model for calculation of the small-x part of the gluon distribution function for a very large ultrarelativistic nucleus at weak coupling. We construct the Feynman diagrams which correspond to the classical Weizs{umlt a}cker-Williams field found previously [Yu. V. Kovchegov, Phys. Rev. D {bold 54}, 5463 (1996)] as a solution of the classical equations of motion for the gluon field in the light-cone gauge. Analyzing these diagrams we obtain a limit for the McLerran-Venugopalan model. We show that as long as this limit is not violated a classical field can be used for the calculation of scattering amplitudes. {copyright} {ital 1997} {ital The American Physical Society}
Atomic quantum simulation of U(N) and SU(N) non-Abelian lattice gauge theories.
Banerjee, D; Bögli, M; Dalmonte, M; Rico, E; Stebler, P; Wiese, U-J; Zoller, P
2013-03-22
Using ultracold alkaline-earth atoms in optical lattices, we construct a quantum simulator for U(N) and SU(N) lattice gauge theories with fermionic matter based on quantum link models. These systems share qualitative features with QCD, including chiral symmetry breaking and restoration at nonzero temperature or baryon density. Unlike classical simulations, a quantum simulator does not suffer from sign problems and can address the corresponding chiral dynamics in real time. PMID:25166816
Model Independent Bounds on Kinetic Mixing
Hook, Anson; Izaguirre, Eder; Wacker, Jay G.; /SLAC
2011-08-22
New Abelian vector bosons can kinetically mix with the hypercharge gauge boson of the Standard Model. This letter computes the model independent limits on vector bosons with masses from 1 GeV to 1 TeV. The limits arise from the numerous e{sup +}e{sup -} experiments that have been performed in this energy range and bound the kinetic mixing by {epsilon} {approx}< 0.03 for most of the mass range studied, regardless of any additional interactions that the new vector boson may have.
Karanikas, A.I.; Ktorides, C.N.; Mavromatos, N.E.
1986-12-01
A recently proposed approach to gauge field theories, by which one formulates them non-locally and subsequently approaches locality arbitrarily close, is applied to U(1) gauge theories. We test the possibility that the aformentioned methodology might introduce a measure in the functional integral which supports non-perturbative calculations in the continuum. In particular, we are able to carry relevant calculations pertaining to the expectation value of the Wilson's loop operator in 3+1, 2+1 and 1+1 dimensions. The results are similar to ones obtained through the lattice regularization of R(1) gauge theory, with the important difference that in our case they refer to continuum U(1) gauge theory, as a function of the bare coupling constant. We further solidify the validity of our approach by conducting a calculation referring to the 2-dimensional scalar Heisenberg model, remaining always in the continuum. copyright 1986 Academic Press, Inc.
S{sub 4}xZ{sub 2} flavor symmetry in supersymmetric extra U(1) model
Daikoku, Y.; Okada, H.
2010-08-01
We propose a E{sub 6} inspired supersymmetric model with a non-Abelian discrete flavor symmetry (S{sub 4} group); that is, SU(3){sub c}xSU(2){sub W}xU(1){sub Y}xU(1){sub X}xS{sub 4}xZ{sub 2}. In our scenario, the additional Abelian gauge symmetry, U(1){sub X}, not only solves the {mu} problem in the minimal supersymmetric standard model but also requires new exotic fields which play an important role in solving flavor puzzles. If our exotic quarks can be embedded into a S{sub 4} triplet, which corresponds to the number of the generation, one finds that dangerous proton decay can be well suppressed. Hence, it might be expected that the generation structure for lepton and quark in the standard model can be understood as a new system in order to stabilize the proton in a supersymmetric standard model. Moreover, because of the nature of the discrete non-Abelian symmetry itself, Yukawa coupling constants of our model are drastically reduced. In our paper, we show two predictive examples of the models for quark sector and lepton sector, respectively.
Specific Heat Anomalies in Solids Described by a Multilevel Model
NASA Astrophysics Data System (ADS)
Souza, Mariano de; Paupitz, Ricardo; Seridonio, Antonio; Lagos, Roberto E.
2016-04-01
In the field of condensed matter physics, specific heat measurements can be considered as a pivotal experimental technique for characterizing the fundamental excitations involved in a certain phase transition. Indeed, phase transitions involving spin (de Souza et al. Phys. B Condens. Matter 404, 494 (2009) and Manna et al. Phys. Rev. Lett. 104, 016403 (2010)), charge (Pregelj et al. Phys. Rev. B 82, 144438 (2010)), lattice (Jesche et al. Phys. Rev. B 81, 134525 (2010)) (phonons) and orbital degrees of freedom, the interplay between ferromagnetism and superconductivity (Jesche et al. Phys. Rev. B 86, 020501 (2012)), Schottky-like anomalies in doped compounds (Lagos et al. Phys. C Supercond. 309, 170 (1998)), electronic levels in finite correlated systems (Macedo and Lagos J. Magn. Magn. Mater. 226, 105 (2001)), among other features, can be captured by means of high-resolution calorimetry. Furthermore, the entropy change associated with a first-order phase transition, no matter its nature, can be directly obtained upon integrating the specific heat over T, i.e., C( T)/ T, in the temperature range of interest. Here, we report on a detailed analysis of the two-peak specific heat anomalies observed in several materials. Employing a simple multilevel model, varying the spacing between the energy levels Δ i = ( E i - E 0) and the degeneracy of each energy level g i , we derive the required conditions for the appearance of such anomalies. Our findings indicate that a ratio of {Δ }2/{Δ }1thickapprox 10 between the energy levels and a high degeneracy of one of the energy levels define the two-peaks regime in the specific heat. Our approach accurately matches recent experimental results. Furthermore, using a mean-field approach, we calculate the specific heat of a degenerate Schottky-like system undergoing a ferromagnetic (FM) phase transition. Our results reveal that as the degeneracy is increased the Schottky maximum in the specific heat becomes narrow while the peak
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.
Abelian and non-abelian topological phases with dipoles
NASA Astrophysics Data System (ADS)
Gorshkov, Alexey
2015-03-01
Topological phases of matter offer a pathway towards fault-tolerant topological quantum computers, in which quantum information is encoded in nonlocal (topological) degrees of freedom and is processed robustly by braiding (i.e. moving around one another) topological defects called anyons. In this talk, we will develop schemes for taking advantage of the tremendous degree of control recently achieved in atomic, molecular, and optical systems - particularly in systems of interacting dipoles - to realize exotic topological phenomena, such as parafermions, Ising anyons, and Fibonacci anyons, that ultimately allow for universal topologically protected quantum computing.
Jackiw-Pi model: A superfield approach
NASA Astrophysics Data System (ADS)
Gupta, Saurabh
2014-12-01
We derive the off-shell nilpotent and absolutely anticommuting Becchi-Rouet-Stora-Tyutin (BRST) as well as anti-BRST transformations s ( a) b corresponding to the Yang-Mills gauge transformations of 3D Jackiw-Pi model by exploiting the "augmented" super-field formalism. We also show that the Curci-Ferrari restriction, which is a hallmark of any non-Abelian 1-form gauge theories, emerges naturally within this formalism and plays an instrumental role in providing the proof of absolute anticommutativity of s ( a) b .
The anisotropic λ-deformed SU (2) model is integrable
NASA Astrophysics Data System (ADS)
Sfetsos, Konstantinos; Siampos, Konstantinos
2015-04-01
The all-loop anisotropic Thirring model interpolates between the WZW model and the non-Abelian T-dual of the anisotropic principal chiral model. We focus on the SU (2) case and we prove that it is classically integrable by providing its Lax pair formulation. We derive its underlying symmetry current algebra and use it to show that the Poisson brackets of the spatial part of the Lax pair, assume the Maillet form. In this way we procure the corresponding r and s matrices which provide non-trivial solutions to the modified Yang-Baxter equation.
Towards realistic standard model from D-brane configurations
Leontaris, G. K.; Tracas, N. D.; Korakianitis, O.; Vlachos, N. D.
2007-12-01
Effective low energy models arising in the context of D-brane configurations with standard model (SM) gauge symmetry extended by several gauged Abelian factors are discussed. The models are classified according to their hypercharge embeddings consistent with the SM spectrum hypercharge assignment. Particular cases are analyzed according to their perspectives and viability as low energy effective field theory candidates. The resulting string scale is determined by means of a two-loop renormalization group calculation. Their implications in Yukawa couplings, neutrinos and flavor changing processes are also presented.
Manna from Heaven or "Clickers" from Hell: Experiences with an Electronic Response System
ERIC Educational Resources Information Center
Hatch, Jay; Jensen, Murray; Moore, Randy
2005-01-01
Instructors used an electronic response system to enhance student-centered learning in large and small college biology classes. The system worked well to engage students in learning the subject matter and to assess their prior knowledge and misconceptions. It provided useful feedback to students as well as instructors. Problems encountered…
Classifying BPS states in supersymmetric gauge theories coupled to higher derivative chiral models
NASA Astrophysics Data System (ADS)
Nitta, Muneto; Sasaki, Shin
2015-06-01
We study N =1 supersymmetric gauge theories coupled with higher derivative chiral models in four dimensions in the off-shell superfield formalism. We solve the equation of motion for the auxiliary fields and find two distinct on-shell structures of the Lagrangian that we call the canonical and noncanonical branches characterized by zero and nonzero auxiliary fields, respectively. We classify Bogomol'nyi-Prasado-Sommerfield (BPS) states of the models in Minkowski and Euclidean spaces. In Minkowski space, we find Abelian and non-Abelian vortices, vortex lumps (or gauged lumps with fractional lump charges) as 1 /2 BPS states in the canonical branch, and higher derivative generalization of vortices and vortex-(BPS)baby Skyrmions (or gauged BPS baby Skyrmions with fractional baby Skyrme charges) as 1 /4 BPS states in the noncanonical branch. In four-dimensional Euclidean space, we find Yang-Mills instantons trapped inside a non-Abelian vortex, intersecting vortices, and intersecting vortex-(BPS)baby Skyrmions as 1 /4 BPS states in the canonical branch but no BPS states in the noncanonical branch other than those in the Minkowski space.
NASA Astrophysics Data System (ADS)
Worman, A.; Kjellin, J. P.; Lindahl, A.; Johansson, H.
2005-05-01
To throw light on coupled hydrological, chemical and microbiological processes in treatment wetlands, this study uses both radioactive water and reactive tracers. A tracer mixture consisting of tritiated water, P-32 in the form of PO4- and N-15 in the form of N2O was injected to the 2.6 hectare large Ekeby wetland, Sweden. From the breakthrough curves of tritium, the mean residence time of water in pond 1 can be estimated to be about 3 to 3.5 days. The total injected activity of phosphorus was 17.98 GBq and about 13.73 GBq was recovered at the outlet during the investigation period ending 10 days and 16 hours after the start of the injection. This implies that 24% of the phosphate solution was removed in the November - December period in which the experiment was performed. The total injected amount of N-15 was 42.1 grams and 29.6 grams was retained at the effluent. This means that 30% of the nitrogen was either retained in the wetland or removed due to denitrification. An analysis of regular monitoring data shows that the annual removal rate in the entire wetland (each flow line passes two ponds in series) is about 50% for total phosphorus and 25% for total nitrogen. Probably, the most important mechanism for this removal is adsorption onto particulate matter and deposition. Analyses of vegetation material indicate that a certain (minor) fraction was adsorbed to submersed and emerging macrophytes, like Elodera Canadensis, Thypa sp. (Cattail) and Glyceria sp. (Manna grass). A 2D mathematical model for both water flow and solute transport could explain the N-transport through the wetland. The model accounts for the rate-limited exchange with bed sediments and denitrification in the water and bed sediment. Independent batch tests indicate a particularly high microbiological activity in the bed sediments. The rate-limited exchange with the bed limits also the denitrification capacity of the wetland.
Superconducting vortices in semilocal models.
Forgács, Péter; Reuillon, Sébastien; Volkov, Mikhail S
2006-02-01
It is shown that the SU(2) semilocal model--the Abelian Higgs model with two complex scalars--admits a new class of stationary, straight string solutions carrying a persistent current and having finite energy per unit length. In the plane orthogonal to their direction they correspond to a nontrivial deformation of the embedded Abrikosov-Nielsen-Olesen (ANO) vortices by the current flowing through them. The new solutions bifurcate with the ANO vortices in the limit of vanishing current. They can be either static or stationary. In the stationary case, the relative phase of the two scalars rotates at constant velocity, giving rise to an electric field and angular momentum, while the energy remains finite. The new static vortex solutions have lower energy than the ANO vortices and could be of considerable importance in various physical systems (from condensed matter to cosmic strings). PMID:16486806
NASA Astrophysics Data System (ADS)
Ma, Ernest; Melić, Blaženka
2013-10-01
A model proposed in 2004 using the non-Abelian discrete symmetry S3 for understanding the flavor structure of quarks and leptons is updated, with special focus on the quark and scalar sectors. We show how the approximate residual symmetries of this model explain both the pattern of the quark mixing matrix and why the recently observed particle of 126 GeV at the Large Hadron Collider is so much like the one Higgs boson of the Standard Model. We identify the strongest phenomenological bounds on the scalar masses of this model, and predict a possibly observable decay b → sτ-μ+ (Bs →τ+μ-), but not b → sτ+μ- (Bs →τ-μ+).
A composite model of quarks and bosons
NASA Astrophysics Data System (ADS)
Moffat, J. W.
2015-01-01
A composite model of quarks and bosons is proposed in which a spin 1/2 isospin doublet ψ is the basic building block of quarks and bosons in the standard model. The ψ has two components v and w with charges Q = (1)/(3)e and Q = 0, respectively, that combine to form the three generations of colored quark flavors. A strong force described by a triplet of massless gluons binds the constituents called geminis. The confining constituent non-Abelian SU(2)C field theory is called constituent dynamics with a confining energy scale ΛCD. The constituent dynamics condensate <\\bar {v}v+\\bar {w}w>!=q 0 spontaneously breaks the electroweak symmetry SU(2)L×U(1)Y→U(1)EM and a triplet of Nambu-Goldstone bosons make the gauge bosons W± and Z0 massive, while retaining a massless photon. A global custodial SU(2)L×SU(2)R symmetry guarantees that the symmetry breaking in the weak interaction sector agrees with electroweak data. The non-Abelian SU(2)C color dynamics satisfies asymptotic freedom, which resolves the gauge and Higgs mass hierarchy problems and makes the model ultraviolet complete. The composite constituent dynamics model can realize a SU(3)C×SU(2)L×U(1)Y electroweak and strong interaction model that satisfies the naturalness principle. The three generations of colorless quarks α and β with charges Q = +1e and Q = 0, respectively, which are predicted to exist in the composite model can form bound states which can be identified with the spectrum of exotic mesons.
Large field excursions from a few site relaxion model
NASA Astrophysics Data System (ADS)
Fonseca, N.; de Lima, L.; Machado, C. S.; Matheus, R. D.
2016-07-01
Relaxion models are an interesting new avenue to explain the radiative stability of the Standard Model scalar sector. They require very large field excursions, which are difficult to generate in a consistent UV completion and to reconcile with the compact field space of the relaxion. We propose an N -site model which naturally generates the large decay constant needed to address these issues. Our model offers distinct advantages with respect to previous proposals: the construction involves non-Abelian fields, allowing for controlled high-energy behavior and more model building possibilities, both in particle physics and inflationary models, and also admits a continuum limit when the number of sites is large, which may be interpreted as a warped extra dimension.
Gauge turbulence, topological defect dynamics, and condensation in Higgs models
Gasenzer, Thomas; McLerran, Larry; Pawlowski, Jan M.; Sexty, Dénes
2014-07-28
The real-time dynamics of topological defects and turbulent configurations of gauge fields for electric and magnetic confinement are studied numerically within a 2+1D Abelian Higgs model. It is shown that confinement is appearing in such systems equilibrating after a strong initial quench such as the overpopulation of the infrared modes. While the final equilibrium state does not support confinement, metastable vortex defect configurations appearing in the gauge field are found to be closely related to the appearance of physically observable confined electric and magnetic charges. These phenomena are seen to be intimately related to the approach of a non-thermal fixed point of the far-from-equilibrium dynamical evolution, signaled by universal scaling in the gauge-invariant correlation function of the Higgs field. Even when the parameters of the Higgs action do not support condensate formation in the vacuum, during this approach, transient Higgs condensation is observed. We discuss implications of these results for the far-from-equilibrium dynamics of Yang–Mills fields and potential mechanisms of how confinement and condensation in non-Abelian gauge fields can be understood in terms of the dynamics of Higgs models. These suggest that there is an interesting new class of dynamics of strong coherent turbulent gauge fields with condensates.
Gauge turbulence, topological defect dynamics, and condensation in Higgs models
Gasenzer, Thomas; McLerran, Larry; Pawlowski, Jan M.; Sexty, Dénes
2014-07-28
The real-time dynamics of topological defects and turbulent configurations of gauge fields for electric and magnetic confinement are studied numerically within a 2+1D Abelian Higgs model. It is shown that confinement is appearing in such systems equilibrating after a strong initial quench such as the overpopulation of the infrared modes. While the final equilibrium state does not support confinement, metastable vortex defect configurations appearing in the gauge field are found to be closely related to the appearance of physically observable confined electric and magnetic charges. These phenomena are seen to be intimately related to the approach of a non-thermal fixedmore » point of the far-from-equilibrium dynamical evolution, signaled by universal scaling in the gauge-invariant correlation function of the Higgs field. Even when the parameters of the Higgs action do not support condensate formation in the vacuum, during this approach, transient Higgs condensation is observed. We discuss implications of these results for the far-from-equilibrium dynamics of Yang–Mills fields and potential mechanisms of how confinement and condensation in non-Abelian gauge fields can be understood in terms of the dynamics of Higgs models. These suggest that there is an interesting new class of dynamics of strong coherent turbulent gauge fields with condensates.« less
NASA Astrophysics Data System (ADS)
Kovchegov, Yuri V.
1996-11-01
We consider a very large ultrarelativistic nucleus. Assuming a simple model of the nucleus and weak coupling we find a classical solution for the gluon field of the nucleus and construct the two-dimensional color charge density for McLerran-Venugopalan model out of it. We prove that the density of states distribution, as a function of color charge density, is Gaussian, confirming the assumption made by McLerran and Venugopalan.
Kovchegov, Y.V.
1996-11-01
We consider a very large ultrarelativistic nucleus. Assuming a simple model of the nucleus and weak coupling we find a classical solution for the gluon field of the nucleus and construct the two-dimensional color charge density for McLerran-Venugopalan model out of it. We prove that the density of states distribution, as a function of color charge density, is Gaussian, confirming the assumption made by McLerran and Venugopalan. {copyright} {ital 1996 The American Physical Society.}
Augmented Superfield Approach to Non-Yang Symmetries of Jackiw-Pi Model: Novel Observations
NASA Astrophysics Data System (ADS)
Gupta, Saurabh; Kumar, R.
2013-02-01
We derive the off-shell nilpotent and absolutely anti-commuting Becchi-Rouet-Stora-Tyutin (BRST) as well as anti-BRST symmetry transformations corresponding to the non-Yang-Mills (NYM) symmetry transformations of (2+1)-dimensional Jackiw-Pi (JP) model within the framework of "augmented" superfield formalism. The Curci-Ferrari (CF) restriction, which is a hallmark of non-Abelian one-form gauge theories, does not appear in this case. One of the novel features of our present investigation is the derivation of proper (anti-)BRST symmetry transformations corresponding to the auxiliary field ρ that cannot be derived by any conventional means.
Gauge invariance and the physical spectrum in the two-Higgs-doublet model
NASA Astrophysics Data System (ADS)
Maas, Axel; Pedro, Leonardo
2016-03-01
Observable states are gauge invariant. In a non-Abelian gauge theory, these are necessarily composite operators. We investigate the spectrum of these operators in the two-Higgs-doublet model. For this purpose, we are working along the lines of the Fröhlich-Morchio-Strocchi mechanism to relate the physical spectrum to the spectrum of the elementary particles. We also investigate the consequences of spontaneous breaking of the global (custodial) symmetry group. Finally, we briefly comment on how to test the results using lattice methods.
A four-dimensional model with the fermionic determinant exactly evaluated
NASA Astrophysics Data System (ADS)
Mignaco, J. A.; Rego Monteiro, M. A.
1986-07-01
A method is presented to compute the fermion determinant of some class of field theories. By this method the following results of the fermion determinant in two dimensions are easily recovered: (i) Schwinger model without reference to a particular gauge. (ii) QCD in the light-cone gauge. (iii) Gauge invariant result of QCD. The method is finally applied to give an analytical solution of the fermion determinant of a four-dimensional, non-abelian, Dirac-like theory with massless fermions interacting with an external vector field through a pseudo-vectorial coupling. Fellow of the Conselho Nacional de Desenvolvimento Cientifico e Tecnologico (CNPq), Brazil.
Dark Matter in the Heavens and at Colliders: Models and Constraints
Primulando, Reinard
2012-08-01
In this dissertation, we investigate various aspects of dark matter detection and model building. Motivated by the cosmic ray positron excess observed by PAMELA, we construct models of decaying dark matter to explain the excess. Specifically we present an explicit, TeV-scale model of decaying dark matter in which the approximate stability of the dark matter candidate is a consequence of a global symmetry that is broken only by instanton-induced operators generated by a non-Abelian dark gauge group. Alternatively, the decaying operator can arise as a Planck suppressed correction in a model with an Abelian discrete symmetry and vector-like states at an intermediate scale that are responsible for generating lepton Yukawa couplings. A flavor-nonconserving dark matter decay is also considered in the case of fermionic dark matter. Assuming a general Dirac structure for the four-fermion contact interactions of interest, the cosmic-ray electron and positron spectra were studied. We show that good fits to the current data can be obtained for both charged-leptonflavor- conserving and flavor-violating decay channels. Motivated by a possible excess of gamma rays in the galactic center, we constructed a supersymmetric leptophilic higgs model to explain the excess. Finally, we consider an improvement on dark matter collider searches using the Razor analysis, which was originally utilized for supersymmetry searches by the CMS collaboration.
Cogenerating and pre-annihilating dark matter by a new gauge interaction in a unified model
NASA Astrophysics Data System (ADS)
Barr, S. M.; Scherrer, Robert J.
2016-05-01
Grand unified theories based on large groups (with rank >= 6) are a natural context for dark matter models. They contain Standard-Model-singlet fermions that could be dark matter candidates, and can contain new non-abelian interactions whose sphalerons convert baryons, leptons, and dark matter into each other, ``cogenerating" a dark matter asymmetry comparable to the baryon asymmetry. In this paper it is shown that the same non-abelian interactions can ``pre-annihilate" the symmetric component of heavy dark matter particles χ, which then decay late into light stable dark matter particles ζ that inherit their asymmetry. We derive cosmological constraints on the parameters of such models. The mass of χ must be < 3000 TeV and their decays must happen when 2 × 10‑7 < Tdec/mχ < 10‑4. It is shown that such decays can come from d=5 operators with coefficients of order 1/MGUT or 1/MPl. We present a simple realization of our model based on the group SU(7).
Model for superconductivity at any temperature
NASA Astrophysics Data System (ADS)
Anber, Mohamed M.; Burnier, Yannis; Sabancilar, Eray; Shaposhnikov, Mikhail
2016-01-01
We construct a 2 +1 dimensional model that sustains superconductivity at all temperatures. This is achieved by introducing a Chern-Simons mixing term between two Abelian gauge fields A and Z . The superfluid is described by a complex scalar charged under Z , whereas a sufficiently strong magnetic field of A forces the superconducting condensate to form at all temperatures. In fact, at finite temperature, the theory exhibits Berezinsky-Kosterlitz-Thouless phase transition due to proliferation of topological vortices admitted by our construction. However, the critical temperature is proportional to the magnetic field of A , and thus, the phase transition can be postponed to high temperatures by increasing the strength of the magnetic field.
Standard model with partial gauge invariance
NASA Astrophysics Data System (ADS)
Chkareuli, J. L.; Kepuladze, Z.
2012-03-01
We argue that an exact gauge invariance may disable some generic features of the Standard Model which could otherwise manifest themselves at high energies. One of them might be related to the spontaneous Lorentz invariance violation (SLIV), which could provide an alternative dynamical approach to QED and Yang-Mills theories with photon and non-Abelian gauge fields appearing as massless Nambu-Goldstone bosons. To see some key features of the new physics expected we propose partial rather than exact gauge invariance in an extended SM framework. This principle applied, in some minimal form, to the weak hypercharge gauge field B μ and its interactions, leads to SLIV with B field components appearing as the massless Nambu-Goldstone modes, and provides a number of distinctive Lorentz breaking effects. Being naturally suppressed at low energies they may become detectable in high energy physics and astrophysics. Some of the most interesting SLIV processes are considered in significant detail.
NASA Astrophysics Data System (ADS)
Grigore, D. R.
2001-07-01
We complete our study of non-Abelian gauge theories in the framework of the Epstein-Glaser approach to renormalization theory including in the model an arbitrary number of Dirac fermions. We consider the consistency of the model up to the third order of the perturbation theory. In the second order we obtain pure group theoretical relations expressing a representation property of the numerical coefficients appearing in the left- and right-handed components of the interaction, Lagrangian. In the third order of the perturbation theory we obtain the the condition of cancellation of the axial anomaly.
Power laws and self-organized criticality in theory and nature
NASA Astrophysics Data System (ADS)
Marković, Dimitrije; Gros, Claudius
2014-03-01
the BTW and the Zhang sandpile models, other variations of toppling rules exist. One possibility is a stochastic sandpile model proposed by Manna (1991b), which was intensively studied as it is solvable analytically. Toppling rules can be divided into Abelian vs. non-Abelian, deterministic vs. stochastic and directed vs. undirected (Milshtein et al., 1998). Modifications of the toppling rules employed often results in a change of the universality class to which the model belongs (Ben-Hur and Biham, 1996; Giacometti and Díaz-Guilera, 1998).Hitherto we described the critical height model, where the start of a toppling process solely depends on the height h. Alternatively, in the critical slope model the avalanche initiation depends on the first derivative of the height function h, or in the critical Laplacian model on the second derivative of the height function. These alternative stability criteria lead either to a different universality class, or to a complete absence of SOC behavior (Manna, 1991a).
Supersymmetric flavor models and the B→φKS anomaly
NASA Astrophysics Data System (ADS)
Agashe, Kaustubh; Carone, Christopher D.
2003-08-01
We consider the flavor structure of supersymmetric theories that can account for the deviation of the observed time-dependent CP asymmetry in B→φKS from the standard model prediction. Assuming simple flavor symmetries and effective field theory, we investigate possible correlations between sizable supersymmetric contributions to b→s transitions and to flavor changing processes that are more tightly constrained. With relatively few assumptions, we determine the properties of minimal Yukawa and soft mass textures that are compatible with the desired supersymmetric flavor-changing effect and constraints. We then present explicit models that are designed (at least approximately) to realize these textures. In particular, we present an Abelian model based on a single U(1) factor and a non-trivial extra-dimensional topography that can explain the CP asymmetry in B→φKS, while suppressing other supersymmetric flavor changing effects through a high degree of squark-quark alignment.
MSSM-like from SU5 × D4 models
NASA Astrophysics Data System (ADS)
Ahl Laamara, R.; Miskaoui, M.; Saidi, E. H.
2016-05-01
Using finite discrete group characters and symmetry breaking by hyperflux as well as constraints on top-quark family, we study minimal low energy effective theory following from SU5 ×D4 models embedded in F-theory with non-abelian flux. Matter curves spectrum of the models is obtained from SU5 ×S5 theory with monodromy S5 by performing two breakings: first from symmetric group S5 to S4 subsymmetry, and next to dihedral D4 subgroup. As a consequence, and depending on the ways of decomposing triplets of S4, we end with three types of D4-models. Explicit constructions of these theories are given and a MSSM-like spectrum is derived.
Fermion masses and mixing in Δ (27 ) flavor model
NASA Astrophysics Data System (ADS)
Abbas, Mohammed; Khalil, Shaaban
2015-03-01
An extension of the Standard Model (SM) based on the non-Abelian discrete group Δ (27 ) is considered. The Δ (27 ) flavor symmetry is spontaneously broken only by gauge singlet scalar fields, therefore our model is free from any flavor changing neutral current (FCNC). We show that the model accounts simultaneously for the observed quark and lepton masses and their mixing. In the quark sector, we find that the up-quark mass matrix is flavor diagonal and the Cabbibo-Kobayashi-Maskawa (CKM) mixing matrix arises from down quarks. In the lepton sector, we show that the charged lepton mass matrix is almost diagonal. We also adopt type-I seesaw mechanism to generate neutrino masses. A deviated mixing matrix from tri-bimaximal Maki-Nakagawa-Sakata (MNS), with a correlation between sin θ13 and sin2θ23 are illustrated.
Flavor symmetry based MSSM: Theoretical models and phenomenological analysis
NASA Astrophysics Data System (ADS)
Babu, K. S.; Gogoladze, Ilia; Raza, Shabbar; Shafi, Qaisar
2014-09-01
We present a class of supersymmetric models in which symmetry considerations alone dictate the form of the soft SUSY breaking Lagrangian. We develop a class of minimal models, denoted as sMSSM—for flavor symmetry-based minimal supersymmetric standard model—that respect a grand unified symmetry such as SO(10) and a non-Abelian flavor symmetry H which suppresses SUSY-induced flavor violation. Explicit examples are constructed with the flavor symmetry being gauged SU(2)H and SO(3)H with the three families transforming as 2+1 and 3 representations, respectively. A simple solution is found in the case of SU(2)H for suppressing the flavor violating D-terms based on an exchange symmetry. Explicit models based on SO(3)H without the D-term problem are developed. In addition, models based on discrete non-Abelian flavor groups are presented which are automatically free from D-term issues. The permutation group S3 with a 2+1 family assignment, as well as the tetrahedral group A4 with a 3 assignment are studied. In all cases, a simple solution to the SUSY CP problem is found, based on spontaneous CP violation leading to a complex quark mixing matrix. We develop the phenomenology of the resulting sMSSM, which is controlled by seven soft SUSY breaking parameters for both the 2+1 assignment and the 3 assignment of fermion families. These models are special cases of the phenomenological MSSM (pMSSM), but with symmetry restrictions. We discuss the parameter space of sMSSM compatible with LHC searches, B-physics constraints and dark matter relic abundance. Fine-tuning in these models is relatively mild, since all SUSY particles can have masses below about 3 TeV.
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.
Gauged Two Higgs Doublet Model confronts the LHC 750 GeV diphoton anomaly
NASA Astrophysics Data System (ADS)
Huang, Wei-Chih; Tsai, Yue-Lin Sming; Yuan, Tzu-Chiang
2016-08-01
In light of the recent 750 GeV diphoton anomaly observed at the LHC, we study the possibility of accommodating the deviation from the standard model prediction based on the recently proposed Gauged Two Higgs Doublet Model. The model embeds two Higgs doublets into a doublet of a non-abelian gauge group SU(2)H, while the standard model SU(2)L right-handed fermion singlets are paired up with new heavy fermions to form SU(2)H doublets, and SU(2)L left-handed fermion doublets are singlets under SU(2)H. An SU(2)H scalar doublet, which provides masses to the new heavy fermions as well as the SU(2)H gauge bosons, can be produced via gluon fusion and subsequently decays into two photons with the new fermions circulating the triangle loops to account for the deviation from the standard model prediction.
Bell diagonal states with maximal Abelian symmetry
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.
Artificial neural networks and Abelian harmonic analysis
NASA Astrophysics Data System (ADS)
Rodriguez, Domingo; Pertuz-Campo, Jairo
1991-12-01
This work deals with the use of artificial neural networks (ANN) for the digital processing of finite discrete time signals. The effort concentrates on the efficient replacement of fast Fourier transform (FFT) algorithms with ANN algorithms in certain engineering and scientific applications. The FFT algorithms are efficient methods of computing the discrete Fourier transform (DFT). The ubiquitous DFT is utilized in almost every digital signal processing application where harmonic analysis information is needed. Applications abound in areas such as audio acoustics, geophysics, biomedicine, telecommunications, astrophysics, etc. To identify more efficient methods to obtain a desired spectral information will result in a reduction in the computational effort required to implement these applications.
Abelian anomaly and neutral pion production
Roberts, H. L. L.; Roberts, C. D.; Bashir, A.; Gutierrez-Guerrero, L. X.; Tandy, P. C.
2010-12-15
We show that in fully self-consistent treatments of the pion, namely, its static properties and elastic and transition form factors, the asymptotic limit of the product Q{sup 2}G{sub {gamma}}{sup *}{sub {gamma}{pi}}{sup 0}(Q{sup 2}), determined a priori by the interaction employed, is not exceeded at any finite value of spacelike momentum transfer. Furthermore, in such a treatment of a vector-vector contact-interaction one obtains a {gamma}{sup *{gamma}{yields}{pi}0} transition form factor that disagrees markedly with all available data. We explain that the contact interaction produces a pion distribution amplitude that is flat and nonvanishing at the endpoints. This amplitude characterizes a pointlike pion bound state. Such a state has the hardest possible form factors (i.e., form factors that become constant at large momentum transfers and hence are in striking disagreement with completed experiments). However, interactions with QCD-like behavior produce soft pions, a valence-quark distribution amplitude that vanishes as {approx}(1-x){sup 2} for x{approx}1, and results that agree with the bulk of existing data. Our analysis supports a view that the large-Q{sup 2} data obtained by the BaBar Collaboration is not an accurate measure of the {gamma}*{gamma}{yields}{pi}{sup 0} form factor.
Cosmological model with gravitational, electromagnetic, and scalar waves
Charach, C.; Malin, S.
1980-06-15
Following Gowdy, Berger, and Misner we construct a new exact solution of the Einstein--Maxwell--massless-scalar-field equations which corresponds to an inhomogeneous closed universe filled with scalar, gravitational, and electromagnetic waves. It is obtained as a result of homogeneity breaking in the corresponding Bianchi type-I universe. The combined effect of the scalar and vector fields on the dynamics of the evolution process and the interactions between the fields involved are systematically investigated. The structure of the initial singularity is studied in detail in both the homogeneous and inhomogeneous cases. The final stage of evolution is studied and interpreted in terms of the quanta of scalar, gravitational, and electromagnetic fields. Possible extensions of the present model to the conformally coupled scalar field and the Abelian solutions of the Yang-Mills field equations are pointed out.
Topological phase transitions in the golden string-net model.
Schulz, Marc Daniel; Dusuel, Sébastien; Schmidt, Kai Phillip; Vidal, Julien
2013-04-01
We examine the zero-temperature phase diagram of the two-dimensional Levin-Wen string-net model with Fibonacci anyons in the presence of competing interactions. Combining high-order series expansions around three exactly solvable points and exact diagonalizations, we find that the non-Abelian doubled Fibonacci topological phase is separated from two nontopological phases by different second-order quantum critical points, the positions of which are computed accurately. These trivial phases are separated by a first-order transition occurring at a fourth exactly solvable point where the ground-state manifold is infinitely many degenerate. The evaluation of critical exponents suggests unusual universality classes. PMID:25167030
All-loop correlators of integrable λ-deformed σ-models
NASA Astrophysics Data System (ADS)
Georgiou, George; Sfetsos, Konstantinos; Siampos, Konstantinos
2016-08-01
We compute the 2- and 3-point functions of currents and primary fields of λ-deformed integrable σ-models characterized also by an integer k. Our results apply for any semisimple group G, for all values of the deformation parameter λ and up to order 1 / k. We deduce the OPEs and equal-time commutators of all currents and primaries. We derive the currents' Poisson brackets which assume Rajeev's deformation of the canonical structure of the isotropic PCM, the underlying structure of the integrable λ-deformed σ-models. We also present analogous results in two limiting cases of special interest, namely for the non-Abelian T-dual of the PCM and for the pseudodual model.
Decorated tensor network renormalization for lattice gauge theories and spin foam models
NASA Astrophysics Data System (ADS)
Dittrich, Bianca; Mizera, Sebastian; Steinhaus, Sebastian
2016-05-01
Tensor network techniques have proved to be powerful tools that can be employed to explore the large scale dynamics of lattice systems. Nonetheless, the redundancy of degrees of freedom in lattice gauge theories (and related models) poses a challenge for standard tensor network algorithms. We accommodate for such systems by introducing an additional structure decorating the tensor network. This allows to explicitly preserve the gauge symmetry of the system under coarse graining and straightforwardly interpret the fixed point tensors. We propose and test (for models with finite Abelian groups) a coarse graining algorithm for lattice gauge theories based on decorated tensor networks. We also point out that decorated tensor networks are applicable to other models as well, where they provide the advantage to give immediate access to certain expectation values and correlation functions.
The problem of neutrino masses in extensions of the Standard Model
NASA Astrophysics Data System (ADS)
Masina, Isabella
2001-07-01
We review the problem of neutrino masses and mixings in the context of Grand Unified Theories. After a brief summary of the present experimental status of neutrino physics, we describe how the see-saw mechanism can automatically account for the large atmospheric mixing angle. We provide two specific examples where this possibility is realized by means of a flavour symmetry. We then review in some detail the various severe problems which plague minimal GUT models (like the doublet-triplet splitting and proton-decay) and which force to investigate the possibility of constructing more elaborate but realistic models. We then show an example of a quasi-realistic SUSY SU(5) model which, by exploiting the crucial presence of an abelian flavour symmetry, does not require any fine-tuning and predicts a satisfactory phenomenology with respect to coupling unification, fermion masses and mixings and bounds from proton decay.
Loth, E.; Tryggvason, G.; Tsuji, Y.; Elghobashi, S. E.; Crowe, Clayton T.; Berlemont, A.; Reeks, M.; Simonin, O.; Frank, Th; Onishi, Yasuo; Van Wachem, B.
2005-09-01
Slurry flows occur in many circumstances, including chemical manufacturing processes, pipeline transfer of coal, sand, and minerals; mud flows; and disposal of dredged materials. In this section we discuss slurry flow applications related to radioactive waste management. The Hanford tank waste solids and interstitial liquids will be mixed to form a slurry so it can be pumped out for retrieval and treatment. The waste is very complex chemically and physically. The ARIEL code is used to model the chemical interactions and fluid dynamics of the waste.
Localization of twisted {N}=left(0,2right) gauged linear sigma models in two dimensions
NASA Astrophysics Data System (ADS)
Closset, Cyril; Gu, Wei; Jia, Bei; Sharpe, Eric
2016-03-01
We study two-dimensional {N}=left(0, 2right) supersymmetric gauged linear sigma models (GLSMs) using supersymmetric localization. We consider {N}=left(0, 2right) theories with an R-symmetry, which can always be defined on curved space by a pseudo-topological twist while preserving one of the two supercharges of flat space. For GLSMs which are deformations of {N}=left(2, 2right) GLSMs and retain a Coulomb branch, we consider the A/2-twist and compute the genus-zero correlation functions of certain pseudo-chiral operators, which generalize the simplest twisted chiral ring operators away from the {N}=left(2, 2right) locus. These correlation functions can be written in terms of a certain residue operation on the Coulomb branch, generalizing the Jeffrey-Kirwan residue prescription relevant for the {N}=left(2, 2right) locus. For abelian GLSMs, we reproduce existing results with new formulas that render the quantum sheaf cohomology relations and other properties manifest. For non-abelian GLSMs, our methods lead to new results. As an example, we briefly discuss the quantum sheaf cohomology of the Grassmannian manifold.
NASA Astrophysics Data System (ADS)
Azaria, P.; Konik, R. M.; Lecheminant, P.; Pálmai, T.; Takács, G.; Tsvelik, A. M.
2016-08-01
In this paper we study a (1 +1 )-dimensional version of the famous Nambu-Jona-Lasinio model of quantum chromodynamics (QCD2) both at zero and at finite baryon density. We use nonperturbative techniques (non-Abelian bosonization and the truncated conformal spectrum approach). When the baryon chemical potential, μ , is zero, we describe the formation of fermion three-quark (nucleons and Δ baryons) and boson (two-quark mesons, six-quark deuterons) bound states. We also study at μ =0 the formation of a topologically nontrivial phase. When the chemical potential exceeds the critical value and a finite baryon density appears, the model has a rich phase diagram which includes phases with a density wave and superfluid quasi-long-range (QLR) order, as well as a phase of a baryon Tomonaga-Luttinger liquid (strange metal). The QLR order results in either a condensation of scalar mesons (the density wave) or six-quark bound states (deuterons).
Fractal frontiers of bursts and cracks in a fiber bundle model of creep rupture.
Danku, Zsuzsa; Kun, Ferenc; Herrmann, Hans J
2015-12-01
We investigate the geometrical structure of breaking bursts generated during the creep rupture of heterogeneous materials. Using a fiber bundle model with localized load sharing we show that bursts are compact geometrical objects; however, their external frontiers have a fractal structure which reflects their growth dynamics. The perimeter fractal dimension of bursts proved to have the universal value 1.25 independent of the external load and of the amount of disorder in the system. We conjecture that according to their geometrical features, breaking bursts fall in the universality class of loop-erased self-avoiding random walks with perimeter fractal dimension 5/4 similar to the avalanches of Abelian sand pile models. The fractal dimension of the growing crack front along which bursts occur proved to increase from 1 to 1.25 as bursts gradually cover the entire front. PMID:26764698
Review of strongly-coupled composite dark matter models and lattice simulations
NASA Astrophysics Data System (ADS)
Kribs, Graham D.; Neil, Ethan T.
2016-08-01
We review models of new physics in which dark matter arises as a composite bound state from a confining strongly-coupled non-Abelian gauge theory. We discuss several qualitatively distinct classes of composite candidates, including dark mesons, dark baryons, and dark glueballs. We highlight some of the promising strategies for direct detection, especially through dark moments, using the symmetries and properties of the composite description to identify the operators that dominate the interactions of dark matter with matter, as well as dark matter self-interactions. We briefly discuss the implications of these theories at colliders, especially the (potentially novel) phenomenology of dark mesons in various regimes of the models. Throughout the review, we highlight the use of lattice calculations in the study of these strongly-coupled theories, to obtain precise quantitative predictions and new insights into the dynamics.
Fractal frontiers of bursts and cracks in a fiber bundle model of creep rupture
NASA Astrophysics Data System (ADS)
Danku, Zsuzsa; Kun, Ferenc; Herrmann, Hans J.
2015-12-01
We investigate the geometrical structure of breaking bursts generated during the creep rupture of heterogeneous materials. Using a fiber bundle model with localized load sharing we show that bursts are compact geometrical objects; however, their external frontiers have a fractal structure which reflects their growth dynamics. The perimeter fractal dimension of bursts proved to have the universal value 1.25 independent of the external load and of the amount of disorder in the system. We conjecture that according to their geometrical features, breaking bursts fall in the universality class of loop-erased self-avoiding random walks with perimeter fractal dimension 5/4 similar to the avalanches of Abelian sand pile models. The fractal dimension of the growing crack front along which bursts occur proved to increase from 1 to 1.25 as bursts gradually cover the entire front.
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)
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)
Dynamical scaling behavior of the one-dimensional conserved directed-percolation universality class.
Kwon, Sungchul; Kim, Yup
2012-05-01
We investigate the dynamical scaling behavior of the static diffusive epidemic process and a fixed-energy Manna sandpile model, undergoing nonequilibrium absorbing phase transitions in one dimension. These models belong to the so-called conserved directed-percolation or Manna universality class characterized by the conservation of the total particle number, activity coupled to a nondiffusive conserved field and infinitely many absorbing states. We measure the dynamical exponents of these models in one dimension by using the critical spreading simulation of a localized activity in absorbing configurations. In the spreading simulations, boundaries are never touched, so the results are free from the finite-size effects. In contrast to the scattered results for the different models from the previous finite-size scaling analyses, we obtain consistent estimates of the dynamical exponents for both models. PMID:23004715
Comments on interactions in the SUSY models
NASA Astrophysics Data System (ADS)
Upadhyay, Sudhaker; Reshetnyak, Alexander; Mandal, Bhabani Prasad
2016-07-01
We consider special supersymmetry (SUSY) transformations with m generators overleftarrow{s}_α , for some class of models and study the physical consequences when making the Grassmann-odd transformations to form an Abelian supergroup with finite parameters and a set of group-like elements with finite parameters being functionals of the field variables. The SUSY-invariant path integral measure within conventional quantization scheme leads to the appearance of the Jacobian under a change of variables generated by such SUSY transformations, which is explicitly calculated. The Jacobian implies, first of all, the appearance of trivial interactions in the transformed action, and, second, the presence of a modified Ward identity which reduces to the standard Ward identities in the case of constant parameters. We examine the case of the {N}=1 and N=2 supersymmetric harmonic oscillators to illustrate the general concept by a simple free model with (1, 1) physical degrees of freedom. It is shown that the interaction terms U_{tr} have a corresponding SUSY-exact form: U_{tr}= big (V_{(1)}overleftarrow{s}; V_{(2)}overleftarrow{bar{s}} overleftarrow{s}big ) generated naturally under such generalized formulation. We argue that the case of a non-trivial interaction cannot be obtained in such a way.
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.
The nonlocal chiral quark model and the muon g - 2 problem
NASA Astrophysics Data System (ADS)
Dorokhov, A. E.; Radzhabov, A. E.; Shamakhov, F. A.; Zhevlakov, A. S.
2016-05-01
In the first part of the review we discuss the effective nonlocal approach in the quantum field theory. It concerns primary the historical retrospective of this approach, and than we concentrate on the interaction of matter particles (fermions and bosons) with the (abelian and nonabelian) gauge fields. In the second part of the review we consider the hadronic corrections (vacuum polarization) to the anomalous magnetic moment of the muon g - 2 factor discussed within the SUf(2) nonlocal chiral quark model. This is considered in the leading and, partially, in the next-to-leading orders (the effect of the fermion propagator dressing due to pion field) of expansion in small parameter 1/ N c ( N c is the number of colors in QCD).
Low energy pion-pion elastic scattering in the Sakai-Sugimoto model
Parthasarathy, R.; Viswanathan, K. S.
2008-06-01
We have considered the holographic large N{sub c} QCD model proposed by Sakai and Sugimoto and evaluated the non-Abelian DBI-action on the D8-brane up to ({alpha}{sup '}){sup 4} terms. Restricting to the pion sector, these corrections give rise to four derivative contact terms for the pion field. We derive the Weinberg's phenemenological Lagrangian. The coefficients of the four derivative terms are determined in terms of g{sub YM}{sup 2}. The low energy pion-pion scattering amplitudes are evaluated. Numerical results are presented with the choice of M{sub KK}=0.94 GeV and N{sub c}=11. The results are compared with the amplitudes calculated using the experimental phase shifts. The agreement with the experimental data is found to be satisfactory.
Instanton-mediated baryon number violation in non-universal gauge extended models
NASA Astrophysics Data System (ADS)
Fuentes-Martín, J.; Portolés, J.; Ruiz-Femenía, P.
2015-01-01
Instanton solutions of non-abelian Yang-Mills theories generate an effective action that may induce lepton and baryon number violations, namely Δ B = Δ L = n f , being n f the number of families coupled to the gauge group. In this article we study instanton mediated processes in a SU(2) ℓ ⊗SU(2) h ⊗U(1) extension of the Standard Model that breaks universality by singularizing the third family. In the construction of the instanton Green functions we account systematically for the inter-family mixing. This allows us to use the experimental bounds on proton decay in order to constrain the gauge coupling of SU(2) h . Tau lepton non-leptonic and radiative decays with Δ B = Δ L = 1 are also analysed.
Algebraic geometry methods associated to the one-dimensional Hubbard model
NASA Astrophysics Data System (ADS)
Martins, M. J.
2016-06-01
In this paper we study the covering vertex model of the one-dimensional Hubbard Hamiltonian constructed by Shastry in the realm of algebraic geometry. We show that the Lax operator sits in a genus one curve which is not isomorphic but only isogenous to the curve suitable for the AdS/CFT context. We provide an uniformization of the Lax operator in terms of ratios of theta functions allowing us to establish relativistic like properties such as crossing and unitarity. We show that the respective R-matrix weights lie on an Abelian surface being birational to the product of two elliptic curves with distinct J-invariants. One of the curves is isomorphic to that of the Lax operator but the other is solely fourfold isogenous. These results clarify the reason the R-matrix can not be written using only difference of spectral parameters of the Lax operator.
Six-dimensional (1,0) superconformal models and higher gauge theory
Palmer, Sam; Sämann, Christian
2013-11-15
We analyze the gauge structure of a recently proposed superconformal field theory in six dimensions. We find that this structure amounts to a weak Courant-Dorfman algebra, which, in turn, can be interpreted as a strong homotopy Lie algebra. This suggests that the superconformal field theory is closely related to higher gauge theory, describing the parallel transport of extended objects. Indeed we find that, under certain restrictions, the field content and gauge transformations reduce to those of higher gauge theory. We also present a number of interesting examples of admissible gauge structures such as the structure Lie 2-algebra of an abelian gerbe, differential crossed modules, the 3-algebras of M2-brane models, and string Lie 2-algebras.
Haymaker, Richard W.; Matsuki, Takayuki
2007-01-01
We address the problem of determining the type I, type II or borderline dual superconductor behavior in maximal Abelian gauge SU(2) through the study of the dual Abrikosov vortex. We find that significant electric currents in the simulation data call into question the use of the dual Ginzburg-Landau Higgs model in interpreting the data. Further, two definitions of the penetration depth parameter take two different values. The splitting of this parameter into two is intricately connected to the existence of electric currents. It is important in our approach that we employ definitions of flux and electric and magnetic currents that respect Maxwell equations exactly for lattice averages independent of lattice spacings. Applied to specific Wilson loop sizes, our conclusions differ from those that use the dual GLH model.
Study of the “non-Abelian” current algebra of a non-linear σ-model
NASA Astrophysics Data System (ADS)
Ghosh, Subir
2006-08-01
A particular form of non-linear σ-model, having a global gauge invariance, is studied. The detailed discussion on current algebra structures reveals the non-Abelian nature of the invariance, with field dependent structure functions. Reduction of the field theory to a point particle framework yields a non-linear harmonic oscillator, which is a special case of similar models studied before in [J.F. Carinena et al., Nonlinearity 17 (2004) 1941, math-ph/0406002; J.F. Carinena et al., in: Proceedings of 10th International Conference in Modern Group Analysis, Larnaca, Cyprus, 2004, p. 39, arxiv:math-ph/0505028; J.F. Carinena et al., Rep. Math. Phys. 54 (2004) 285, arxiv:hep-th/0501106]. The connection with non-commutative geometry is also established.
Kinetic energy for the nuclear Yang-Mills collective model
NASA Astrophysics Data System (ADS)
Rosensteel, George; Sparks, Nick
2015-10-01
The Bohr-Mottelson-Frankfurt model of nuclear rotations and quadrupole vibrations is a foundational model in nuclear structure physics. The model, also called the geometrical collective model or simply GCM, has two hidden mathematical structures, one Lie group theoretic and the other differential geometric. Although the group structure has been understood for some time, the geometric structure is a new unexplored feature that shares the same mathematical origin as Yang-Mills, viz., a vector bundle with a non-abelian structure group and a connection. Using the de Rham Laplacian ▵ = * d * d from differential geometry for the kinetic energy extends significantly the physical scope of the GCM model. This Laplacian contains a ``magnetic'' term due to the coupling between base manifold rotational and fiber vorticity degrees of freedom. When the connection specializes to irrotational flow, the Laplacian reduces to the Bohr-Mottelson kinetic energy operator. More generally, the connection yields a moment of inertia that is intermediate between the extremes of irrotational flow and rigid body motion.
Models of neutrino mass, mixing and CP violation
NASA Astrophysics Data System (ADS)
King, Stephen F.
2015-12-01
In this topical review we argue that neutrino mass and mixing data motivates extending the Standard Model (SM) to include a non-Abelian discrete flavour symmetry in order to accurately predict the large leptonic mixing angles and {C}{P} violation. We begin with an overview of the SM puzzles, followed by a description of some classic lepton mixing patterns. Lepton mixing may be regarded as a deviation from tri-bimaximal mixing, with charged lepton corrections leading to solar mixing sum rules, or tri-maximal lepton mixing leading to atmospheric mixing rules. We survey neutrino mass models, using a roadmap based on the open questions in neutrino physics. We then focus on the seesaw mechanism with right-handed neutrinos, where sequential dominance (SD) can account for large lepton mixing angles and {C}{P} violation, with precise predictions emerging from constrained SD (CSD). We define the flavour problem and discuss progress towards a theory of favour using GUTs and discrete family symmetry. We classify models as direct, semidirect or indirect, according to the relation between the Klein symmetry of the mass matrices and the discrete family symmetry, in all cases focussing on spontaneous {C}{P} violation. Finally we give two examples of realistic and highly predictive indirect models with CSD, namely an A to Z of flavour with Pati-Salam and a fairly complete A 4 × SU(5) SUSY GUT of flavour, where both models have interesting implications for leptogenesis.
Proton stability and light Z' inspired by string derived models
Faraggi, Alon E.; Mehta, Viraf M.
2011-10-15
Proton stability is one of the most perplexing puzzles in particle physics. While the renormalizable standard model forbids proton decay mediating operators due to accidental global symmetries, many of its extensions introduce such dimension four, five and six operators. Furthermore, it is, in general, expected that quantum gravity only respects local gauge, or discreet, symmetries. String theory provides the arena to study particle physics in a consistent framework of perturbative quantum gravity. An appealing proposition, in this context, is that the dangerous operators are suppressed by an Abelian gauge symmetry, which is broken near the TeV scale. A viable U(1) symmetry should also be anomaly free, be family universal, and allow the generation of fermion masses via the Higgs mechanism. We discuss such U(1) symmetries that arise in quasirealistic free fermionic heterotic-string derived models. Ensuring that the U(1) symmetry is anomaly free at the low scale requires that the standard model spectrum is augmented by additional states that are compatible with the charge assignments in the string models. We construct such string-inspired models and discuss some of their phenomenological implications.
General mirror pairs for gauged linear sigma models
NASA Astrophysics Data System (ADS)
Aspinwall, Paul S.; Plesser, M. Ronen
2015-11-01
We carefully analyze the conditions for an abelian gauged linear σ-model to exhibit nontrivial IR behavior described by a nonsingular superconformal field theory determining a superstring vacuum. This is done without reference to a geometric phase, by associating singular behavior to a noncompact space of (semi-)classical vacua. We find that models determined by reflexive combinatorial data are nonsingular for generic values of their parameters. This condition has the pleasant feature that the mirror of a nonsingular gauged linear σ-model is another such model, but it is clearly too strong and we provide an example of a non-reflexive mirror pair. We discuss a weaker condition inspired by considering extremal transitions, which is also mirror symmetric and which we conjecture to be sufficient. We apply these ideas to extremal transitions and to understanding the way in which both Berglund-Hübsch mirror symmetry and the Vafa-Witten mirror orbifold with discrete torsion can be seen as special cases of the general combinatorial duality of gauged linear σ-models. In the former case we encounter an example showing that our weaker condition is still not necessary.
F-theory duals of singular heterotic K3 models
NASA Astrophysics Data System (ADS)
Lüdeling, Christoph; Ruehle, Fabian
2015-01-01
We study F-theory duals of singular heterotic K3 models that correspond to Abelian toroidal orbifolds T4/ZN . While our focus is on the standard embedding, we also comment on models with Wilson lines and more general gauge embeddings. In the process of constructing the duals, we work out a Weierstrass description of the heterotic toroidal orbifold models, which exhibit singularities of Kodaira type I0* , IV * , II I * , and II * . This construction unveils properties like the instanton number per fixed point and a correlation between the orbifold order and the multiplicities in the Dynkin diagram. The results from the Weierstrass description are then used to restrict the complex structure of the F-theory Calabi-Yau threefold such that the gauge group and the matter spectrum of the heterotic theories are reproduced. We also comment on previous approaches that have been employed to construct the duality and point out the differences and limitations in our case. Our results show explicitly how the various orbifold models are connected and described in F-theory.
Generalised geometrical CP violation in a T ' lepton flavour model
NASA Astrophysics Data System (ADS)
Girardi, Ivan; Meroni, Aurora; Petcov, S. T.; Spinrath, Martin
2014-02-01
We analyse the interplay of generalised CP transformations and the non-Abelian discrete group T ' and use the semi-direct product G f = T ' ⋊ H CP, as family symmetry acting in the lepton sector. The family symmetry is shown to be spontaneously broken in a geometrical manner. In the resulting flavour model, naturally small Majorana neutrino masses for the light active neutrinos are obtained through the type I see-saw mechanism. The known masses of the charged leptons, lepton mixing angles and the two neutrino mass squared differences are reproduced by the model with a good accuracy. The model allows for two neutrino mass spectra with normal ordering (NO) and one with inverted ordering (IO). For each of the three spectra the absolute scale of neutrino masses is predicted with relatively small uncertainty. The value of the Dirac CP violation (CPV) phase δ in the lepton mixing matrix is predicted to be δ = π/2 or 3 π/2. Thus, the CP violating effects in neutrino oscillations are predicted to be maximal (given the values of the neutrino mixing angles) and experimentally observable. We present also predictions for the sum of the neutrino masses, for the Majorana CPV phases and for the effective Majorana mass in neutrinoless double beta decay. The predictions of the model can be tested in a variety of ongoing and future planned neutrino experiments.
Left-right symmetric heterotic-string derived models
Cleaver, Gerald B.; Faraggi, Alon E.; Savage, Christopher
2001-03-15
Recently it was demonstrated that free fermionic heterotic strings can produce models with solely the minimal supersymmetric standard model states in the low energy spectrum. This unprecedented result provides further strong evidence for the possibility that the true string vacuum shares some of the properties of the free fermionic models. Past free fermionic models have focused on several possible unbroken observable SO(10) subgroups at the string scale, which include the flipped SU(5) (FSU5), the Pati-Salam (PS) string models, and the string standard-like models (SLM). We extend this study to include the case in which the SO(10) symmetry is broken to the left-right symmetric (LRS) gauge group, SO(10){yields}SU(3){sub C}xU(1){sub B-L}xSU(2){sub L}xSU(2){sub R}. We present several models of this type and discuss their phenomenological features. The most striking new outcome of the LRS string models, in contrast with the case of the FSU5, the PS, and the SLM string models, is that they can produce effective field theories that are free of Abelian anomalies. We discuss the distinction between the two types of free fermionic models which result in the presence, or absence, of an anomalous U(1). As a counterexample we also present a LRS model that does contain an anomalous U(1). Additionally, we discuss how in string models the standard model spectrum may arise from the three 16 representations of SO(10), while the weak hypercharge does not have the canonical SO(10) embedding.
NASA Astrophysics Data System (ADS)
Grigore, D. R.; Scharf, G.
2003-12-01
We consider the supersymmetric vector multiplet in a purely quantum framework. We obtain some discrepancies with respect to the literature in the expression of the super-propagator and we prove that the model is consistent only for positive mass. The gauge structure is constructed purely deductive and leads to the introduction of scalar ghost superfields, in analogy to the usual gauge theories. The construction of a consistent supersymmetric gauge theory based on the vector model depends crucially on the definition of gauge invariance. We find some significant difficulties to impose a supersymmetric gauge invariance condition for the usual expressions from the literature.
Two hundred heterotic standard models on smooth Calabi-Yau threefolds
NASA Astrophysics Data System (ADS)
Anderson, Lara B.; Gray, James; Lukas, Andre; Palti, Eran
2011-11-01
We construct heterotic standard models by compactifying on smooth Calabi-Yau three-folds in the presence of purely Abelian internal gauge fields. A systematic search over complete intersection Calabi-Yau manifolds with less than six Kähler parameters leads to over 200 such models which we present. Each of these models has precisely the matter spectrum of the minimal supersymmetric standard model, at least one pair of Higgs doublets, the standard model gauge group, and no exotics. For about 100 of these models there are four additional U(1) symmetries which are Green-Schwarz anomalous and, hence, massive. In the remaining cases, three U(1) symmetries are anomalous, while the fourth, massless one can be spontaneously broken by singlet vacuum expectation values. The presence of additional global U(1) symmetries, together with the possibility of switching on singlet vacuum expectation values, leads to a rich phenomenology which is illustrated for a particular example. Our database of standard models, which can be further enlarged by simply extending the computer-based search, allows for a detailed and systematic phenomenological analysis of string standard models, covering issues such as the structure of Yukawa couplings, R-parity violation, proton stability, and neutrino masses.
Decay of the standard model Higgs field after inflation
NASA Astrophysics Data System (ADS)
Figueroa, Daniel G.; García-Bellido, Juan; Torrentí, Francisco
2015-10-01
We study the nonperturbative dynamics of the standard model (SM) after inflation, in the regime where the SM is decoupled from (or weakly coupled to) the inflationary sector. We use classical lattice simulations in an expanding box in (3 +1 ) dimensions, modeling the SM gauge interactions with both global and Abelian-Higgs analogue scenarios. We consider different postinflationary expansion rates. During inflation, the Higgs forms a condensate, which starts oscillating soon after inflation ends. Via nonperturbative effects, the oscillations lead to a fast decay of the Higgs into the SM species, transferring most of the energy into Z and W± bosons. All species are initially excited far away from equilibrium, but their interactions lead them into a stationary stage, with exact equipartition among the different energy components. From there on, the system eventually reaches equilibrium. We have characterized in detail, in the different expansion histories considered, the evolution of the Higgs and of its dominant decay products until equipartition is established. We provide a useful mapping between simulations with different parameters, from which we derive a master formula for the Higgs decay time as a function of the coupling constants, Higgs initial amplitude and postinflationary expansion rate.
The nucleon-nucleon potential in the chromodielectric soliton model
NASA Astrophysics Data System (ADS)
Koepf, W.; Wilets, L.; Pepin, S.; Stancu, F.
The short and medium range parts of the nucleon-nucleon interaction are being studied in the framework of the chromodielectric soliton model. The model consists of current quarks, gluons in the abelian approximation, and a scalar sigma field which simulates the nonabelian interactions of the gluons and governs the medium through the dielectric function kappa(sigma). Absolute color confinement is effected by the vanishing of the dielectric in vacuum; this also removes the troublesome van der Waals problem. The authors distinguish between spatial confinement, which arises from the self energy of the quarks in medium (excluding MFA contributions), and color confinement which is effected through OGE in the MFA (including the corresponding self energy contributions). The static (adiabatic) energies are computed as a function of deformation (generalized bag separation) in a constrained MFA. Six quark molecular-type wave functions in all important space-spin-isospin-color configurations are included. The gluon propagator is solved in the deformed dielectric medium. The resultant Hamiltonian matrix is diagonalized. Dynamics are handled in the generator coordinate method, which leads to the Hill-Wheeler integral equation. In the present case, this yields a set of coupled equations corresponding to the various configurations. Although this can be approximated by a set of differential equations, they propose to solve the integral equations with some regularization scheme.
Monte Carlo simulation of CP sup N minus 1 models
Campostrini, M.; Rossi, P.; Vicari, E. )
1992-09-15
Numerical simulations of two-dimensional CP{sup {ital N}{minus}1} models are performed at {ital N}=2, 10, and 21. The lattice action adopted depends explicitly on the gauge degrees of freedom and shows precocious scaling. Our tests of scaling are the stability of adimensional physical quantities (second moment of the correlation function versus inverse mass gap, magnetic susceptibility versus square correlation length) and rotation invariance. Topological properties of the models are explored by measuring the topological susceptibility and by extracting the Abelian string tension. Several different (local and nonlocal) lattice definitions of topological charge are discussed and compared. The qualitative physical picture derived from the continuum 1/{ital N} expansion is confirmed, and agreement with quantitative 1/{ital N} predictions is satisfactory. Variant (Symanzik-improved) actions are considered in the CP{sup 1}{approx}O(3) case and agreement with universality and previous simulations (when comparable) is found. The simulation algorithm is an efficient picture of over-heat-bath and microcanonical algorithms. The dynamical features and critical exponents of the algorithm are discussed in detail.
NASA Astrophysics Data System (ADS)
Klevers, Denis; Taylor, Washington
2016-06-01
We give an explicit construction of a class of F-theory models with matter in the three-index symmetric (4) representation of SU(2). This matter is realized at codimen-sion two loci in the F-theory base where the divisor carrying the gauge group is singular; the associated Weierstrass model does not have the form associated with a generic SU(2) Tate model. For 6D theories, the matter is localized at a triple point singularity of arithmetic genus g = 3 in the curve supporting the SU(2) group. This is the first explicit realization of matter in F-theory in a representation corresponding to a genus contribution greater than one. The construction is realized by "unHiggsing" a model with a U(1) gauge factor under which there is matter with charge q = 3. The resulting SU(2) models can be further unHiggsed to realize non-Abelian G 2 × SU(2) models with more conventional matter content or SU(2)3 models with trifundamental matter. The U(1) models used as the basis for this construction do not seem to have a Weierstrass realization in the general form found by Morrison-Park, suggesting that a generalization of that form may be needed to incorporate models with arbitrary matter representations and gauge groups localized on singular divisors.
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2013-07-22
... Manna, Trustee; Mario John Manna's IRA Account; Claudia Brown Moore; Claudia Brown Moore's IRA Account... 17, 2013. Michael J. Lewandowski, Associate Secretary of the Board. BILLING CODE 6210-01-P...
Two- and three-body color flux tubes in the chromodielectric model
NASA Astrophysics Data System (ADS)
Martens, Gunnar; Greiner, Carsten; Leupold, Stefan; Mosel, Ulrich
2004-12-01
Using the framework of the chromodielectric model we perform an analysis of color electric flux tubes in mesonlike qq¯ and baryonlike qqq quark configurations. We discuss the Abelian color structure of the model and point out a symmetry in color space as a remnant of the SU(3) symmetry of QCD. The generic features of the model are discussed by varying the model parameters. We fix these parameters by reproducing the string tension τ=980 MeV/fm and the transverse width ρ=0.35 fm of the qq¯ flux tube obtained in lattice calculations. We use a bag constant B1/4=(240-260) MeV, a glueball mass mg=(1000-1700) MeV, and a strong coupling constant CFαs=0.2-0.3. We show that the asymptotic string profile of an infinitely long flux tube is already reached for qq¯ separations R≥1.0 fm. A connection to the dual color superconductor is made by extracting a magnetic current from the model equations and a qualitative agreement between the two descriptions of confinement is shown. In the study of the qqq system we observe a Δ-like geometry for the color electric fields and a Y-like geometry in the scalar fields both in the energy density distribution and in the corresponding potentials. The resulting total qqq potential is described neither by the Δ-picture nor by the Y-picture alone.
G2HDM: Gauged Two Higgs Doublet Model
NASA Astrophysics Data System (ADS)
Huang, Wei-Chih; Tsai, Yue-Lin Sming; Yuan, Tzu-Chiang
2016-04-01
A novel model embedding the two Higgs doublets in the popular two Higgs doublet models into a doublet of a non-abelian gauge group SU(2) H is presented. The Standard Model SU(2) L right-handed fermion singlets are paired up with new heavy fermions to form SU(2) H doublets, while SU(2) L left-handed fermion doublets are singlets under SU(2) H . Distinctive features of this anomaly-free model are: (1) Electroweak symmetry breaking is induced from spontaneous symmetry breaking of SU(2) H via its triplet vacuum expectation value; (2) One of the Higgs doublet can be inert, with its neutral component being a dark matter candidate as protected by the SU(2) H gauge symmetry instead of a discrete Z 2 symmetry in the usual case; (3) Unlike Left-Right Symmetric Models, the complex gauge fields ( W 1 ' ∓ W 2 ' ) (along with other complex scalar fields) associated with the SU(2) H do not carry electric charges, while the third component W 3 ' can mix with the hypercharge U(1) Y gauge field and the third component of SU(2) L ; (4) Absence of tree level flavour changing neutral current is guaranteed by gauge symmetry; and etc. In this work, we concentrate on the mass spectra of scalar and gauge bosons in the model. Constraints from previous Z' data at LEP and the Large Hadron Collider measurements of the Standard Model Higgs mass, its partial widths of γγ and Zγ modes are discussed.
A compact 341 model at TeV scale
Dias, A.G.; Pinheiro, P.R.D.; Pires, C.A. S de; Rodrigues da Silva, P.S.
2014-10-15
We build a gauge model based on the SU(3){sub c}⊗SU(4){sub L}⊗U(1){sub X} symmetry where the scalar spectrum needed to generate gauge boson and fermion masses has a smaller scalar content than usually assumed in literature. We compute the running of its abelian gauge coupling and show that a Landau pole shows up at the TeV scale, a fact that we use to consistently implement those fermion masses that are not generated by Yukawa interactions, including neutrino masses. This is appropriately achieved by non renormalizable effective operators, suppressed by the Landau pole scale. Also, SU(3){sub c}⊗SU(3){sub L}⊗U(1){sub N} models embedded in this gauge structure are bound to be strongly coupled at this same energy scale, contrary to what is generally believed, and neutrino mass generation is rather explained through the same effective operators used in the larger gauge group. Besides, their nice features, as the existence of cold dark matter candidates and the ability to reproduce the observed standard model Higgs-like phenomenology, are automatically inherited by our model. Finally, our results imply that this model is constrained to be observed or discarded soon, since it must be realized at the currently probed energy scale in LHC. - Highlights: • We build a SU(4){sub L}⊗U(1){sub N} electroweak model with a reduced scalar spectrum. • The existence of a Landau pole at TeV scale is investigated. • Fermion masses in this model, including neutrinos, emerge from effective operators. • Imposition of an extra Z{sub 2} symmetry avoids fast proton decay.
Critical dimensions for chiral bosons
Mezincescu, L.; Nepomechie, R.I.
1988-05-15
We give the Lagrangian formulation of a Bose model in 1+1 dimensions which describes a free chiral Lie-algebra-valued current. This model is a non-Abelian generalization of the chiral scalar model of Siegel. Both the Abelian and non-Abelian actions have a gauge invariance, which becomes anomalous when the models are quantized. The condition that this anomaly be canceled coincides with the string no-ghost condition.
Topological sigma models & dissipative hydrodynamics
NASA Astrophysics Data System (ADS)
Haehl, Felix M.; Loganayagam, R.; Rangamani, Mukund
2016-04-01
We outline a universal Schwinger-Keldysh effective theory which describes macroscopic thermal fluctuations of a relativistic field theory. The basic ingredients of our construction are three: a doubling of degrees of freedom, an emergent abelian symmetry associated with entropy, and a topological (BRST) supersymmetry imposing fluctuationdissipation theorem. We illustrate these ideas for a non-linear viscous fluid, and demonstrate that the resulting effective action obeys a generalized fluctuation-dissipation theorem, which guarantees a local form of the second law.
Charged Q -balls in gauge mediated SUSY breaking models
NASA Astrophysics Data System (ADS)
Hong, Jeong-Pyong; Kawasaki, Masahiro; Yamada, Masaki
2015-09-01
It is known that after Affleck-Dine baryogenesis, spatial inhomogeneities of Affleck-Dine field grow into nontopological solitons called Q-balls. In gauge mediated supersymmetry (SUSY) breaking models, sufficiently large Q-balls with baryon charge are stable while Q-balls with lepton charge can always decay into leptons. For a Q-ball that carries nonzero B and L charges, the difference between the baryonic component and the leptonic component in decay rate may induce nonzero electric charge on the Q-ball. This implies that a charged Q-ball, also called gauged Q-ball, may emerge in our universe. In this paper, we investigate two complex scalar fields, a baryonic scalar field and a leptonic one, in an Abelian gauge theory. We find stable solutions of gauged Q-balls for different baryon and lepton charges. Those solutions show that a Coulomb potential arises and the Q-ball becomes electrically charged as expected. It is energetically favored that some amount of leptonic component decays, but there is an upper bound on its amount due to the Coulomb force. The baryonic decay also becomes possible by virtue of electrical repulsion, but we find that the evolution itself stops before it occurs mainly due to the Schwinger limit, so that the charged Q-balls eventually survive in the universe.
The 750 GeV di-photon LHC excess and extra Z^' s in heterotic-string derived models
NASA Astrophysics Data System (ADS)
Faraggi, Alon E.; Rizos, John
2016-03-01
The ATLAS and CMS collaborations recently recorded possible di-photon excess at 750 GeV and a less significant di-boson excess around 1.9 TeV. Such excesses may be produced in heterotic string derived Z^' models, where the di-photon excess may be connected with the Standard Model singlet scalar responsible for the Z^' symmetry breaking, whereas the di-boson excess arises from production of the extra vector boson. Additional vector-like states in the string Z^' model are instrumental to explain the relatively large width of the di-photon events and mandated by anomaly cancellation to be in the vicinity of the Z^' breaking scale. Wilson line breaking of the non-Abelian gauge symmetries in the string models naturally gives rise to dark matter candidates. Future collider experiments will discriminate between the high-scale heterotic-string models, which preserve the perturbative unification paradigm indicated by the Standard Model data, versus the low scale string models. We also discuss the possibility for the production of the diphoton events with high scale U(1)_{Z^' } breaking.
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.
Spectral properties of the two-dimensional t- J model near the Mott transition
NASA Astrophysics Data System (ADS)
Kohno, Masanori
The single-particle spectral function of the two-dimensional t- J model near the Mott transition is studied using cluster perturbation theory to clarify how the spectral-weight distribution transforms to that of the Mott insulator as the doping concentration decreases. Various anomalous features observed in cuprate high-temperature superconductors are collectively explained in the two-dimensional t- J model near the Mott transition as in the two-dimensional Hubbard model. The results imply that the spectral features are primarily related to the proximity of the antiferromagnetic Mott insulator, which has a low-energy spin-wave mode but no low-energy charge excitation, and to the presence of states characterized by different energy scales rather than to the presence of double occupancy, which is completely removed in the t- J model. The results are confirmed to remain almost unchanged as the cluster size is increased from 4 ×4 to 6 ×6 sites in cluster perturbation theory by using the non-Abelian dynamical density-matrix renormalization group method.
Pauli-Villars Regularization of Non-Abelian Gauge Theories
NASA Astrophysics Data System (ADS)
Hiller, J. R.
2016-04-01
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.
Non-Abelian energy loss at finite opacity.
Gyulassy, M; Levai, P; Vitev, I
2000-12-25
A systematic expansion in opacity, L/lambda, is used to clarify the nonlinear behavior of induced gluon radiation in quark-gluon plasmas. The inclusive differential gluon distribution is calculated up to second order in opacity and compared to the zeroth order (factorization) limit. The opacity expansion makes it possible to take finite kinematic constraints into account that suppress jet quenching in nuclear collisions below RHIC (square root of s = 200 AGeV) energies. PMID:11136040
Non Abelian structures and the geometric phase of entangled qudits
Oxman, L.E. Khoury, A.Z.
2014-12-15
In this work, we address some important topological and algebraic aspects of two-qudit states evolving under local unitary operations. The projective invariant subspaces and evolutions are connected with the common elements characterizing the su(d) Lie algebra and their representations. In particular, the roots and weights turn out to be natural quantities to parametrize cyclic evolutions and fractional phases. This framework is then used to recast the coset contribution to the geometric phase in a form that generalizes the usual monopole-like formula for a single qubit.
Non-Abelian magnetic black strings versus black holes
NASA Astrophysics Data System (ADS)
Mazharimousavi, S. Habib; Halilsoy, M.
2016-05-01
We present d+1 -dimensional pure magnetic Yang-Mills (YM) black strings (or 1-branes) induced by the d -dimensional Einstein-Yang-Mills-Dilaton black holes. The Born-Infeld version of the YM field makes our starting point which goes to the standard YM field through a limiting procedure. The lifting from black holes to black strings (with less number of fields) is done by adding an extra, compact coordinate. This amounts to the change of horizon topology from S^{d-2} to a product structure. Our black string in 5 dimensions is a rather special one, with uniform Hawking temperature and non-asymptotically flat structure. As the YM charge becomes large the string gets thinner to tend into a breaking point and transform into a 4-dimensional black hole.
Neutrino transitional magnetic moment and non-Abelian discrete symmetry
Chang, D. Fermi National Laboratory, P.O. Box 500, Batavia, IL ); Keung, W. Fermi National Laboratory, P.O. Box 500, Batavia, IL ); Senjanovic, G. Bartol Research Institute, University of Delaware, Newark, DE )
1990-09-01
We propose a mechanism which naturally will give rise to a small mass but a large transitional magnetic moment for the neutrino such that the solar-neutrino deficit problem can be explained. The idea is a discrete version of Voloshin's SU(2) mechanism. An example of such a mechanism using the quaternion group is illustrated.
Jet broadening in unstable non-Abelian plasmas
Dumitru, Adrian; Schenke, Bjoern; Strickland, Michael; Nara, Yasushi
2008-08-15
We perform numerical simulations of the SU(2) Boltzmann-Vlasov equation including both hard elastic particle collisions and soft interactions mediated by classical Yang-Mills fields. Using this technique we calculate the momentum-space broadening of high-energy jets in real time for both locally isotropic and anisotropic plasmas. In both cases we introduce a separation scale that separates hard and soft interactions and demonstrate that our results for jet broadening are independent of the precise separation scale chosen. For an isotropic plasma this allows us to calculate the jet transport coefficient q-circumflex including hard and soft nonequilibrium dynamics. For an anisotropic plasma the jet transport coefficient becomes a tensor with q-circumflex{sub L}{ne}q-circumflex{sub perpendicular}. We find that for weakly coupled anisotropic plasmas the fields develop unstable modes, forming configurations where B{sub perpendicular}>E{sub perpendicular} and E{sub z}>B{sub z}, which lead to q-circumflex{sub L}>q-circumflex{sub perpendicular}. We study whether the effect is strong enough to explain the experimental observation that high-energy jets traversing the plasma perpendicular to the beam axis experience much stronger broadening in rapidity, {delta}{eta}, than in azimuth, {delta}{phi}.
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.
Abelian functions for cyclic trigonal curves of genus 4
NASA Astrophysics Data System (ADS)
Baldwin, S.; Eilbeck, J. C.; Gibbons, J.; Ônishi, Y.
2008-04-01
We discuss the theory of generalized Weierstrass σ and ℘-functions defined on a trigonal curve of genus 4, following earlier work on the genus 3 case. The specific example of the "purely trigonal" (or "cyclic trigonal") curve y3=x5+λ4x4+λ3x3+λ2x2+λ1x+λ0 is discussed in detail, including a list of some of the associated partial differential equations satisfied by the ℘-functions, and the derivation of addition formulae.
Z ', Higgses and heavy neutrinos in U(1)' models: from the LHC to the GUT scale
NASA Astrophysics Data System (ADS)
Accomando, Elena; Corianò, Claudio; Rose, Luigi Delle; Fiaschi, Juri; Marzo, Carlo; Moretti, Stefano
2016-07-01
We study a class of non-exotic minimal U(1)' extensions of the Standard Model, which includes all scenarios that are anomaly-free with the ordinary fermion content augmented by one Right-Handed neutrino per generation, wherein the new Abelian gauge group is spontaneously broken by the non-zero Vacuum Expectation Value of an additional Higgs singlet field, in turn providing mass to a Z ' state. By adopting the B - L example, whose results can be recast into those pertaining to the whole aforementioned class, and allowing for both scalar and gauge mixing, we first extract the surviving parameter space in presence of up-to-date theoretical and experimental constraints. Over the corresponding parameter configurations, we then delineate the high energy behaviour of such constructs in terms of their stability and perturbativity. Finally, we highlight key production and decay channels of the new states entering the spectra of this class of models, i.e., heavy neutrinos, a second Higgs state and the Z ', which are amenable to experimental investigation at the Large Hadron Collider. We therefore set the stage to establish a direct link between measurements obtainable at the Electro-Weak scale and the dynamics of the underlying model up to those where a Grand Unification Theory embedding a U(1)' can be realised.
Topological Symmetry, Spin Liquids and CFT Duals of Polyakov Model with Massless Fermions
Unsal, Mithat
2008-04-30
We prove the absence of a mass gap and confinement in the Polyakov model with massless complex fermions in any representation of the gauge group. A U(1){sub *} topological shift symmetry protects the masslessness of one dual photon. This symmetry emerges in the IR as a consequence of the Callias index theorem and abelian duality. For matter in the fundamental representation, the infrared limits of this class of theories interpolate between weakly and strongly coupled conformal field theory (CFT) depending on the number of flavors, and provide an infinite class of CFTs in d = 3 dimensions. The long distance physics of the model is same as certain stable spin liquids. Altering the topology of the adjoint Higgs field by turning it into a compact scalar does not change the long distance dynamics in perturbation theory, however, non-perturbative effects lead to a mass gap for the gauge fluctuations. This provides conceptual clarity to many subtle issues about compact QED{sub 3} discussed in the context of quantum magnets, spin liquids and phase fluctuation models in cuprate superconductors. These constructions also provide new insights into zero temperature gauge theory dynamics on R{sup 2,1} and R{sup 2,1} x S{sup 1}. The confined versus deconfined long distance dynamics is characterized by a discrete versus continuous topological symmetry.
NASA Astrophysics Data System (ADS)
Tavares, Gustavo Marques
The Standard Model of particle physics describes all known elementary particles and their interactions. Despite its great experimental success, we know that the Standard Model is not a complete description of Nature and therefore new phenomena should be observed at higher energies. In the coming years the Large Hadron Collider will test the Standard Model by colliding protons with center of mass energies of up to 14 TeV providing some of the most stringent tests on the Standard Model. Experimental searches for Dark Matter provide a complementary program to test physics at the weak scale. In the near future new experimental data coming from direct detection experiments, and from satellites and telescopes will drastically improve our sensitivity to weak scale dark matter. This could lead to the first direct observation of dark matter, and thus of physics beyond the Standard Model. In this thesis I propose different extensions of the Standard Model and discuss their experimental consequences. I first discuss models for Axigluons, which are spin one particles in the adjoint representation of the SU(3) color gauge group. These models were motivated by the measurement of higher than predicted forward-backward asymmetry in top quark pair production at the Tevatron. I study different scenarios for Axigluon models that can explain the Tevatron result and explore their signatures at the Large Hadron Collider. Second I discuss the implications of ultraviolet scale invariance for the Standard Model, which has been advocated as a solution to the hierarchy problem. I show that in order to solve the hierarchy problem with scale invariance, new physics is required not far from the weak scale. In the last part of this thesis I propose a new model for dark matter, in which dark matter is charged under a hidden non-Abelian gauge group. This leads to modifications in the sensitivity of the usual experimental searches for dark matter in addition to distinct signatures in the Cosmic
e/sup +/e/sup -/ interactions at very high energy: searching beyond the standard model
Dorfan, J.
1983-04-01
These lectures discuss e/sup +/e/sup -/ interactions at very high energies with a particular emphasis on searching the standard model which we take to be SU(3)/sub color/..lambda.. SU(2) ..lambda.. U(1). The highest e/sup +/e/sup -/ collision energy exploited to date is at PETRA where data have been taken at 38 GeV. We will consider energies above this to be the very high energy frontier. The lectures will begin with a review of the collision energies which will be available in the upgraded machines of today and the machines planned for tomorrow. Without going into great detail, we will define the essential elements of the standard model. We will remind ourselves that some of these essential elements have not yet been verified and that part of the task of searching beyond the standard model will involve experiments aimed at this verification. For if we find the standard model lacking, then clearly we are forced to find an alternative. So we will investigate how the higher energy e/sup +/e/sup -/ collisions can be used to search for the top quark, the neutral Higgs scalar, provide true verification of the non-Abelian nature of QCD, etc. Having done this we will look at tests of models involving simple extensions of the standard model. Models considered are those without a top quark, those with charged Higgs scalars, with multiple and/or composite vector bosons, with additional generations and possible alternative explanations for the PETRA three jet events which don't require gluon bremsstrahlung. From the simple extensions of the standard model we will move to more radical alternatives, alternatives which have arisen from the unhappiness with the gauge hierarchy problem of the standard model. Technicolor, Supersymmetry and composite models will be discussed. In the final section we will summarize what the future holds in terms of the search beyond the standard model.
Deconfined Quantum Criticality, Scaling Violations, and Classical Loop Models
NASA Astrophysics Data System (ADS)
Nahum, Adam; Chalker, J. T.; Serna, P.; Ortuño, M.; Somoza, A. M.
2015-10-01
Numerical studies of the transition between Néel and valence bond solid phases in two-dimensional quantum antiferromagnets give strong evidence for the remarkable scenario of deconfined criticality, but display strong violations of finite-size scaling that are not yet understood. We show how to realize the universal physics of the Néel-valence-bond-solid (VBS) transition in a three-dimensional classical loop model (this model includes the subtle interference effect that suppresses hedgehog defects in the Néel order parameter). We use the loop model for simulations of unprecedentedly large systems (up to linear size L =512 ). Our results are compatible with a continuous transition at which both Néel and VBS order parameters are critical, and we do not see conventional signs of first-order behavior. However, we show that the scaling violations are stronger than previously realized and are incompatible with conventional finite-size scaling, even if allowance is made for a weakly or marginally irrelevant scaling variable. In particular, different approaches to determining the anomalous dimensions ηVBS and ηN é el yield very different results. The assumption of conventional finite-size scaling leads to estimates that drift to negative values at large sizes, in violation of the unitarity bounds. In contrast, the decay with distance of critical correlators on scales much smaller than system size is consistent with large positive anomalous dimensions. Barring an unexpected reversal in behavior at still larger sizes, this implies that the transition, if continuous, must show unconventional finite-size scaling, for example, from an additional dangerously irrelevant scaling variable. Another possibility is an anomalously weak first-order transition. By analyzing the renormalization group flows for the noncompact CP n -1 field theory (the n -component Abelian Higgs model) between two and four dimensions, we give the simplest scenario by which an anomalously weak first
NASA Astrophysics Data System (ADS)
Borah, Debasish; Dasgupta, Arnab; Adhikari, Rathin
2015-10-01
We attempt to simultaneously explain the recently observed 3.55 keV x-ray line in the analysis of XMM-Newton telescope data and the Galactic Center gamma ray excess observed by the Fermi Gamma Ray Space Telescope within an Abelian gauge extension of the standard model. We consider a two component dark matter scenario with tree level mass difference 3.55 keV such that the heavier one can decay into the lighter one and a photon with energy 3.55 keV. The lighter dark matter candidate is protected from decaying into the standard model particles by a remnant Z2 symmetry into which the Abelian gauge symmetry gets spontaneously broken. If the mass of the dark matter particle is chosen to be within 31-40 GeV, then this model can also explain the Galactic Center gamma ray excess if the dark matter annihilation into b b ¯ pairs has a cross section of ⟨σ v ⟩≃(1.4 -2.0 )×1 0-26 cm3/s . We constrain the model from the requirement of producing correct dark matter relic density, 3.55 keV x-ray line flux, and Galactic Center gamma ray excess. We also impose the bounds coming from dark matter direct detection experiments as well as collider limits on additional gauge boson mass and gauge coupling. We also briefly discuss how this model can give rise to subelectron volt neutrino masses at tree level as well as the one-loop level while keeping the dark matter mass at a few tens of giga-electron volts. We also constrain the model parameters from the requirement of keeping the one-loop mass difference between two dark matter particles below a kilo-electron volt. We find that the constraints from light neutrino mass and kilo-electron volt mass splitting between two dark matter components show more preference for opposite C P eigenvalues of the two fermion singlet dark matter candidates in the model.
Supergravity background of λ-deformed model for AdS2 × S2 supercoset
NASA Astrophysics Data System (ADS)
Borsato, R.; Tseytlin, A. A.; Wulff, L.
2016-04-01
Starting with the F ˆ / G supercoset model corresponding to the AdSn ×Sn superstring one can define the λ-model of arxiv:arXiv:1409.1538 either as a deformation of the F ˆ / F ˆ gauged WZW model or as an integrable one-parameter generalisation of the non-abelian T-dual of the AdSn ×Sn superstring sigma model with respect to the whole supergroup F ˆ . Here we consider the case of n = 2 and find the explicit form of the 4d target space background for the λ-model for the PSU (1 , 1 | 2) / SO (1 , 1) × SO (2) supercoset. We show that this background represents a solution of type IIB 10d supergravity compactified on a 6-torus with only metric, dilaton Φ and the RR 5-form (represented by a 2-form F in 4d) being non-trivial. This implies that the λ-model is Weyl invariant at the quantum level and thus defines a consistent superstring sigma model. The supergravity solution we find is different from the one in arXiv:1410.1886 which should correspond to a version of the λ-model where only the bosonic subgroup of F ˆ is gauged. Still, the two solutions have equivalent scaling limit of arxiv:arXiv:1504.07213 leading to the isometric background for the metric and eΦ F which is related to the η-deformed AdS2 ×S2 sigma model of arXiv:1309.5850. Similar results are expected in the AdS3 ×S3 and AdS5 ×S5 cases.
Basic Brackets of a 2D Model for the Hodge Theory Without its Canonical Conjugate Momenta
NASA Astrophysics Data System (ADS)
Kumar, R.; Gupta, S.; Malik, R. P.
2016-06-01
We deduce the canonical brackets for a two (1+1)-dimensional (2D) free Abelian 1-form gauge theory by exploiting the beauty and strength of the continuous symmetries of a Becchi-Rouet-Stora-Tyutin (BRST) invariant Lagrangian density that respects, in totality, six continuous symmetries. These symmetries entail upon this model to become a field theoretic example of Hodge theory. Taken together, these symmetries enforce the existence of exactly the same canonical brackets amongst the creation and annihilation operators that are found to exist within the standard canonical quantization scheme. These creation and annihilation operators appear in the normal mode expansion of the basic fields of this theory. In other words, we provide an alternative to the canonical method of quantization for our present model of Hodge theory where the continuous internal symmetries play a decisive role. We conjecture that our method of quantization is valid for a class of field theories that are tractable physical examples for the Hodge theory. This statement is true in any arbitrary dimension of spacetime.
Tribimaximal mixing and Cabibbo angle in S{sub 4} flavor model with supersymmetry
Ishimori, Hajime; Saga, Kouta; Shimizu, Yusuke; Tanimoto, Morimitsu
2010-06-01
We present a flavor model of quarks and leptons with the non-Abelian discrete symmetry S{sub 4} in the framework of the SU(5) supersymmetric grand unified theory. Three generations of 5-plets in SU(5) are assigned to 3 of S{sub 4} while the first and second generations of 10-plets in SU(5) are assigned to 2 of S{sub 4}, and the third generation of 10-plet is assigned to 1 of S{sub 4}. Right-handed neutrinos are also assigned to 2 for the first and second generations and 1{sup '} for the third generation. We predict the Cabibbo angle as well as the tribimaximal mixing of neutrino flavors. We also predict the nonvanishing U{sub e3} of the neutrino flavor mixing due to higher dimensional mass operators. Our predicted Cabibbo-Kobayashi-Maskawa mixing angles and the CP violation are consistent with experimental values. We also study supersymmetry breaking terms in the slepton sector. Our model leads to smaller values of flavor changing neutral currents than the present experimental bounds.
The standard model and its generalizations in the Epstein-Glaser approach to renormalization theory
NASA Astrophysics Data System (ADS)
Grigore, D. R.
2000-12-01
We continue our study of non-Abelian gauge theories in the framework of the Epstein-Glaser approach to renormalization theory. We consider the case when massive spin-1 bosons are present in the theory and we modify appropriately the analysis of the origin of the gauge invariance performed in a preceding paper in the case of null-mass spin-1 bosons. Then we are able to extend a result of Dütsch and Scharf concerning the uniqueness of the standard model, consistent with renormalization theory. In fact we consider the most general case, i.e. the consistent interaction of r spin-1 bosons, and we do not impose any restrictions on the gauge group and the mass spectrum of the theory. We show that, besides the natural emergence of a group structure (as in the massless case), we obtain new conditions of a group theoretical nature, namely the existence of a certain representation of the gauge group associated to the Higgs fields. Some other mass relations connecting the structure constants of the gauge group and the masses of the bosons emerge naturally. The proof is carried out using the Epstein-Glaser approach to renormalization theory.
NASA Astrophysics Data System (ADS)
Amari, Yuki; Klimas, Paweł; Sawado, Nobuyuki
2016-07-01
The C PN extended Skyrme-Faddeev model possesses planar soliton solutions. We consider quantum aspects of the solutions applying collective coordinate quantization in regime of rigid body approximation. In order to discuss statistical properties of the solutions we include an Abelian Chern-Simons term (the Hopf term) in the Lagrangian. Since Π3(C P1)=Z then for N =1 the term becomes an integer. On the other hand for N >1 it became perturbative because Π3(C PN) is trivial. The prefactor of the Hopf term (anyon angle) Θ is not quantized and its value depends on the physical system. The corresponding fermionic models can fix value of the angle Θ for all N in a way that the soliton with N =1 is not an anyon type whereas for N >1 it is always an anyon even for Θ =n π , n ∈Z . We quantize the solutions and calculate several mass spectra for N =2 . Finally we discuss generalization for N ≧3 .
New simple A{sub 4} neutrino model for nonzero {theta}{sub 13} and large {delta}{sub CP}
Ishimori, Hajime
2013-05-23
In a new simple application of the non-Abelian discrete symmetry A{sub 4} to charged-lepton and neutrino mass matrices, we show that for the current experimental central value of sin{sup 2} 2{theta}{sub 13} Asymptotically-Equal-To 0.1, leptonic CP violation is necessarily large, i.e. Double-Vertical-Line tan{delta}{sub CP} Double-Vertical-Line > 1.3. We also consider T{sub 7} model with one parameter to be complex, thus allowing for one Dirac CP phase {delta}{sub CP} and two Majorana CP phases {alpha}{sub 1,2}. We find a slight modification to this correlation as a function of {delta}{sub CP}. For a given set of input values of {Delta}m{sup 2}{sub 21}, {Delta}m{sup 2}{sub 32}, {theta}{sub 12}, and {theta}{sub 13}, we obtain sin{sup 2} 2{theta}{sub 23} and m{sub ee} (the effective Majorana neutrino mass in neutrinoless double beta decay) as functions of tan {delta}{sub CP}. We find that the structure of this model always yields small Double-Vertical-Line tan {delta}{sub CP} Double-Vertical-Line .
Nehaniv, Chrystopher L; Rhodes, John; Egri-Nagy, Attila; Dini, Paolo; Morris, Eric Rothstein; Horváth, Gábor; Karimi, Fariba; Schreckling, Daniel; Schilstra, Maria J
2015-07-28
Interaction computing is inspired by the observation that cell metabolic/regulatory systems construct order dynamically, through constrained interactions between their components and based on a wide range of possible inputs and environmental conditions. The goals of this work are to (i) identify and understand mathematically the natural subsystems and hierarchical relations in natural systems enabling this and (ii) use the resulting insights to define a new model of computation based on interactions that is useful for both biology and computation. The dynamical characteristics of the cellular pathways studied in systems biology relate, mathematically, to the computational characteristics of automata derived from them, and their internal symmetry structures to computational power. Finite discrete automata models of biological systems such as the lac operon, the Krebs cycle and p53-mdm2 genetic regulation constructed from systems biology models have canonically associated algebraic structures (their transformation semigroups). These contain permutation groups (local substructures exhibiting symmetry) that correspond to 'pools of reversibility'. These natural subsystems are related to one another in a hierarchical manner by the notion of 'weak control'. We present natural subsystems arising from several biological examples and their weak control hierarchies in detail. Finite simple non-Abelian groups are found in biological examples and can be harnessed to realize finitary universal computation. This allows ensembles of cells to achieve any desired finitary computational transformation, depending on external inputs, via suitably constrained interactions. Based on this, interaction machines that grow and change their structure recursively are introduced and applied, providing a natural model of computation driven by interactions. PMID:26078349
Majorana fermions in semiconductor nanowires: fundamentals, modeling, and experiment.
Stanescu, T D; Tewari, S
2013-06-12
After a recent series of rapid and exciting developments, the long search for the Majorana fermion-the elusive quantum entity at the border between particles and antiparticles-has produced the first positive experimental results, but is not over yet. Originally proposed by E Majorana in the context of particle physics, Majorana fermions have a condensed matter analogue in the zero-energy bound states emerging in topological superconductors. A promising route to engineering topological superconductors capable of hosting Majorana zero modes consists of proximity coupling semiconductor thin films or nanowires with strong spin-orbit interaction to conventional s-wave superconductors in the presence of an external Zeeman field. The Majorana zero mode is predicted to emerge above a certain critical Zeeman field as a zero-energy state localized near the order parameter defects, namely, vortices for thin films and wire ends for the nanowire. These Majorana bound states are expected to manifest non-Abelian quantum statistics, which makes them ideal building blocks for fault-tolerant topological quantum computation. This review provides an update on the current status of the search for Majorana fermions in semiconductor nanowires by focusing on the recent developments, in particular the period following the first reports of experimental signatures consistent with the realization of Majorana bound states in semiconductor nanowire-superconductor hybrid structures. We start with a discussion of the fundamental aspects of the subject, followed by considerations on the realistic modeling, which is a critical bridge between theoretical predictions based on idealized conditions and the real world, as probed experimentally. The last part is dedicated to a few intriguing issues that were brought to the fore by the recent encouraging experimental advances. PMID:23665894
Majorana fermions in semiconductor nanowires: fundamentals, modeling, and experiment
NASA Astrophysics Data System (ADS)
Stanescu, T. D.; Tewari, S.
2013-06-01
After a recent series of rapid and exciting developments, the long search for the Majorana fermion—the elusive quantum entity at the border between particles and antiparticles—has produced the first positive experimental results, but is not over yet. Originally proposed by E Majorana in the context of particle physics, Majorana fermions have a condensed matter analogue in the zero-energy bound states emerging in topological superconductors. A promising route to engineering topological superconductors capable of hosting Majorana zero modes consists of proximity coupling semiconductor thin films or nanowires with strong spin-orbit interaction to conventional s-wave superconductors in the presence of an external Zeeman field. The Majorana zero mode is predicted to emerge above a certain critical Zeeman field as a zero-energy state localized near the order parameter defects, namely, vortices for thin films and wire ends for the nanowire. These Majorana bound states are expected to manifest non-Abelian quantum statistics, which makes them ideal building blocks for fault-tolerant topological quantum computation. This review provides an update on the current status of the search for Majorana fermions in semiconductor nanowires by focusing on the recent developments, in particular the period following the first reports of experimental signatures consistent with the realization of Majorana bound states in semiconductor nanowire-superconductor hybrid structures. We start with a discussion of the fundamental aspects of the subject, followed by considerations on the realistic modeling, which is a critical bridge between theoretical predictions based on idealized conditions and the real world, as probed experimentally. The last part is dedicated to a few intriguing issues that were brought to the fore by the recent encouraging experimental advances.
Two- and three-body color flux tubes in the chromodielectric model
Martens, Gunnar; Leupold, Stefan; Mosel, Ulrich; Greiner, Carsten
2004-12-01
Using the framework of the chromodielectric model we perform an analysis of color electric flux tubes in mesonlike qq and baryonlike qqq quark configurations. We discuss the Abelian color structure of the model and point out a symmetry in color space as a remnant of the SU(3) symmetry of QCD. The generic features of the model are discussed by varying the model parameters. We fix these parameters by reproducing the string tension {tau}=980 MeV/fm and the transverse width {rho}=0.35 fm of the qq flux tube obtained in lattice calculations. We use a bag constant B{sup 1/4}=(240-260) MeV, a glueball mass m{sub g}=(1000-1700) MeV, and a strong coupling constant C{sub F}{alpha}{sub s}=0.2-0.3. We show that the asymptotic string profile of an infinitely long flux tube is already reached for qq separations R{>=}1.0 fm. A connection to the dual color superconductor is made by extracting a magnetic current from the model equations and a qualitative agreement between the two descriptions of confinement is shown. In the study of the qqq system we observe a {delta}-like geometry for the color electric fields and a Y-like geometry in the scalar fields both in the energy density distribution and in the corresponding potentials. The resulting total qqq potential is described neither by the {delta}-picture nor by the Y-picture alone.
Gaussian effective potential for the standard model SU(2)xU(1) electroweak theory
Siringo, Fabio; Marotta, Luca
2008-07-01
The Gaussian effective potential is derived for the non-Abelian SU(2)xU(1) gauge theory of electroweak interactions. At variance with naive derivations, the Gaussian effective potential is proven to be a genuine variational tool in any gauge. The role of ghosts is discussed and the unitarity gauge is shown to be the only choice which allows calculability without insertion of further approximations. The full non-Abelian calculation confirms the existence of a light Higgs boson in the nonperturbative strong coupling regime of the Higgs sector.
Yang-Mills Magnetofluid Unification
Bambah, Bindu A.; Mahajan, Swadesh M.; Mukku, Chandrasekher
2006-08-18
We generalize the hybrid magnetofluid model of a charged fluid interacting with an electromagnetic field to the dynamics of a relativistic hot fluid interacting with a non-Abelian field. The fluid itself is endowed with a non-Abelian charge and the consequences of this generalization are worked out. Applications of this formalism to the quark gluon plasma are suggested.
Edery, Ariel; Graham, Noah; MacDonald, Ilana
2009-06-15
Under dimensional reduction, a system in D spacetime dimensions will not necessarily yield its D-1-dimensional analog version. Among other things, this result will depend on the boundary conditions and the dimension D of the system. We investigate this question for scalar and Abelian gauge fields under boundary conditions that obey the symmetries of the action. We apply our findings to the Casimir piston, an ideal system for detecting boundary effects. Our investigation is not limited to extra dimensions and we show that the original piston scenario proposed in 2004, a toy model involving a scalar field in 3D (2+1) dimensions, can be obtained via dimensional reduction from a more realistic 4D electromagnetic (EM) system. We show that for perfect conductor conditions, a D-dimensional EM field reduces to a D-1 scalar field and not its lower-dimensional version. For Dirichlet boundary conditions, no theory is recovered under dimensional reduction and the Casimir pressure goes to zero in any dimension. This ''zero Dirichlet'' result is useful for understanding the EM case. We then identify two special systems where the lower-dimensional version is recovered in any dimension: systems with perfect magnetic conductor (PMC) and Neumann boundary conditions. We show that these two boundary conditions can be obtained from a variational procedure in which the action vanishes outside the bounded region. The fields are free to vary on the surface and have zero modes, which survive after dimensional reduction.
NASA Astrophysics Data System (ADS)
Alvarez, Pedro D.; Pais, Pablo; Rodríguez, Eduardo; Salgado-Rebolledo, Patricio; Zanelli, Jorge
2015-09-01
A Chern-Simons system in 2+1 dimensions invariant under local Lorentz rotations, SU(2) gauge transformations, and local {N}=2 supersymmetry (SUSY) transformations is proposed. The field content is that of (2+1)-gravity plus an SU(2) gauge field, a spin-1/2 fermion charged with respect to SU(2) and a trivial free abelian gauge field. A peculiarity of the model is the absence of gravitini, although it includes gravity and SUSY. Likewise, no gauginos are present. All the parameters involved in the system are either protected by gauge invariance or emerge as integration constants. An effective mass and effective cosmological constant emerge by spontaneous breaking of local scaling invariance. The vacuum sector is defined by configurations with locally flat Lorentz and SU(2) connections sporting nontrivial global charges. Three-dimensional Lorentz-flat geometries are spacetimes of locally constant negative—or zero—Riemann curvature, which include Minkowski space, AdS3, BTZ black holes, and point particles. These solutions admit different numbers of globally defined, covariantly constant spinors and are therefore good candidates for stable ground states. The fermionic sector in this system could describe the dynamics of electrons in graphene in the long wavelength limit near the Dirac points, with the spin degree of freedom of the electrons represented by the SU(2) label. If this is the case, the SU(2) gauge field would produce a spin-spin interaction giving rise to strong correlation of electron pairs.
ERIC Educational Resources Information Center
Freeman, Thomas J.
This paper discusses six different models of organizational structure and leadership, including the scalar chain or pyramid model, the continuum model, the grid model, the linking pin model, the contingency model, and the circle or democratic model. Each model is examined in a separate section that describes the model and its development, lists…
ten Cate, Jacob M
2015-01-01
Developing experimental models to understand dental caries has been the theme in our research group. Our first, the pH-cycling model, was developed to investigate the chemical reactions in enamel or dentine, which lead to dental caries. It aimed to leverage our understanding of the fluoride mode of action and was also utilized for the formulation of oral care products. In addition, we made use of intra-oral (in situ) models to study other features of the oral environment that drive the de/remineralization balance in individual patients. This model addressed basic questions, such as how enamel and dentine are affected by challenges in the oral cavity, as well as practical issues related to fluoride toothpaste efficacy. The observation that perhaps fluoride is not sufficiently potent to reduce dental caries in the present-day society triggered us to expand our knowledge in the bacterial aetiology of dental caries. For this we developed the Amsterdam Active Attachment biofilm model. Different from studies on planktonic ('single') bacteria, this biofilm model captures bacteria in a habitat similar to dental plaque. With data from the combination of these models, it should be possible to study separate processes which together may lead to dental caries. Also products and novel agents could be evaluated that interfere with either of the processes. Having these separate models in place, a suggestion is made to design computer models to encompass the available information. Models but also role models are of the utmost importance in bringing and guiding research and researchers. PMID:25871413
Brennen, Gavin K.; Ellinas, Demosthenes; Kendon, Viv; Pachos, Jiannis K. Tsohantjis, Ioannis; Wang Zhenghan
2010-03-15
The one dimensional quantum walk of anyonic systems is presented. The anyonic walker performs braiding operations with stationary anyons of the same type ordered canonically on the line of the walk. Abelian as well as non-Abelian anyons are studied and it is shown that they have very different properties. Abelian anyonic walks demonstrate the expected quadratic quantum speedup. Non-Abelian anyonic walks are much more subtle. The exponential increase of the system's Hilbert space and the particular statistical evolution of non-Abelian anyons give a variety of new behaviors. The position distribution of the walker is related to Jones polynomials, topological invariants of the links created by the anyonic world-lines during the walk. Several examples such as the SU(2){sub k} and the quantum double models are considered that provide insight to the rich diffusion properties of anyons.
MODEL DEVELOPMENT - DOSE MODELS
Model Development
Humans are exposed to mixtures of chemicals from multiple pathways and routes. These exposures may result from a single event or may accumulate over time if multiple exposure events occur. The traditional approach of assessing risk from a single chemica...
NASA Astrophysics Data System (ADS)
Li, Qin; Zhao, Yongxin; Wu, Xiaofeng; Liu, Si
There can be multitudinous models specifying aspects of the same system. Each model has a bias towards one aspect. These models often override in specific aspects though they have different expressions. A specification written in one model can be refined by introducing additional information from other models. The paper proposes a concept of promoting models which is a methodology to obtain refinements with support from cooperating models. It refines a primary model by integrating the information from a secondary model. The promotion principle is not merely an academic point, but also a reliable and robust engineering technique which can be used to develop software and hardware systems. It can also check the consistency between two specifications from different models. A case of modeling a simple online shopping system with the cooperation of the guarded design model and CSP model illustrates the practicability of the promotion principle.
Models, Part IV: Inquiry Models.
ERIC Educational Resources Information Center
Callison, Daniel
2002-01-01
Discusses models for information skills that include inquiry-oriented activities. Highlights include WebQuest, which uses Internet resources supplemented with videoconferencing; Minnesota's Inquiry Process based on the Big Six model for information problem-solving; Indiana's Student Inquiry Model; constructivist learning models for inquiry; and…
Yost, S.A.
1991-05-01
Radom matrix models based on an integral over supermatrices are proposed as a natural extension of bosonic matrix models. The subtle nature of superspace integration allows these models to have very different properties from the analogous bosonic models. Two choices of integration slice are investigated. One leads to a perturbative structure which is reminiscent of, and perhaps identical to, the usual Hermitian matrix models. Another leads to an eigenvalue reduction which can be described by a two component plasma in one dimension. A stationary point of the model is described.
Yost, S.A. . Dept. of Physics and Astronomy)
1992-09-30
In this paper, random matrix models based on an integral over supermatrices are proposed as a natural extension of bosonic matrix models. The subtle nature of superspace integration allows these models to have very different properties from the analogous bosonic models. Two choices of integration slice are investigated. One leads to a perturbative structure which is reminiscent of, and perhaps identical to, the usual Hermitian matrix models. Another leads to an eigenvalue reduction which can be described by a two-component plasma in one dimension. A stationary point of the model is described.
NASA Astrophysics Data System (ADS)
Cvetič, Mirjam; Klevers, Denis; Piragua, Hernan; Taylor, Washington
2015-11-01
We construct the general form of an F-theory compactification with two U(1) factors based on a general elliptically fibered Calabi-Yau manifold with Mordell-Weil group of rank two. This construction produces broad classes of models with diverse matter spectra, including many that are not realized in earlier F-theory constructions with U(1)×U(1) gauge symmetry. Generic U(1)×U(1) models can be related to a Higgsed non-Abelian model with gauge group SU(2)×SU(2)×SU(3), SU(2)3×SU(3), or a subgroup thereof. The nonlocal horizontal divisors of the Mordell-Weil group are replaced with local vertical divisors associated with the Cartan generators of non-Abelian gauge groups from Kodaira singularities. We give a global resolution of codimension two singularities of the Abelian model; we identify the full anomaly free matter content, and match it to the unHiggsed non-Abelian model. The non-Abelian Weierstrass model exhibits a new algebraic description of the singularities in the fibration that results in the first explicit construction of matter in the symmetric representation of SU(3). This matter is realized on double point singularities of the discriminant locus. The construction suggests a generalization to U(1) k factors with k > 2, which can be studied by Higgsing theories with larger non-Abelian gauge groups.
Models-3 is a third generation air quality modeling system that contains a variety of tools to perform research and analysis of critical environmental questions and problems. These tools provide regulatory analysts and scientists with quicker results, greater scientific accuracy ...
This presentation presented information on entrainment models. Entrainment models use entrainment hypotheses to express the continuity equation. The advantage is that plume boundaries are known. A major disadvantage is that the problems that can be solved are rather simple. The ...
Gauge invariant coupling of fields to torsion: A string inspired model
Bhattacharjee, Srijit; Chatterjee, Ayan
2011-05-15
In a consistent heterotic string theory, the Kalb-Ramond field, which is the source of space-time torsion, is augmented by Yang-Mills and gravitational Chern-Simons terms. When compactified to 4 dimensions and in the field theory limit, such additional terms give rise to interactions with interesting astrophysical predictions like rotation of plane of polarization for electromagnetic and gravitational waves. On the other hand, if one is also interested in coupling 2- or 3-form (Abelian or non-Abelian) gauge fields to torsion, one needs another class of interaction. In this paper, we shall study this interaction and offer some astrophysical and cosmological predictions. We explicitly calculate the Coleman-Weinberg potential for this theory. We also comment on the possibility of such terms in loop quantum gravity where, if the Barbero-Immirzi parameter is promoted to a field, acts as a source for torsion.
NASA Technical Reports Server (NTRS)
Rubesin, Morris W.
1987-01-01
Recent developments at several levels of statistical turbulence modeling applicable to aerodynamics are briefly surveyed. Emphasis is on examples of model improvements for transonic, two-dimensional flows. Experience with the development of these improved models is cited to suggest methods of accelerating the modeling process necessary to keep abreast of the rapid movement of computational fluid dynamics into the computation of complex three-dimensional flows.
NASA Technical Reports Server (NTRS)
1981-01-01
A model is presented which quantifies the electromagnetic modes (field configurations) in the immediate vicinity of the rectenna element. Specifically, the waveguide model characterizes the electromagnetic modes generated by planar waves normal to the array. The model applies only to incidence normal to the array.
Phoenix (formerly referred to as the Second Generation Model or SGM) is a global general equilibrium model designed to analyze energy-economy-climate related questions and policy implications in the medium- to long-term. This model disaggregates the global economy into 26 industr...
ERIC Educational Resources Information Center
James, W. G. G.
1970-01-01
Discusses the historical development of both the wave and the corpuscular photon model of light. Suggests that students should be informed that the two models are complementary and that each model successfully describes a wide range of radiation phenomena. Cites 19 references which might be of interest to physics teachers and students. (LC)
Hydrological models are mediating models
NASA Astrophysics Data System (ADS)
Babel, L. V.; Karssenberg, D.
2013-08-01
Despite the increasing role of models in hydrological research and decision-making processes, only few accounts of the nature and function of models exist in hydrology. Earlier considerations have traditionally been conducted while making a clear distinction between physically-based and conceptual models. A new philosophical account, primarily based on the fields of physics and economics, transcends classes of models and scientific disciplines by considering models as "mediators" between theory and observations. The core of this approach lies in identifying models as (1) being only partially dependent on theory and observations, (2) integrating non-deductive elements in their construction, and (3) carrying the role of instruments of scientific enquiry about both theory and the world. The applicability of this approach to hydrology is evaluated in the present article. Three widely used hydrological models, each showing a different degree of apparent physicality, are confronted to the main characteristics of the "mediating models" concept. We argue that irrespective of their kind, hydrological models depend on both theory and observations, rather than merely on one of these two domains. Their construction is additionally involving a large number of miscellaneous, external ingredients, such as past experiences, model objectives, knowledge and preferences of the modeller, as well as hardware and software resources. We show that hydrological models convey the role of instruments in scientific practice by mediating between theory and the world. It results from these considerations that the traditional distinction between physically-based and conceptual models is necessarily too simplistic and refers at best to the stage at which theory and observations are steering model construction. The large variety of ingredients involved in model construction would deserve closer attention, for being rarely explicitly presented in peer-reviewed literature. We believe that devoting
Model Experiments and Model Descriptions
NASA Technical Reports Server (NTRS)
Jackman, Charles H.; Ko, Malcolm K. W.; Weisenstein, Debra; Scott, Courtney J.; Shia, Run-Lie; Rodriguez, Jose; Sze, N. D.; Vohralik, Peter; Randeniya, Lakshman; Plumb, Ian
1999-01-01
The Second Workshop on Stratospheric Models and Measurements Workshop (M&M II) is the continuation of the effort previously started in the first Workshop (M&M I, Prather and Remsberg [1993]) held in 1992. As originally stated, the aim of M&M is to provide a foundation for establishing the credibility of stratospheric models used in environmental assessments of the ozone response to chlorofluorocarbons, aircraft emissions, and other climate-chemistry interactions. To accomplish this, a set of measurements of the present day atmosphere was selected. The intent was that successful simulations of the set of measurements should become the prerequisite for the acceptance of these models as having a reliable prediction for future ozone behavior. This section is divided into two: model experiment and model descriptions. In the model experiment, participant were given the charge to design a number of experiments that would use observations to test whether models are using the correct mechanisms to simulate the distributions of ozone and other trace gases in the atmosphere. The purpose is closely tied to the needs to reduce the uncertainties in the model predicted responses of stratospheric ozone to perturbations. The specifications for the experiments were sent out to the modeling community in June 1997. Twenty eight modeling groups responded to the requests for input. The first part of this section discusses the different modeling group, along with the experiments performed. Part two of this section, gives brief descriptions of each model as provided by the individual modeling groups.
Model Reduction in Groundwater Modeling
NASA Astrophysics Data System (ADS)
Yeh, W. W. G.
2014-12-01
Model reduction has been shown to be a very effective method for reducing the computational burden of large-scale simulations. Model reduction techniques preserve much of the physical knowledge of the system and primarily seek to remove components from the model that do not provide significant information of interest. Proper Orthogonal Decomposition (POD) is a model reduction technique by which a system of ordinary equations is projected onto a much smaller subspace in such a way that the span of the subspace is equal to the span of the original full model space. Basically, the POD technique selects a small number of orthonormal basis functions (principal components) that span the spatial variability of the solutions. In this way the state variable (head) is approximated by a linear combination of these basis functions and, using a Galerkin projection, the dimension of the problem is significantly reduced. It has been shown that for a highly discritized model, the reduced model can be two to three orders of magnitude smaller than the original model and runs 1,000 faster. More importantly, the reduced model captures the dominating characteristics of the full model and produces sufficiently accurate solutions. One of the major tasks in the development of the reduced model is the selection of snapshots which are used to determine the dominant eigenvectors. This paper discusses ways to optimize the snapshot selection. Additionally, the paper also discusses applications of the reduced model to parameter estimation, Monte Carlo simulation and experimental design in groundwater modeling.
Bois, Frederic Y; Brochot, Céline
2016-01-01
Pharmacokinetics is the study of the fate of xenobiotics in a living organism. Physiologically based pharmacokinetic (PBPK) models provide realistic descriptions of xenobiotics' absorption, distribution, metabolism, and excretion processes. They model the body as a set of homogeneous compartments representing organs, and their parameters refer to anatomical, physiological, biochemical, and physicochemical entities. They offer a quantitative mechanistic framework to understand and simulate the time-course of the concentration of a substance in various organs and body fluids. These models are well suited for performing extrapolations inherent to toxicology and pharmacology (e.g., between species or doses) and for integrating data obtained from various sources (e.g., in vitro or in vivo experiments, structure-activity models). In this chapter, we describe the practical development and basic use of a PBPK model from model building to model simulations, through implementation with an easily accessible free software. PMID:27311461
Varieties of Abelian mirror symmetry on {R}{{P}}^2× {{S}}^1
NASA Astrophysics Data System (ADS)
Mori, Hironori; Tanaka, Akinori
2016-02-01
We study 3d mirror symmetry with loop operators, Wilson loop and Vortex loop, and multi-flavor mirror symmetry through utilizing the {R}{{P}}^2× {{S}}^1 index formula. The key identity which makes the above description work well is the mod 2 version of the Fourier analysis, and we study such structure, the S-operation in the context of a SL(2,{Z}) action on 3d SCFTs. We observed that two types of the parity conditions basically associated with gauge symmetries which we call {P} -type and {C}{P} -type are interchanged under mirror symmetry. We will also comment on the T-operation.
Cichy, Agnieszka; Polak, Tomasz P.
2015-03-15
The ground state of ultracold fermions in the presence of effects of orbital and Zeeman magnetic fields is analyzed. Five different states are found: unpolarized superconducting state, partially and fully polarized normal states and phase separated regions, partially or fully polarized. The system, in the presence of orbital synthetic magnetic field effects, shows non-monotonous changes of the phase boundaries when electron concentration is varied. We observe not only reentrant phenomena, but also density dependent oscillations of different areas of the phase diagram. Moreover the chemical potential shows oscillatory behavior and discontinuities with respect to changes in the number of fermions.
Phase synchronization of non-Abelian oscillators on small-world networks
NASA Astrophysics Data System (ADS)
Gu, Zhi-Ming; Zhao, Ming; Zhou, Tao; Zhu, Chen-Ping; Wang, Bing-Hong
2007-02-01
In this Letter, by extending the concept of Kuramoto oscillator to the left-invariant flow on general Lie group, we investigate the generalized phase synchronization on networks. The analyses and simulations of some typical dynamical systems on Watts Strogatz networks are given, including the n-dimensional torus, the identity component of 3-dimensional general linear group, the special unitary group, and the special orthogonal group. In all cases, the greater disorder of networks will predict better synchronizability, and the small-world effect ensures the global synchronization for sufficiently large coupling strength. The collective synchronized behaviors of many dynamical systems, such as the integrable systems, the two-state quantum systems and the top systems, can be described by the present phase synchronization frame. In addition, it is intuitive that the low-dimensional systems are more easily to synchronize, however, to our surprise, we found that the high-dimensional systems display obviously synchronized behaviors in regular networks, while these phenomena cannot be observed in low-dimensional systems.
On Pauli's Invention of Non-Abelian Kaluza-Klein Theory in 1953
NASA Astrophysics Data System (ADS)
Straumann, N.
2002-12-01
There are documents which show that Wolfgang Pauli developed in 1953 the first consistent generalization of the five-dimensional theory of Kaluza, Klein, Fock and others to a higher dimensional internal space. Because he saw no way to give masses to the gauge bosons, he refrained from publishing his results formally.
Abelian solutions of the soliton equations and Riemann-Schottky problems
NASA Astrophysics Data System (ADS)
Krichever, Igor M.
2008-12-01
The present article is an exposition of the author's talk at the conference dedicated to the 70th birthday of S.P. Novikov. The talk contained the proof of Welters' conjecture which proposes a solution of the classical Riemann-Schottky problem of characterizing the Jacobians of smooth algebraic curves in terms of the existence of a trisecant of the associated Kummer variety, and a solution of another classical problem of algebraic geometry, that of characterizing the Prym varieties of unramified covers.
Regular non-Abelian vacua in N=4, SO(4) gauged supergravity
Chamseddine, Ali H.; Volkov, Mikhail S.
2004-10-15
We present a family of globally regular N=1 vacua in the D=4, N=4 gauged supergravity of Gates and Zwiebach. These solutions are labeled by the ratio {xi} of the two gauge couplings, and for {xi}=0 they reduce to the supergravity monopole previously used for constructing the gravity dual of N=1 super Yang-Mills theory. For {xi}>0 the solutions are asymptotically anti- de Sitter, but with an excess of the solid angle, and they reduce exactly to anti-de Sitter for {xi}=1. Solutions with {xi}<0 are topologically R{sup 1}xS{sup 3}, and for {xi}=-2 they become R{sup 1}xS{sup 3} geometrically. All solutions with {xi}{ne}0 can be promoted to D=11 to become vacua of M-theory.
Solitons and black holes in non-Abelian Einstein-Born-Infeld theory
NASA Astrophysics Data System (ADS)
Dyadichev, V. V.; Gal'tsov, D. V.
2000-08-01
Recently it was shown that the Born-Infeld modification of the quadratic Yang-Mills action gives rise to classical particle-like solutions in the flat space which have a striking similarity with the Bartnik-McKinnon solutions obtained within the gravity coupled Yang-Mills theory. We show that both families of solutions are continuously related within the framework of the Einstein-Born-Infeld theory via interpolating sequences of parameters. We also investigate an internal structure of the associated black holes and find that the Born-Infeld non-linearity changes drastically the black hole interior typical for the usual quadratic Yang-Mills theory. In the latter case a generic solution exhibits violent metric oscillations near the singularity. In the Born-Infeld case the generic interior solution is smooth, the metric tends to the standard Schwarzschild type singularity, and we did not observe internal horizons. Smoothing of the `violent' EYM singularity may be interpreted as a result of non-gravitational quantum effects.
Simple finite-dimensional right-alternative superalgebras of Abelian type of characteristic zero
NASA Astrophysics Data System (ADS)
Pchelintsev, S. V.; Shashkov, O. V.
2015-06-01
We classify simple finite-dimensional right-alternative superalgebras A=A_0\\oplus A_1 over a field of characteristic zero in which the even part A_0 is associative and commutative, while A_1 is an associative A_0-bimodule. We prove that every such superalgebra A=A_0\\oplus A_1 is obtained by doubling the semisimple even part A_0, and the multiplication in A is defined using a suitable automorphism and a linear operator acting on A_0.
Capitulation in Abelian extensions of some fields ℚ (√{p1p2q , }i )
NASA Astrophysics Data System (ADS)
Azizi, Abdelmalek; Zekhnini, Abdelkader; Taous, Mohammed
2016-02-01
We study the capitulation of the 2-ideal classes of an infinite family of imaginary biquadratic number fields consisting of fields k =ℚ (√{p1p2q , }i ), where i =√{-1 } and p1 ≡ p2 ≡ -q ≡ 1 (mod 4) are different primes. For each of the three quadratic extensions K /k inside the absolute genus field k(*) of k , we compute the capitulation kernel of K /k . Then we deduce that each strongly ambiguous class of k /ℚ (i ) capitulates already in k(*), which is smaller than the relative genus field (k/ℚ (i )) *.
NASA Astrophysics Data System (ADS)
Louboutin, Stephane R.
2007-03-01
Let \\{K_m\\} be a parametrized family of simplest real cyclic cubic, quartic, quintic or sextic number fields of known regulators, e.g., the so-called simplest cubic and quartic fields associated with the polynomials P_m(x) Dx^3 -mx^2-(m+3)x+1 and P_m(x) Dx^4 -mx^3-6x^2+mx+1 . We give explicit formulas for powers of the Gaussian sums attached to the characters associated with these simplest number fields. We deduce a method for computing the exact values of these Gaussian sums. These values are then used to efficiently compute class numbers of simplest fields. Finally, such class number computations yield many examples of real cyclotomic fields Q(zeta_p)^+ of prime conductors pge 3 and class numbers h_p^+ greater than or equal to p . However, in accordance with Vandiver's conjecture, we found no example of p for which p divides h_p^+ .
H. Yang
1999-11-04
The purpose of this analysis and model report (AMR) for the Ventilation Model is to analyze the effects of pre-closure continuous ventilation in the Engineered Barrier System (EBS) emplacement drifts and provide heat removal data to support EBS design. It will also provide input data (initial conditions, and time varying boundary conditions) for the EBS post-closure performance assessment and the EBS Water Distribution and Removal Process Model. The objective of the analysis is to develop, describe, and apply calculation methods and models that can be used to predict thermal conditions within emplacement drifts under forced ventilation during the pre-closure period. The scope of this analysis includes: (1) Provide a general description of effects and heat transfer process of emplacement drift ventilation. (2) Develop a modeling approach to simulate the impacts of pre-closure ventilation on the thermal conditions in emplacement drifts. (3) Identify and document inputs to be used for modeling emplacement ventilation. (4) Perform calculations of temperatures and heat removal in the emplacement drift. (5) Address general considerations of the effect of water/moisture removal by ventilation on the repository thermal conditions. The numerical modeling in this document will be limited to heat-only modeling and calculations. Only a preliminary assessment of the heat/moisture ventilation effects and modeling method will be performed in this revision. Modeling of moisture effects on heat removal and emplacement drift temperature may be performed in the future.
NASA Technical Reports Server (NTRS)
Druyan, Leonard M.
2012-01-01
Climate models is a very broad topic, so a single volume can only offer a small sampling of relevant research activities. This volume of 14 chapters includes descriptions of a variety of modeling studies for a variety of geographic regions by an international roster of authors. The climate research community generally uses the rubric climate models to refer to organized sets of computer instructions that produce simulations of climate evolution. The code is based on physical relationships that describe the shared variability of meteorological parameters such as temperature, humidity, precipitation rate, circulation, radiation fluxes, etc. Three-dimensional climate models are integrated over time in order to compute the temporal and spatial variations of these parameters. Model domains can be global or regional and the horizontal and vertical resolutions of the computational grid vary from model to model. Considering the entire climate system requires accounting for interactions between solar insolation, atmospheric, oceanic and continental processes, the latter including land hydrology and vegetation. Model simulations may concentrate on one or more of these components, but the most sophisticated models will estimate the mutual interactions of all of these environments. Advances in computer technology have prompted investments in more complex model configurations that consider more phenomena interactions than were possible with yesterday s computers. However, not every attempt to add to the computational layers is rewarded by better model performance. Extensive research is required to test and document any advantages gained by greater sophistication in model formulation. One purpose for publishing climate model research results is to present purported advances for evaluation by the scientific community.
NASA Astrophysics Data System (ADS)
Sun, Fadi; Ye, Jinwu; Liu, Wu-Ming
2016-07-01
In this paper, we study the rotated ferromagnetic Heisenberg model (RFHM) in two different transverse fields, hx and hz, which can be intuitively visualized as studying spin-orbit coupling (SOC) effects in two-dimensional (2D) Ising or anisotropic X Y model in a transverse field. At a special SOC class, it was found in our previous work [Phys. Rev. A 92, 043609 (2015), 10.1103/PhysRevA.92.043609] that the RFHM at a zero field owns an exact spin-orbit coupled ground state called the Y -x state. It supports not only the commensurate magnons (called C -C0 and C -Cπ ), but also the incommensurate magnons (called C-IC). These magnons are nonrelativistic, not embedded in the exact ground state, so need to be thermally excited or generated by various external probes. Their dramatic response under a longitudinal hy field was recently worked out by Sun et al. [arXiv:1502.05338]. Here we find they respond very differently under the two transverse fields. Any hx (hz) introduces quantum fluctuations to the ground state and changes the collinear Y -x state to a canted coplanar Y X -x (Y Z -x ) state. The C -C0,C -Cπ , and C-IC magnons become relativistic and sneak into the quantum ground state. We determine the competing boundaries among the C -C0,C -Cπ , and C-IC magnons, especially the detailed dispersions of the C-IC magnons inside the canted phases, which can be mapped out by the transverse spin structure factors. As hx (hz) increases further, the C -C0 magnons always win the competition and emerge as the seeds to drive a transition from the Y X -x (or Y Z -x ) to the ferromagnetic along the X (orZ ) direction called the X -FM (or Z -FM) phase. We show that the transition is in the 3D Ising universality class and it becomes the 3D X Y transition at the two Abelian points. We evaluate these magnons' contributions to magnetization and specific heat at low temperatures which can be measured by various established experimental techniques. The nature of the finite
Braby, L.A.
1990-09-01
The biological effects of ionizing radiation exposure are the result of a complex sequence of physical, chemical, biochemical, and physiological interactions. One way to begin a search for an understanding of health effects of radiation is through the development of phenomenological models of the response. Many models have been presented and tested in the slowly evolving process of characterizing cellular response. A range of models covering different endpoints and phenomena has developed in parallel. Many of these models employ similar assumptions about some underlying processes while differing about the nature of others. An attempt is made to organize many of the models into groups with similar features and to compare the consequences of those features with the actual experimental observations. It is assumed that by showing that some assumptions are inconsistent with experimental observations, the job of devising and testing mechanistic models can be simplified. 43 refs., 13 figs.
Burr, M.T.
1995-04-01
As developers make progress on independent power projects around the world, models for success are beginning to emerge. Different models are evolving to create ownership structures that accomoate a complex system of regulatory requirements. Other frameworks make use of previously untapped fuel resources, or establish new sources of financing; however, not all models may be applied to a given project. This article explores how developers are finding new alternatives for overcoming development challenges that are common to projects in many countries.
V. Chipman
2002-10-05
The purpose of the Ventilation Model is to simulate the heat transfer processes in and around waste emplacement drifts during periods of forced ventilation. The model evaluates the effects of emplacement drift ventilation on the thermal conditions in the emplacement drifts and surrounding rock mass, and calculates the heat removal by ventilation as a measure of the viability of ventilation to delay the onset of peak repository temperature and reduce its magnitude. The heat removal by ventilation is temporally and spatially dependent, and is expressed as the fraction of heat carried away by the ventilation air compared to the fraction of heat produced by radionuclide decay. One minus the heat removal is called the wall heat fraction, or the remaining amount of heat that is transferred via conduction to the surrounding rock mass. Downstream models, such as the ''Multiscale Thermohydrologic Model'' (BSC 2001), use the wall heat fractions as outputted from the Ventilation Model to initialize their post-closure analyses. The Ventilation Model report was initially developed to analyze the effects of preclosure continuous ventilation in the Engineered Barrier System (EBS) emplacement drifts, and to provide heat removal data to support EBS design. Revision 00 of the Ventilation Model included documentation of the modeling results from the ANSYS-based heat transfer model. The purposes of Revision 01 of the Ventilation Model are: (1) To validate the conceptual model for preclosure ventilation of emplacement drifts and verify its numerical application in accordance with new procedural requirements as outlined in AP-SIII-10Q, Models (Section 7.0). (2) To satisfy technical issues posed in KTI agreement RDTME 3.14 (Reamer and Williams 2001a). Specifically to demonstrate, with respect to the ANSYS ventilation model, the adequacy of the discretization (Section 6.2.3.1), and the downstream applicability of the model results (i.e. wall heat fractions) to initialize post
Computational studies of model disordered and strongly correlated electronic systems
NASA Astrophysics Data System (ADS)
Johri, Sonika
cannot be achieved perfectly in experiments. A chapter of this thesis is devoted to studying signatures of incomplete localization in a disordered system with interacting particles which is coupled to a bath. . Strongly interacting particles can also give rise to topological phases of matter that have exotic emergent properties, such as quasiparticles with fractional charges and anyonic, or perhaps even non-Abelian statistics. In addition to their intrinsic novelty, these particles (e.g. Majorana fermions) may be the building blocks of future quantum computers. The third part of my thesis focuses on the best experimentally known realizations of such systems - the fractional quantum Hall effect (FQHE) which occurs in two-dimensional electron gases in a strong perpendicular magnetic field. It has been observed in systems such as semiconductor heterostructures and, more recently, graphene. I have developed software for exact diagonalization of the many-body FQHE problem on the surface of a cylinder, a hitherto unstudied type of geometry. This geometry turns out to be optimal for the DMRG algorithm. Using this new geometry, I have studied properties of various fractionally-filled states, computing the overlap between exact ground states and model wavefunctions, their edge excitations, and entanglement spectra. I have calculated the sizes and tunneling amplitudes of quasiparticles, information which is needed to design the interferometers used to experimentally measure their Aharanov-Bohm phase. I have also designed numerical probes of the recently discovered geometric degree of freedom of FQHE states.
Model Selection for Geostatistical Models
Hoeting, Jennifer A.; Davis, Richard A.; Merton, Andrew A.; Thompson, Sandra E.
2006-02-01
We consider the problem of model selection for geospatial data. Spatial correlation is typically ignored in the selection of explanatory variables and this can influence model selection results. For example, the inclusion or exclusion of particular explanatory variables may not be apparent when spatial correlation is ignored. To address this problem, we consider the Akaike Information Criterion (AIC) as applied to a geostatistical model. We offer a heuristic derivation of the AIC in this context and provide simulation results that show that using AIC for a geostatistical model is superior to the often used approach of ignoring spatial correlation in the selection of explanatory variables. These ideas are further demonstrated via a model for lizard abundance. We also employ the principle of minimum description length (MDL) to variable selection for the geostatistical model. The effect of sampling design on the selection of explanatory covariates is also explored.
NASA Technical Reports Server (NTRS)
Bardina, Jorge E.
1995-01-01
The objective of this work is to develop, verify, and incorporate the baseline two-equation turbulence models which account for the effects of compressibility into the three-dimensional Reynolds averaged Navier-Stokes (RANS) code and to provide documented descriptions of the models and their numerical procedures so that they can be implemented into 3-D CFD codes for engineering applications.
ERIC Educational Resources Information Center
Washington State Board for Community Coll. Education, Olympia.
Computerized formula-driven budget models are used by the Washington community college system to define resource needs for legislative budget requests and to distribute legislative appropriations among 22 community college districts. This manual outlines the sources of information needed to operate the model and illustrates the principles on which…
ERIC Educational Resources Information Center
Budiansky, Stephen
1980-01-01
This article discusses the need for more accurate and complete input data and field verification of the various models of air pollutant dispension. Consideration should be given to changing the form of air quality standards based on enhanced dispersion modeling techniques. (Author/RE)
ERIC Educational Resources Information Center
Oh, Phil Seok; Oh, Sung Jin
2013-01-01
Modeling in science has been studied by education researchers for decades and is now being applied broadly in school. It is among the scientific practices featured in the "Next Generation Science Standards" ("NGSS") (Achieve Inc. 2013). This article describes modeling activities in an extracurricular science club in a high…
ERIC Educational Resources Information Center
Ballard, W.L.
1968-01-01
The article discusses models of synchronic and diachronic phonology and suggests changes in them. The basic generative model of phonology is outlined with the author's reinterpretations. The systematic phonemic level is questioned in terms of its unreality with respect to linguistic performance and its lack of validity with respect to historical…
Hestenes, D. )
1993-03-01
Guidelines for constructing point particle models of the electron with [ital zitterbewegung] and other features of the Dirac theory are discussed. Such models may at least be useful approximations to the Dirac theory, but the more exciting possibility is that this approach may lead to a more fundamental reality. 6 refs.
Veronica J. Rutledge
2013-01-01
The absence of industrial scale nuclear fuel reprocessing in the U.S. has precluded the necessary driver for developing the advanced simulation capability now prevalent in so many other countries. Thus, it is essential to model complex series of unit operations to simulate, understand, and predict inherent transient behavior and feedback loops. A capability of accurately simulating the dynamic behavior of advanced fuel cycle separation processes will provide substantial cost savings and many technical benefits. The specific fuel cycle separation process discussed in this report is the off-gas treatment system. The off-gas separation consists of a series of scrubbers and adsorption beds to capture constituents of interest. Dynamic models are being developed to simulate each unit operation involved so each unit operation can be used as a stand-alone model and in series with multiple others. Currently, an adsorption model has been developed within Multi-physics Object Oriented Simulation Environment (MOOSE) developed at the Idaho National Laboratory (INL). Off-gas Separation and REcoverY (OSPREY) models the adsorption of off-gas constituents for dispersed plug flow in a packed bed under non-isothermal and non-isobaric conditions. Inputs to the model include gas, sorbent, and column properties, equilibrium and kinetic data, and inlet conditions. The simulation outputs component concentrations along the column length as a function of time from which breakthrough data is obtained. The breakthrough data can be used to determine bed capacity, which in turn can be used to size columns. It also outputs temperature along the column length as a function of time and pressure drop along the column length. Experimental data and parameters were input into the adsorption model to develop models specific for krypton adsorption. The same can be done for iodine, xenon, and tritium. The model will be validated with experimental breakthrough curves. Customers will be given access to