Discrete gauge symmetry in continuum theories
Krauss, L.M.; Wilczek, F.
1989-03-13
We point out that local symmetries can masquerade as discrete global symmetries to an observer equipped with only low-energy probes. The existence of the underlying local gauge invariance can, however, result in observable Aharonov-Bohm-type effects. Black holes can therefore carry discrete gauge charges: a form of nonclassical ''hair.'' Neither black-hole evaporation, wormholes, nor anything else can violate discrete gauge symmetries. In supersymmetric unified theories such discrete symmetries can forbid proton-decay amplitudes that might otherwise be catastrophic.
Superheavy dark matter with discrete gauge symmetries
NASA Astrophysics Data System (ADS)
Hamaguchi, K.; Nomura, Yasunori; Yanagida, T.
1998-11-01
We show that there are discrete gauge symmetries which naturally protect heavy X particles from decaying into ordinary light particles in the supersymmetric standard model. This makes the proposal that superheavy X particles constitute part of the dark matter in the present universe very attractive. It is more interesting that there is a class of discrete gauge symmetries which naturally accommodates a long-lived unstable X particle. We find that in some discrete Z10 models, for example, a superheavy X particle has a lifetime of τX~=1011-1026 yr for a mass of MX~=1013-1014 GeV. This long lifetime is guaranteed by the absence of lower dimensional operators (of light particles) coupled to the X. We briefly discuss a possible explanation for the recently observed ultrahigh-energy cosmic ray events by the decay of this unstable X particle.
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.
Long lived superheavy dark matter with discrete gauge symmetries
NASA Astrophysics Data System (ADS)
Hamaguchi, K.; Nomura, Yasunori; Yanagida, T.
1999-03-01
The recently observed ultrahigh energy (UHE) cosmic rays beyond the Greisen-Zatsepin-Kuzmin bound can be explained by the decays of some superheavy X particles forming a part of dark matter in our universe. We consider various discrete gauge symmetries ZN to ensure the required long lifetime (τX~=1010-1022 yr) of the X particle to explain the UHE cosmic rays in the minimal supersymmetric standard model (MSSM) with massive Majorana neutrinos. We show that there is no anomaly-free discrete gauge symmetry to make the lifetime of the X particle sufficiently long in the MSSM with the X particle. We find, however, possible solutions to this problem especially by enlarging the particle contents in the MSSM. We show a number of solutions introducing an extra pair of singlets Y and Y¯ which have fractional ZN(N=2,3) charges. The present experimental constraints on the X particle are briefly discussed.
Proton Stability in Grand Unified Theories and Discrete Gauge Symmetries
Mohapatra, R. N.
2008-05-13
Most supersymmetric grand unified theories face the problem of rapid proton decay coming either from R-parity violating interactions and/or from Planck scale induced R-parity conserving operators, possibly induced by non-perturbative Planck scale effects such as black holes or wormholes. In this talk, I argue in favor of the possibility that a natural way to resolve this problem is to assume that there are new discrete or continuous gauge symmetries accompanying these theories that resolve these problems while at the same time allowing enough flexibility to have a viable model. I discuss this for left-right and SO(10) theories and discuss the profound impact such considerations have on the construction of realistic GUT models. I then discuss a recently proposed SO(10) model which has only apparently string inspired multiplets and has enough structure to be a realistic model.
Model for neutrino masses and dark matter with a discrete gauge symmetry
NASA Astrophysics Data System (ADS)
Chang, We-Fu; Wong, Chi-Fong
2012-01-01
A simple renormalizable U(1) gauge model is constructed to explain the smallness of the active neutrino masses and provide the stable cold dark matter candidate simultaneously. The local U(1) symmetry is assumed to be spontaneously broken by a scalar field around the TeV scale. The active neutrino masses are then generated at one-loop level. This model contains several cold dark matter candidates whose stability is guaranteed by a residual discrete gauge Z2 symmetry à la the Krauss-Wilczek mechanism. Unlike the other dark matter models, no further global discrete or continuous symmetry is introduced. Moreover, the masses of all fermionic degrees of freedom beyond the standard model are closely related to the scale of spontaneous breaking of U(1); thus they could be probed at or below the TeV scale. The possible cosmological and phenomenological consequences are briefly discussed.
Gauge symmetry from decoupling
NASA Astrophysics Data System (ADS)
Wetterich, C.
2017-02-01
Gauge symmetries emerge from a redundant description of the effective action for light degrees of freedom after the decoupling of heavy modes. This redundant description avoids the use of explicit constraints in configuration space. For non-linear constraints the gauge symmetries are non-linear. In a quantum field theory setting the gauge symmetries are local and can describe Yang-Mills theories or quantum gravity. We formulate gauge invariant fields that correspond to the non-linear light degrees of freedom. In the context of functional renormalization gauge symmetries can emerge if the flow generates or preserves large mass-like terms for the heavy degrees of freedom. They correspond to a particular form of gauge fixing terms in quantum field theories.
Spontaneous Breaking of Lie Groups to Discrete Symmetries
NASA Astrophysics Data System (ADS)
Rachlin, Bradley; Kephart, Thomas
2017-01-01
Many models of beyond Standard Model physics connect flavor symmetry with a discrete group. Having this symmetry arise spontaneously from a gauge theory maintains compatibility with quantum gravity and prevents anomalies. We detail ways to set up Higgs potentials to break gauge groups to discrete symmetries of interest. The scalar mass spectra are examined. Research Assistantship funded by Department of Energy (DOE).
From physical symmetries to emergent gauge symmetries
NASA Astrophysics Data System (ADS)
Barceló, Carlos; Carballo-Rubio, Raúl; Di Filippo, Francesco; Garay, Luis J.
2016-10-01
Gauge symmetries indicate redundancies in the description of the relevant degrees of freedom of a given field theory and restrict the nature of observable quantities. One of the problems faced by emergent theories of relativistic fields is to understand how gauge symmetries can show up in systems that contain no trace of these symmetries at a more fundamental level. In this paper we start a systematic study aimed to establish a satisfactory mathematical and physical picture of this issue, dealing first with abelian field theories. We discuss how the trivialization, due to the decoupling and lack of excitation of some degrees of freedom, of the Noether currents associated with physical symmetries leads to emergent gauge symmetries in specific situations. An example of a relativistic field theory of a vector field is worked out in detail in order to make explicit how this mechanism works and to clarify the physics behind it. The interplay of these ideas with well-known results of importance to the emergent gravity program, such as the Weinberg-Witten theorem, are discussed.
A nilpotent symmetry of quantum gauge theories
NASA Astrophysics Data System (ADS)
Lahiri, Amitabha
2001-09-01
For the Becchi-Rouet-Stora-Tyutin invariant extended action for any gauge theory, there exists another off-shell nilpotent symmetry. For linear gauges, it can be elevated to a symmetry of the quantum theory and used in the construction of the quantum effective action. Generalizations for nonlinear gauges and actions with higher-order ghost terms are also possible.
Invariants of broken discrete symmetries.
Kalozoumis, P A; Morfonios, C; Diakonos, F K; Schmelcher, P
2014-08-01
The parity and Bloch theorems are generalized to the case of broken global symmetry. Local inversion or translation symmetries in one dimension are shown to yield invariant currents that characterize wave propagation. These currents map the wave function from an arbitrary spatial domain to any symmetry-related domain. Our approach addresses any combination of local symmetries, thus applying, in particular, to acoustic, optical, and matter waves. Nonvanishing values of the invariant currents provide a systematic pathway to the breaking of discrete global symmetries.
Invariants of Broken Discrete Symmetries
NASA Astrophysics Data System (ADS)
Kalozoumis, P. A.; Morfonios, C.; Diakonos, F. K.; Schmelcher, P.
2014-08-01
The parity and Bloch theorems are generalized to the case of broken global symmetry. Local inversion or translation symmetries in one dimension are shown to yield invariant currents that characterize wave propagation. These currents map the wave function from an arbitrary spatial domain to any symmetry-related domain. Our approach addresses any combination of local symmetries, thus applying, in particular, to acoustic, optical, and matter waves. Nonvanishing values of the invariant currents provide a systematic pathway to the breaking of discrete global symmetries.
Entwinement in discretely gauged theories
NASA Astrophysics Data System (ADS)
Balasubramanian, V.; Bernamonti, A.; Craps, B.; De Jonckheere, T.; Galli, F.
2016-12-01
We develop the notion of "entwinement" to characterize the amount of quantum entanglement between internal, discretely gauged degrees of freedom in a quantum field theory. This concept originated in the program of reconstructing spacetime from entanglement in holographic duality. We define entwinement formally in terms of a novel replica method which uses twist operators charged in a representation of the discrete gauge group. In terms of these twist operators we define a non-local, gauge-invariant object whose expectation value computes entwinement in a standard replica limit. We apply our method to the computation of entwinement in symmetric orbifold conformal field theories in 1+1 dimensions, which have an S N gauging. Such a theory appears in the weak coupling limit of the D1-D5 string theory which is dual to AdS3 at strong coupling. In this context, we show how certain kinds of entwinement measure the lengths, in units of the AdS scale, of non-minimal geodesics present in certain excited states of the system which are gravitationally described as conical defects and the M = 0 BTZ black hole. The possible types of entwinement that can be computed define a very large new class of quantities characterizing the fine structure of quantum wavefunctions.
On Gauging Symmetry of Modular Categories
NASA Astrophysics Data System (ADS)
Cui, Shawn X.; Galindo, César; Plavnik, Julia Yael; Wang, Zhenghan
2016-12-01
Topological order of a topological phase of matter in two spacial dimensions is encoded by a unitary modular (tensor) category (UMC). A group symmetry of the topological phase induces a group symmetry of its corresponding UMC. Gauging is a well-known theoretical tool to promote a global symmetry to a local gauge symmetry. We give a mathematical formulation of gauging in terms of higher category formalism. Roughly, given a UMC with a symmetry group G, gauging is a 2-step process: first extend the UMC to a G-crossed braided fusion category and then take the equivariantization of the resulting category. Gauging can tell whether or not two enriched topological phases of matter are different, and also provides a way to construct new UMCs out of old ones. We derive a formula for the {H^4}-obstruction, prove some properties of gauging, and carry out gauging for two concrete examples.
Gauged twistor spinors and symmetry operators
NASA Astrophysics Data System (ADS)
Ertem, Ümit
2017-03-01
We consider gauged twistor spinors which are supersymmetry generators of supersymmetric and superconformal field theories in curved backgrounds. We show that the spinor bilinears of gauged twistor spinors satisfy the gauged conformal Killing-Yano equation. We prove that the symmetry operators of the gauged twistor spinor equation can be constructed from ordinary conformal Killing-Yano forms in constant curvature backgrounds. This provides a way to obtain gauged twistor spinors from ordinary twistor spinors.
BRST symmetry in the general gauge theories
NASA Astrophysics Data System (ADS)
Hyuk-Jae, Lee; Jae, Hyung, Yee
1994-01-01
By using the residual gauge symmetry interpretation of BRST invariance we have constructed a new BRST formulation for general gauge theories including those with open algebras. For theories with open gauge algebra the formulation leads to a BRST invariant effective action which does not contain any higher order terms in the ghost fields.
Anomalous discrete symmetries in three dimensions and group cohomology.
Kapustin, Anton; Thorngren, Ryan
2014-06-13
We study 't Hooft anomalies for a global discrete internal symmetry G. We construct examples of bosonic field theories in three dimensions with a nonvanishing 't Hooft anomaly for a discrete global symmetry. We also construct field theories in three dimensions with a global discrete internal symmetry G(1) × G(2) such that gauging G(1) necessarily breaks G(2) and vice versa. This is analogous to the Adler-Bell-Jackiw axial anomaly in four dimensions and parity anomaly in three dimensions.
Dynamical Symmetry Breaking of Extended Gauge Symmetries
NASA Astrophysics Data System (ADS)
Appelquist, Thomas; Shrock, Robert
2003-05-01
We construct asymptotically free gauge theories exhibiting dynamical breaking of the left-right gauge group GLR=SU(3)c×SU(2)L×SU(2)R×U(1)B-L, and its extension to the Pati-Salam gauge group G422=SU(4)PS×SU(2)L×SU(2)R. The models incorporate technicolor for electroweak breaking, and extended technicolor for the breaking of GLR and G422 and the generation of fermion masses. They include a seesaw mechanism for neutrino masses, without a grand unified theory (GUT) scale. These models explain why GLR and G422 break to SU(3)c×SU(2)L×U(1)Y, and why this takes place at a scale (˜103 TeV) large compared to the electroweak scale, but much smaller than a GUT scale.
Unification mechanism for gauge and spacetime symmetries
NASA Astrophysics Data System (ADS)
László, András
2017-03-01
A group theoretical mechanism for unification of local gauge and spacetime symmetries is introduced. No-go theorems prohibiting such unification are circumvented by slightly relaxing the usual requirement on the gauge group: only the so called Levi factor of the gauge group needs to be compact semisimple, not the entire gauge group. This allows a non-conventional supersymmetry-like extension of the gauge group, glueing together the gauge and spacetime symmetries, but not needing any new exotic gauge particles. It is shown that this new relaxed requirement on the gauge group is nothing but the minimal condition for energy positivity. The mechanism is demonstrated to be mathematically possible and physically plausible on a \\text{U}(1) based gauge theory setting. The unified group, being an extension of the group of spacetime symmetries, is shown to be different than that of the conventional supersymmetry group, thus overcoming the McGlinn and Coleman–Mandula no-go theorems in a non-supersymmetric way.
Unity of quark and lepton interactions with symplectic gauge symmetry
Rajpoot, S.
1982-07-01
Properties of symplectic groups are reviewed and the gauge structure of Sp(2n) derived. The electroweak unification of leptons within Sp(8) gauge symmetry and grand unification of quarks and leptons within Sp(10) gauge symmetry are discussed.
Beyond the standard gauging: gauge symmetries of Dirac sigma models
NASA Astrophysics Data System (ADS)
Chatzistavrakidis, Athanasios; Deser, Andreas; Jonke, Larisa; Strobl, Thomas
2016-08-01
In this paper we study the general conditions that have to be met for a gauged extension of a two-dimensional bosonic σ-model to exist. In an inversion of the usual approach of identifying a global symmetry and then promoting it to a local one, we focus directly on the gauge symmetries of the theory. This allows for action functionals which are gauge invariant for rather general background fields in the sense that their invariance conditions are milder than the usual case. In particular, the vector fields that control the gauging need not be Killing. The relaxation of isometry for the background fields is controlled by two connections on a Lie algebroid L in which the gauge fields take values, in a generalization of the common Lie-algebraic picture. Here we show that these connections can always be determined when L is a Dirac structure in the H-twisted Courant algebroid. This also leads us to a derivation of the general form for the gauge symmetries of a wide class of two-dimensional topological field theories called Dirac σ-models, which interpolate between the G/G Wess-Zumino-Witten model and the (Wess-Zumino-term twisted) Poisson sigma model.
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.
Discretized Abelian Chern-Simons gauge theory on arbitrary graphs
NASA Astrophysics Data System (ADS)
Sun, Kai; Kumar, Krishna; Fradkin, Eduardo
2015-09-01
In this paper, we show how to discretize the Abelian Chern-Simons gauge theory on generic planar lattices/graphs (with or without translational symmetries) embedded in arbitrary two-dimensional closed orientable manifolds. We find that, as long as a one-to-one correspondence between vertices and faces can be defined on the graph such that each face is paired up with a neighboring vertex (and vice versa), a discretized Abelian Chern-Simons theory can be constructed consistently. We further verify that all the essential properties of the Chern-Simons gauge theory are preserved in the discretized setup. In addition, we find that the existence of such a one-to-one correspondence is not only a sufficient condition for discretizing a Chern-Simons gauge theory but, for the discretized theory to be nonsingular and to preserve some key properties of the topological field theory, this correspondence is also a necessary one. A specific example will then be provided, in which we discretize the Abelian Chern-Simons gauge theory on a tetrahedron.
Gauge Transformations as Spacetime Symmetries
Angeles, Rene; Napsuciale, Mauro
2009-04-20
Weinberg has shown that massless fields of helicity {+-}1(vector fields) do not transform homogeneously under Unitary Lorentz Transformations (LT). We calculate explicitly the inhomogeneous term. We show that imposing strict invariance of the Lagrangian under LT for an iteracting Dirac field requires the fermion field to transform with a space-time (and photon creation and annihilation operators) dependent phase and dictates the interaction terms as those arising from the conventional gauge principle.
Approximate gauge symmetry of composite vector bosons
NASA Astrophysics Data System (ADS)
Suzuki, Mahiko
2010-08-01
It can be shown in a solvable field theory model that the couplings of the composite vector bosons made of a fermion pair approach the gauge couplings in the limit of strong binding. Although this phenomenon may appear accidental and special to the vector bosons made of a fermion pair, we extend it to the case of bosons being constituents and find that the same phenomenon occurs in a more intriguing way. The functional formalism not only facilitates computation but also provides us with a better insight into the generating mechanism of approximate gauge symmetry, in particular, how the strong binding and global current conservation conspire to generate such an approximate symmetry. Remarks are made on its possible relevance or irrelevance to electroweak and higher symmetries.
Entanglement entropy and nonabelian gauge symmetry
NASA Astrophysics Data System (ADS)
Donnelly, William
2014-11-01
Entanglement entropy has proven to be an extremely useful concept in quantum field theory. Gauge theories are of particular interest, but for these systems the entanglement entropy is not clearly defined because the physical Hilbert space does not factor as a tensor product according to regions of space. Here we review a definition of entanglement entropy that applies to abelian and nonabelian lattice gauge theories. This entanglement entropy is obtained by embedding the physical Hilbert space into a product of Hilbert spaces associated to regions with boundary. The latter Hilbert spaces include degrees of freedom on the entangling surface that transform like surface charges under the gauge symmetry. These degrees of freedom are shown to contribute to the entanglement entropy, and the form of this contribution is determined by the gauge symmetry. We test our definition using the example of two-dimensional Yang-Mills theory, and find that it agrees with the thermal entropy in de Sitter space, and with the results of the Euclidean replica trick. We discuss the possible implications of this result for more complicated gauge theories, including quantum gravity.
Discrete symmetries and de Sitter spacetime
Cotăescu, Ion I. Pascu, Gabriel
2014-11-24
Aspects of the ambiguity in defining quantum modes on de Sitter spacetime using a commuting system composed only of differential operators are discussed. Discrete symmetries and their actions on the wavefunction in commonly used coordinate charts are reviewed. It is argued that the system of commuting operators can be supplemented by requiring the invariance of the wavefunction to combined discrete symmetries- a criterion which selects a single state out of the α-vacuum family. Two such members of this family are singled out by particular combined discrete symmetries- states between which exists a well-known thermality relation.
Dark matter and gauged flavor symmetries
Bishara, Fady; Greljo, Admir; Kamenik, Jernej F.; ...
2015-12-21
We investigate the phenomenology of flavored dark matter (DM). DM stability is guaranteed by an accidental Z3 symmetry, a subgroup of the standard model (SM) flavor group that is not broken by the SM Yukawa interactions. We consider an explicit realization where the quark part of the SM flavor group is fully gauged. If the dominant interactions between DM and visible sector are through flavor gauge bosons, as we show for Dirac fermion flavored DM, then the DM mass is bounded between roughly 0.5 TeV and 5 TeV if the DM multiplet mass is split only radiatively. In general, however,more » no such relation exists. We demonstrate this using scalar flavored DM where the main interaction with the SM is through the Higgs portal. For both cases we derive constraints from flavor, cosmology, direct and indirect DM detection, and collider searches.« less
Dark matter and gauged flavor symmetries
Bishara, Fady; Greljo, Admir; Kamenik, Jernej F.; Stamou, Emmanuel; Zupan, Jure
2015-12-21
We investigate the phenomenology of flavored dark matter (DM). DM stability is guaranteed by an accidental Z_{3} symmetry, a subgroup of the standard model (SM) flavor group that is not broken by the SM Yukawa interactions. We consider an explicit realization where the quark part of the SM flavor group is fully gauged. If the dominant interactions between DM and visible sector are through flavor gauge bosons, as we show for Dirac fermion flavored DM, then the DM mass is bounded between roughly 0.5 TeV and 5 TeV if the DM multiplet mass is split only radiatively. In general, however, no such relation exists. We demonstrate this using scalar flavored DM where the main interaction with the SM is through the Higgs portal. For both cases we derive constraints from flavor, cosmology, direct and indirect DM detection, and collider searches.
The role of gauge symmetry in spintronics
Sobreiro, R.F.
2011-12-15
In this work we employ a field theoretical approach to explain the nature of the non-conserved spin current in spintronics. In particular, we consider the usual U(1) gauge theory for the electromagnetism at classical level in order to obtain the broken continuity equation involving the spin current and spin-transfer torque. Inspired by the recent work of A. Vernes, B. L. Gyorffy and P. Weinberger where they obtain such an equation in terms of relativistic quantum mechanics, we formalize their result in terms of the well known currents of field theory such as the Bargmann-Wigner current and the chiral current. Thus, an interpretation of spintronics is provided in terms of Noether currents (conserved or not) and symmetries of the electromagnetism. In fact, the main result of the present work is that the non-conservation of the spin current is associated with the gauge invariance of physical observables where the breaking term is proportional to the chiral current. Moreover, we generalize their result by including the electromagnetic field as a dynamical field instead of an external one.
Discrete flavour symmetries from the Heisenberg group
NASA Astrophysics Data System (ADS)
Floratos, E. G.; Leontaris, G. K.
2016-04-01
Non-abelian discrete symmetries are of particular importance in model building. They are mainly invoked to explain the various fermion mass hierarchies and forbid dangerous superpotential terms. In string models they are usually associated to the geometry of the compactification manifold and more particularly to the magnetised branes in toroidal compactifications. Motivated by these facts, in this note we propose a unified framework to construct representations of finite discrete family groups based on the automorphisms of the discrete and finite Heisenberg group. We focus in particular, on the PSL2 (p) groups which contain the phenomenologically interesting cases.
Neutrino mass and mixing with discrete symmetry.
King, Stephen F; Luhn, Christoph
2013-05-01
This is a review paper about neutrino mass and mixing and flavour model building strategies based on discrete family symmetry. After a pedagogical introduction and overview of the whole of neutrino physics, we focus on the PMNS mixing matrix and the latest global fits following the Daya Bay and RENO experiments which measure the reactor angle. We then describe the simple bimaximal, tri-bimaximal and golden ratio patterns of lepton mixing and the deviations required for a non-zero reactor angle, with solar or atmospheric mixing sum rules resulting from charged lepton corrections or residual trimaximal mixing. The different types of see-saw mechanism are then reviewed as well as the sequential dominance mechanism. We then give a mini-review of finite group theory, which may be used as a discrete family symmetry broken by flavons either completely, or with different subgroups preserved in the neutrino and charged lepton sectors. These two approaches are then reviewed in detail in separate chapters including mechanisms for flavon vacuum alignment and different model building strategies that have been proposed to generate the reactor angle. We then briefly review grand unified theories (GUTs) and how they may be combined with discrete family symmetry to describe all quark and lepton masses and mixing. Finally, we discuss three model examples which combine an SU(5) GUT with the discrete family symmetries A₄, S₄ and Δ(96).
Unification of gauge, family, and flavor symmetries illustrated in gauged SU(12) models
Albright, Carl H.; Feger, Robert P.; Kephart, Thomas W.
2016-04-25
In this study, to explain quark and lepton masses and mixing angles, one has to extend the standard model, and the usual practice is to put the quarks and leptons into irreducible representations of discrete groups. We argue that discrete flavor symmetries (and their concomitant problems) can be avoided if we extend the gauge group. In the framework of SU(12) we give explicit examples of models having varying degrees of predictability obtained by scanning over groups and representations and identifying cases with operators contributing to mass and mixing matrices that need little fine- tuning of prefactors. Fitting with quark andmore » lepton masses run to the GUT scale and known mixing angles allows us to make predictions for the neutrino masses and hierarchy, the octant of the atmospheric mixing angle, leptonic CP violation, Majorana phases, and the effective mass observed in neutrinoless double beta decay.« less
Unification of gauge, family, and flavor symmetries illustrated in gauged SU(12) models
Albright, Carl H.; Feger, Robert P.; Kephart, Thomas W.
2016-04-25
In this study, to explain quark and lepton masses and mixing angles, one has to extend the standard model, and the usual practice is to put the quarks and leptons into irreducible representations of discrete groups. We argue that discrete flavor symmetries (and their concomitant problems) can be avoided if we extend the gauge group. In the framework of SU(12) we give explicit examples of models having varying degrees of predictability obtained by scanning over groups and representations and identifying cases with operators contributing to mass and mixing matrices that need little fine- tuning of prefactors. Fitting with quark and lepton masses run to the GUT scale and known mixing angles allows us to make predictions for the neutrino masses and hierarchy, the octant of the atmospheric mixing angle, leptonic CP violation, Majorana phases, and the effective mass observed in neutrinoless double beta decay.
Invariance, symmetry and periodicity in gauge theories
Jackiw, R
1980-02-01
The interplay between gauge transformations and coordinate transformations is discussed; the theory will aid in understanding the mixing of space-time and internal degrees of freedom. The subject is presented under the following headings: coordinate transformation laws for arbitrary fields, coordinate transformation laws for gauge fields, properties of symmetric gauge fields, construction of symmetric gauge fields, physical significance of gauge transformations, and magnetic monopole topology without Higgs fields. The paper ends with conclusions and suggestions for further research. (RWR)
Gauge transformations of constrained discrete modified KP systems with self-consistent sources
NASA Astrophysics Data System (ADS)
Huang, Ran; Song, Tao; Li, Chuanzhong
In this paper, we firstly recall some basic facts about the discrete KP(d-KP) and discrete modified KP(d-mKP) hierarchies, and then we find that d-KP hierarchy and d-mKP hierarchy are linked by a gauge transformation. What’s more, we give three gauge transformation operators of the d-mKP hierarchy and give their successive applications. We further construct the ghost symmetry and use this symmetry to give the definition the d-mKP hierarchy with self-consistent sources. We also give gauge transformations of a newly defined constrained d-mKP(cd-mKP) hierarchy and the constrained d-mKP hierarchy with self-consistent sources(cd-mKPHSCSs).
On gauge independence for gauge models with soft breaking of BRST symmetry
NASA Astrophysics Data System (ADS)
Reshetnyak, Alexander
2014-12-01
A consistent quantum treatment of general gauge theories with an arbitrary gauge-fixing in the presence of soft breaking of the BRST symmetry in the field-antifield formalism is developed. It is based on a gauged (involving a field-dependent parameter) version of finite BRST transformations. The prescription allows one to restore the gauge-independence of the effective action at its extremals and therefore also that of the conventional S-matrix for a theory with BRST-breaking terms being additively introduced into a BRST-invariant action in order to achieve a consistency of the functional integral. We demonstrate the applicability of this prescription within the approach of functional renormalization group to the Yang-Mills and gravity theories. The Gribov-Zwanziger action and the refined Gribov-Zwanziger action for a many-parameter family of gauges, including the Coulomb, axial and covariant gauges, are derived perturbatively on the basis of finite gauged BRST transformations starting from Landau gauge. It is proved that gauge theories with soft breaking of BRST symmetry can be made consistent if the transformed BRST-breaking terms satisfy the same soft BRST symmetry breaking condition in the resulting gauge as the untransformed ones in the initial gauge, and also without this requirement.
Variational Tricomplex, Global Symmetries and Conservation Laws of Gauge Systems
NASA Astrophysics Data System (ADS)
Sharapov, Alexey A.
2016-10-01
Using the concept of variational tricomplex endowed with a presymplectic structure, we formulate the general notion of symmetry. We show that each generalized symmetry of a gauge system gives rise to a sequence of conservation laws that are represented by on-shell closed forms of various degrees. This extends the usual Noether's correspondence between global symmetries and conservation laws to the case of lower-degree conservation laws and not necessarily variational equations of motion. Finally, we equip the space of conservation laws of a given degree with a Lie bracket and establish a homomorphism of the resulting Lie algebra to the Lie algebra of global symmetries.
NASA Astrophysics Data System (ADS)
Hsu, Jong-Ping
2014-02-01
A generalization of the usual gauge symmetry leads to fourth-order gauge field equations, which imply a new constant force independent of distances. The force associated with the new U1 gauge symmetry is repulsive among baryons. Such a constant force based on baryon charge conservation gives a field-theoretic understanding of the accelerated cosmic expansion in the observable portion of the universe dominated by baryon galaxies. In consistent with all conservation laws and known forces, a simple rotating "dumbbell model" of the universe is briefly discussed.
Cosmology of biased discrete symmetry breaking
NASA Technical Reports Server (NTRS)
Gelmini, Graciela B.; Gleiser, Marcelo; Kolb, Edward W.
1988-01-01
The cosmological consequences of spontaneous breaking of an approximate discrete symmetry are studied. The breaking leads to formation of proto-domains of false and true vacuum separated by domain walls of thickness determined by the mass scale of the model. The cosmological evolution of the walls is extremely sensitive to the magnitude of the biasing; several scenarios are possible, depending on the interplay between the surface tension on the walls and the volume pressure from the biasing. Walls may disappear almost immediately after they form, or may live long enough to dominate the energy density of the Universe and cause power-law inflation. Limits are obtained on the biasing that characterizes each possible scenario.
Quantum walks and non-Abelian discrete gauge theory
NASA Astrophysics Data System (ADS)
Arnault, Pablo; Di Molfetta, Giuseppe; Brachet, Marc; Debbasch, Fabrice
2016-07-01
A family of discrete-time quantum walks (DTQWs) on the line with an exact discrete U(N ) gauge invariance is introduced. It is shown that the continuous limit of these DTQWs, when it exists, coincides with the dynamics of a Dirac fermion coupled to usual U(N ) gauge fields in two-dimensional spacetime. A discrete generalization of the usual U(N ) curvature is also constructed. An alternate interpretation of these results in terms of superimposed U(1 ) Maxwell fields and SU(N ) gauge fields is discussed in the Appendix. Numerical simulations are also presented, which explore the convergence of the DTQWs towards their continuous limit and which also compare the DTQWs with classical (i.e., nonquantum) motions in classical SU(2 ) fields. The results presented in this paper constitute a first step towards quantum simulations of generic Yang-Mills gauge theories through DTQWs.
Enhanced gauge symmetries on elliptic K3
NASA Astrophysics Data System (ADS)
Bonora, L.; Reina, C.; Zampa, A.
1999-04-01
We show that the geometry of K3 surfaces with singularities of type A-D-E contains enough information to reconstruct a copy of the Lie algebra associated to the given Dynkin diagram. We apply this construction to explain the enhancement of symmetry in F and IIA theories compactified on singular K3's.
Gauge Theories and Spontaneous Symmetry Breaking.
1980-11-01
breaking spontaneous symmetric breaking , Higgs mechanism bifurcation problem RATr0ACT’fwwdhn om pea71 Ul nonmevi dumad #~lyb block Im.,) his report is a...field theories. It was felt that the symmetry breaking used by the physicists LiI (a procedure known as the Higgs mechanism) is not precisely a...feeling, after some discussions, that the symmctry breaking used by the phyalciuts (a procedure known as the Higgs mechanism) is not precisely a
Classically conformal radiative neutrino model with gauged B - L symmetry
NASA Astrophysics Data System (ADS)
Okada, Hiroshi; Orikasa, Yuta
2016-09-01
We propose a classically conformal model in a minimal radiative seesaw, in which we employ a gauged B - L symmetry in the standard model that is essential in order to work the Coleman-Weinberg mechanism well that induces the B - L symmetry breaking. As a result, nonzero Majorana mass term and electroweak symmetry breaking simultaneously occur. In this framework, we show a benchmark point to satisfy several theoretical and experimental constraints. Here theoretical constraints represent inert conditions and Coleman-Weinberg condition. Experimental bounds come from lepton flavor violations (especially μ → eγ), the current bound on the Z‧ mass at the CERN Large Hadron Collider, and neutrino oscillations.
Dual-BRST symmetry: 6D Abelian 3-form gauge theory
NASA Astrophysics Data System (ADS)
Kumar, R.; Krishna, S.; Shukla, A.; Malik, R. P.
2012-04-01
Within the framework of the Becchi-Rouet-Stora-Tyutin (BRST) formalism, we demonstrate the existence of the novel off-shell nilpotent (anti-)dual-BRST symmetries in the context of a six (5+1)-dimensional (6D) free Abelian 3-form gauge theory. Under these local and continuous symmetry transformations, the total gauge-fixing term of the Lagrangian density remains invariant. This observation should be contrasted with the off-shell nilpotent (anti-)BRST symmetry transformations, under which, the total kinetic term of the theory remains invariant. The anticommutator of the above nilpotent (anti-)BRST and (anti-)dual-BRST transformations leads to the derivation of a bosonic symmetry in the theory. There exists a discrete symmetry transformation in the theory which provides a thread of connection between the nilpotent (anti-)BRST and (anti-)dual-BRST transformations. This theory is endowed with a ghost-scale symmetry, too. We discuss the algebra of these symmetry transformations and show that the structure of the algebra is reminiscent of the algebra of de Rham cohomological operators of differential geometry.
SU(2) gauge symmetry in gravity phase space
NASA Astrophysics Data System (ADS)
Cianfrani, Francesco
2012-05-01
The Hamiltonian formulation of the Holst action in vacuum and in the presence of matter fields is analyzed in a generic local Lorentz frame. It is elucidated how the SU(2) gauge symmetry is inferred by reducing the set of constraints to a first-class one. The consequences of the proposed approach for Loop Quantum Gravity and Spin Foam models are discussed.
Normal forms and gauge symmetry of local dynamics
NASA Astrophysics Data System (ADS)
Lyakhovich, S. L.; Sharapov, A. A.
2009-08-01
A systematic procedure is proposed for deriving all the gauge symmetries of the general, not necessarily variational, equations of motion. For the variational equations, this procedure reduces to the Dirac-Bergmann algorithm for the constrained Hamiltonian systems with certain extension: it remains applicable beyond the scope of Dirac's conjecture. Even though no pairing exists between the constraints and the gauge symmetry generators in general nonvariational dynamics, certain counterparts still can be identified of the first- and second-class constraints without appealing to any Poisson structure. It is shown that the general local gauge dynamics can be equivalently reformulated in an involutive normal form. The last form of dynamics always admits the BRST embedding, which does not require the classical equations to follow from any variational principle.
Exact solutions with noncommutative symmetries in Einstein and gauge gravity
NASA Astrophysics Data System (ADS)
Vacaru, Sergiu I.
2005-04-01
We present new classes of exact solutions with noncommutative symmetries constructed in vacuum Einstein gravity (in general, with nonzero cosmological constant), five-dimensional (5D) gravity and (anti) de Sitter gauge gravity. Such solutions are generated by anholonomic frame transforms and parametrized by generic off-diagonal metrics. For certain particular cases, the new classes of metrics have explicit limits with Killing symmetries but, in general, they may be characterized by certain anholonomic noncommutative matrix geometries. We argue that different classes of noncommutative symmetries can be induced by exact solutions of the field equations in commutative gravity modeled by a corresponding moving real and complex frame geometry. We analyze two classes of black ellipsoid solutions (in the vacuum case and with cosmological constant) in four-dimensional gravity and construct the analytic extensions of metrics for certain classes of associated frames with complex valued coefficients. The third class of solutions describes 5D wormholes which can be extended to complex metrics in complex gravity models defined by noncommutative geometric structures. The anholonomic noncommutative symmetries of such objects are analyzed. We also present a descriptive account how the Einstein gravity can be related to gauge models of gravity and their noncommutative extensions and discuss such constructions in relation to the Seiberg-Witten map for the gauge gravity. Finally, we consider a formalism of vielbeins deformations subjected to noncommutative symmetries in order to generate solutions for noncommutative gravity models with Moyal (star) product.
Mirror symmetry in three dimensions via gauged linear quivers
NASA Astrophysics Data System (ADS)
Dey, Anindya; Hanany, Amihay; Koroteev, Peter; Mekareeya, Noppadol
2014-06-01
Starting from mirror pairs consisting only of linear (framed A-type) quivers, we demonstrate that a wide class of three-dimensional quiver gauge theories with = 4 supersymmetry and their mirror duals can be obtained by suitably gauging flavor symmetries. Infinite families of mirror pairs including various quivers of D and E-type and their affine extensions, star-shaped quivers, and quivers with symplectic gauge groups may be generated in this fashion. We present two different computational strategies to perform the aforementioned gauging procedure — one of them involves = 2* classical parameter space description, while the other one uses partition functions of the = 4 theories on S 3. The partition function, in particular, turns out to be an extremely efficient tool for implementing this gauging procedure as it readily generalizes to arbitrary size of the quiver and arbitrary rank of the gauge group at each node. For most examples of mirror pairs obtained via this procedure, we perform additional checks of mirror symmetry using the Hilbert series.
Symmetry induced compression of discrete phase space
NASA Astrophysics Data System (ADS)
Krawczyk, Małgorzata J.
2011-06-01
A compressed representation is described of the state space of discrete systems with some kind of symmetry of its states. An initial state space is represented as a network of states. Two states are linked if some single process leads from one state to another. The network can be compressed by a grouping of states into classes. States in the same class are represented by nodes of equal degree. Further, subclasses are defined: states belong to the same subclass if their neighbouring states belong to the same subclasses. The goal is that the equilibrium probability distribution of states in the initial network can be found from the probability of subclasses in the compressed network. The approach is applied to three exemplary systems: two pieces of a triangular lattice (25 and 36 nodes) with Ising spins at the lattice nodes, and a roundabout with three access roads and three exit roads. The compression is from 3630 ground states to 12 subclasses, from 263 640 ground states to 409 subclasses, and from 729 states to 55 subclasses, respectively.
Symmetry, winding number, and topological charge of vortex solitons in discrete-symmetry media
Garcia-March, Miguel-Angel; Zacares, Mario; Sahu, Sarira; Ceballos-Herrera, Daniel E.
2009-05-15
We determine the functional behavior near the discrete rotational symmetry axis of discrete vortices of the nonlinear Schroedinger equation. We show that these solutions present a central phase singularity whose charge is restricted by symmetry arguments. Consequently, we demonstrate that the existence of high-charged discrete vortices is related to the presence of other off-axis phase singularities, whose positions and charges are also restricted by symmetry arguments. To illustrate our theoretical results, we offer two numerical examples of high-charged discrete vortices in photonic crystal fibers showing hexagonal discrete rotational invariance.
Large gauge symmetries and asymptotic states in QED
NASA Astrophysics Data System (ADS)
Gabai, Barak; Sever, Amit
2016-12-01
Large Gauge Transformations (LGT) are gauge transformations that do not vanish at infinity. Instead, they asymptotically approach arbitrary functions on the conformal sphere at infinity. Recently, it was argued that the LGT should be treated as an infinite set of global symmetries which are spontaneously broken by the vacuum. It was established that in QED, the Ward identities of their induced symmetries are equivalent to the Soft Photon Theorem. In this paper we study the implications of LGT on the S-matrix between physical asymptotic states in massive QED. In appose to the naively free scattering states, physical asymptotic states incorporate the long range electric field between asymptotic charged particles and were already constructed in 1970 by Kulish and Faddeev. We find that the LGT charge is independent of the particles' momenta and may be associated to the vacuum. The soft theorem's manifestation as a Ward identity turns out to be an outcome of not working with the physical asymptotic states.
Gauge symmetry breaking in gravity and auxiliary effective action
NASA Astrophysics Data System (ADS)
Akhavan, Amin
2017-02-01
In the context of the covariant symmetry breaking in gravity, we study the quantum aspect of Chamseddine-Mukhanov model by making use of path integral method. Utilizing one of the gauge fixing constraints, we remove the specific ghost degree of freedom. In continuation, we define an auxiliary effective action. Introducing an auxiliary field, we will have a new dynamic field in addition to the fundamental field.
SU(3) family gauge symmetry and the axion
Appelquist, Thomas; Bai Yang; Piai, Maurizio
2007-04-01
We analyze the structure of a recently proposed effective field theory (EFT) for the generation of quark and lepton mass ratios and mixing angles, based on the spontaneous breaking of an SU(3) family gauge symmetry at a high scale F. We classify the Yukawa operators necessary to seed the masses, making use of the continuous global symmetries that they preserve. One global U(1), in addition to baryon number and electroweak hypercharge, remains unbroken after the inclusion of all operators required by standard model fermion phenomenology. An associated vacuum symmetry insures the vanishing of the first-family quark and charged-lepton masses in the absence of the family gauge interaction. If this U(1) symmetry is taken to be exact in the EFT, broken explicitly by only the QCD-induced anomaly, and if the breaking scale F is taken to lie in the range 10{sup 9}-10{sup 12} GeV, then the associated Nambu-Goldstone boson is a potential QCD axion.
Revolving D-branes and spontaneous gauge-symmetry breaking
NASA Astrophysics Data System (ADS)
Iso, Satoshi; Kitazawa, Noriaki
2015-12-01
We propose a new mechanism of spontaneous gauge-symmetry breaking in the world-volume theory of revolving D-branes around a fixed point of orbifolds. In this paper, we consider a simple model of the T^6/Z_3 orbifold on which we put D3-branes, D7-branes, and their anti-branes. The configuration breaks supersymmetry, but the Ramond-Ramond tadpole cancellation conditions are satisfied. A set of three D3-branes at an orbifold fixed point can separate from the point, but, when they move perpendicular to the anti-D7-branes put on the fixed point, they are pulled back due to an attractive interaction between the D3- and anti-D7-branes. In order to stabilize the separation of the D3-branes at nonzero distance, we consider revolution of the D3-branes around the fixed point. Then the gauge symmetry on the D3-branes is spontaneously broken, and the rank of the gauge group is reduced. The distance can be set at will by appropriately choosing the angular momentum of the revolving D3-branes, which should be determined by the initial condition of the cosmological evolution of the D-brane configurations. The distance corresponds to the vacuum expectation values of brane moduli fields in the world-volume theory and, if it is written as M/M_s^2 in terms of the string scale M_s, the scale of gauge-symmetry breaking is given by M. Angular momentum conservation of revolving D3-branes assures the stability of the scale M against M_s.
Generalized gaugino condensation in super Yang-Mills theories: Discrete R symmetries and vacua
NASA Astrophysics Data System (ADS)
Kehayias, John
2010-12-01
One can define generalized models of gaugino condensation as theories that dynamically break a discrete R symmetry but do not break supersymmetry. We consider general examples consisting of gauge and matter fields and the minimal number of gauge-singlet fields to avoid flat directions in the potential. We explore which R symmetries can arise and their spontaneous breaking. In general, we find that the discrete symmetry is Z2b0R, and the number of supersymmetric vacua is b0, where b0 is the coefficient of the one-loop beta function. Results are presented for various groups, including SU(Nc), SO(Nc), Sp(2Nc), and G2, for various numbers of flavors, Nf, by several methods. This analysis can also apply to the other exceptional groups and, thus, all simple Lie groups. We also comment on model-building applications where a discrete R symmetry, broken by the singlet vacuum expectation values, can account for μ-type terms and allow a realistic Higgs spectrum naturally.
Gauge transformation and symmetries of the commutative multicomponent BKP hierarchy
NASA Astrophysics Data System (ADS)
Li, Chuanzhong
2016-01-01
In this paper, we defined a new multi-component B type Kadomtsev-Petviashvili (BKP) hierarchy that takes values in a commutative subalgebra of {gl}(N,{{C}}). After this, we give the gauge transformation of this commutative multicomponent BKP (CMBKP) hierarchy. Meanwhile, we construct a new constrained CMBKP hierarchy that contains some new integrable systems, including coupled KdV equations under a certain reduction. After this, the quantum torus symmetry and quantum torus constraint on the tau function of the commutative multi-component BKP hierarchy will be constructed.
Duality, Gauge Symmetries, Renormalization Groups and the BKT Transition
NASA Astrophysics Data System (ADS)
José, Jorge V.
2013-06-01
In this chapter, I will briefly review, from my own perspective, the situation within theoretical physics at the beginning of the 1970s, and the advances that played an important role in providing a solid theoretical and experimental foundation for the Berezinskii-Kosterlitz-Thouless theory (BKT). Over this period, it became clear that the Abelian gauge symmetry of the 2D-XY model had to be preserved to get the right phase structure of the model. In previous analyses, this symmetry was broken when using low order calculational approximations. Duality transformations at that time for two-dimensional models with compact gauge symmetries were introduced by José, Kadanoff, Nelson and Kirkpatrick (JKKN). Their goal was to analyze the phase structure and excitations of XY and related models, including symmetry breaking fields which are experimentally important. In a separate context, Migdal had earlier developed an approximate Renormalization Group (RG) algorithm to implement Wilson's RG for lattice gauge theories. Although Migdal's RG approach, later extended by Kadanoff, did not produce a true phase transition for the XY model, it almost did asymptotically in terms of a non-perturbative expansion in the coupling constant with an essential singularity. Using these advances, including work done on instantons (vortices), JKKN analyzed the behavior of the spin-spin correlation functions of the 2D XY-model in terms of an expansion in temperature and vortex-pair fugacity. Their analysis led to a perturbative derivation of RG equations for the XY model which are the same as those first derived by Kosterlitz for the two-dimensional Coulomb gas. JKKN's results gave a theoretical formulation foundation and justification for BKT's sound physical assumptions and for the validity of their calculational approximations that were, in principle, strictly valid only at very low temperatures, away from the critical TBKT temperature. The theoretical predictions were soon tested
Duality, Gauge Symmetries, Renormalization Groups and the BKT Transition
NASA Astrophysics Data System (ADS)
José, Jorge V.
2017-03-01
In this chapter, I will briefly review, from my own perspective, the situation within theoretical physics at the beginning of the 1970s, and the advances that played an important role in providing a solid theoretical and experimental foundation for the Berezinskii-Kosterlitz-Thouless theory (BKT). Over this period, it became clear that the Abelian gauge symmetry of the 2D-XY model had to be preserved to get the right phase structure of the model. In previous analyses, this symmetry was broken when using low order calculational approximations. Duality transformations at that time for two-dimensional models with compact gauge symmetries were introduced by José, Kadanoff, Nelson and Kirkpatrick (JKKN). Their goal was to analyze the phase structure and excitations of XY and related models, including symmetry breaking fields which are experimentally important. In a separate context, Migdal had earlier developed an approximate Renormalization Group (RG) algorithm to implement Wilson’s RG for lattice gauge theories. Although Migdal’s RG approach, later extended by Kadanoff, did not produce a true phase transition for the XY model, it almost did asymptotically in terms of a non-perturbative expansion in the coupling constant with an essential singularity. Using these advances, including work done on instantons (vortices), JKKN analyzed the behavior of the spin-spin correlation functions of the 2D XY-model in terms of an expansion in temperature and vortex-pair fugacity. Their analysis led to a perturbative derivation of RG equations for the XY model which are the same as those first derived by Kosterlitz for the two-dimensional Coulomb gas. JKKN’s results gave a theoretical formulation foundation and justification for BKT’s sound physical assumptions and for the validity of their calculational approximations that were, in principle, strictly valid only at very low temperatures, away from the critical TBKT temperature. The theoretical predictions were soon tested
PREFACE: 4th Symposium on Prospects in the Physics of Discrete Symmetries (DISCRETE2014)
NASA Astrophysics Data System (ADS)
Di Domenico, Antonio; Mavromatos, Nick E.; Mitsou, Vasiliki A.; Skliros, Dimitri P.
2015-07-01
The DISCRETE 2014: Fourth Symposium in the Physics of Discrete Symmetries took place at King's College London, Strand Campus, London WC2R 2LS, from Tuesday, December 2 2014 till Saturday, December 6 2014. This is the fourth Edition of the DISCRETE conference series, which is a biannual event, having been held previously in Valencia (Discrete'08), Rome (Discrete2010) and Lisbon (Discrete2012). The topics covered at the DISCRETE series of conferences are: T, C, P, CP symmetries; accidental symmetries (B, L conservation); CPT symmetry, decoherence and entangled states, Lorentz symmetry breaking (phenomenology and current bounds); neutrino mass and mixing; implications for cosmology and astroparticle physics, dark matter searches; experimental prospects at LHC, new facilities. In DISCRETE 2014 we have also introduced two new topics: cosmological aspects of non-commutative space-times as well as PT symmetric Hamiltonians (non-Hermitian but with real eigenvalues), a topic that has wide applications in particle physics and beyond. The conference was opened by the King's College London Vice Principal on Research and Innovation, Mr Chris Mottershead, followed by a welcome address by the Chair of DISCRETE 2014 (Professor Nick E. Mavromatos). After these introductory talks, the scientific programme of the DISCRETE 2014 symposium started. Following the tradition of DISCRETE series of conferences, the talks (138 in total) were divided into plenary-review talks (25), invited research talks (50) and shorter presentations (63) — selected by the conveners of each session in consultation with the organisers — from the submitted abstracts. We have been fortunate to have very high-quality, thought stimulating and interesting talks at all levels, which, together with the discussions among the participants, made the conference quite enjoyable. There were 152 registered participants for the event.
LHC Higgs signatures from extended electroweak gauge symmetry
NASA Astrophysics Data System (ADS)
Abe, Tomohiro; Chen, Ning; He, Hong-Jian
2013-01-01
We study LHC Higgs signatures from the extended electroweak gauge symmetry SU(2) ⊗ SU(2) ⊗ U(1). Under this gauge structure, we present an effective UV completion of the 3-site moose model with ideal fermion delocalization, which contains two neutral Higgs states ( h, H) plus three new gauge bosons ( W ' , Z '). We study the unitarity, and reveal that the exact E 2 cancellation in the longitudinal V L V L scattering amplitudes is achieved by the joint role of exchanging both spin-1 new gauge bosons W ' /Z ' and spin-0 Higgs bosons h/H. We identify the lighter Higgs state h with mass 125 GeV, and derive the unitarity bound on the mass of heavier Higgs boson H. The parameter space of this model is highly predictive. We study the production and decay signals of this 125 GeV Higgs boson h at the LHC. We demonstrate that the h Higgs boson can naturally have enhanced signals in the diphoton channel gg → h → γγ, while the event rates in the reactions gg → h → W W ∗ and gg → h → ZZ ∗ are generally suppressed relative to the SM expectation. Searching the h Higgs boson via the associated production and the vector boson fusions are also discussed for our model. We further analyze the LHC signals of the heavier Higgs boson H as a new physics discriminator from the SM. For wide mass-ranges of H, we derive constraints from the existing LHC searches, and study the discovery potential of H at the LHC (8 TeV) and LHC (14 TeV).
Doubled lattice Chern-Simons-Yang-Mills theories with discrete gauge group
NASA Astrophysics Data System (ADS)
Caspar, S.; Mesterházy, D.; Olesen, T. Z.; Vlasii, N. D.; Wiese, U.-J.
2016-11-01
We construct doubled lattice Chern-Simons-Yang-Mills theories with discrete gauge group G in the Hamiltonian formulation. Here, these theories are considered on a square spatial lattice and the fundamental degrees of freedom are defined on pairs of links from the direct lattice and its dual, respectively. This provides a natural lattice construction for topologically-massive gauge theories, which are invariant under parity and time-reversal symmetry. After defining the building blocks of the doubled theories, paying special attention to the realization of gauge transformations on quantum states, we examine the dynamics in the group space of a single cross, which is spanned by a single link and its dual. The dynamics is governed by the single-cross electric Hamiltonian and admits a simple quantum mechanical analogy to the problem of a charged particle moving on a discrete space affected by an abstract electromagnetic potential. Such a particle might accumulate a phase shift equivalent to an Aharonov-Bohm phase, which is manifested in the doubled theory in terms of a nontrivial ground-state degeneracy on a single cross. We discuss several examples of these doubled theories with different gauge groups including the cyclic group Z(k) ⊂ U(1) , the symmetric group S3 ⊂ O(2) , the binary dihedral (or quaternion) group D¯2 ⊂ SU(2) , and the finite group Δ(27) ⊂ SU(3) . In each case the spectrum of the single-cross electric Hamiltonian is determined exactly. We examine the nature of the low-lying excited states in the full Hilbert space, and emphasize the role of the center symmetry for the confinement of charges. Whether the investigated doubled models admit a non-Abelian topological state which allows for fault-tolerant quantum computation will be addressed in a future publication.
A Vector-Like Fourth Generation with A Discrete Symmetry From Split-UED
Kong, Kyoungchul; Park, Seong Chan; Rizzo, Thomas G.; /SLAC
2011-08-19
Split-UED allows for the possibility that the lowest lying KK excitations of the Standard Model fermions can be much lighter than the corresponding gauge or Higgs KK states. This can happen provided the fermion bulk masses are chosen to be large, in units of the inverse compactification radius, 1/R, and negative. In this setup, all of the other KK states would be effectively decoupled from low energy physics. Such a scenario would then lead to an apparent vector-like fourth generation with an associated discrete symmetry that allows us to accommodate a dark matter candidate. In this paper the rather unique phenomenology presented by this picture will be examined.
Confinement/deconfinement transition from symmetry breaking in gauge/gravity duality
NASA Astrophysics Data System (ADS)
Čubrović, Mihailo
2016-10-01
We study the confinement/deconfinement transition in a strongly coupled system triggered by an independent symmetry-breaking quantum phase transition in gauge/gravity duality. The gravity dual is an Einstein-scalar-dilaton system with AdS near-boundary behavior and soft wall interior at zero scalar condensate. We study the cases of neutral and charged condensate separately. In the former case the condensation breaks the discrete {Z}_2 symmetry while a charged condensate breaks the continuous U(1) symmetry. After the condensation of the order parameter, the non-zero vacuum expectation value of the scalar couples to the dilaton, changing the soft wall geometry into a non-confining and anisotropically scale-invariant infrared metric. In other words, the formation of long-range order is immediately followed by the deconfinement transition and the two critical points coincide. The confined phase has a scale — the confinement scale (energy gap) which vanishes in the deconfined case. Therefore, the breaking of the symmetry of the scalar ( {Z}_2 or U(1)) in turn restores the scaling symmetry in the system and neither phase has a higher overall symmetry than the other. When the scalar is charged the phase transition is continuous which goes against the Ginzburg-Landau theory where such transitions generically only occur discontinuously. This phenomenon has some commonalities with the scenario of deconfined criticality. The mechanism we have found has applications mainly in effective field theories such as quantum magnetic systems. We briefly discuss these applications and the relation to real-world systems.
NASA Astrophysics Data System (ADS)
Luo, Lin
2017-02-01
In this paper, based on a discrete spectral problem and the corresponding zero curvature representation, the isospectral and nonisospectral lattice hierarchies are proposed. An algebraic structure of discrete zero curvature equations is then established for such integrable systems. the commutation relations of Lax operators corresponding to the isospectral and non-isospectral lattice flows are worked out, the master symmetries of each lattice equation in the isospectral hierarchyand are generated, thus a τ-symmetry algebra for the lattice integrable systems is engendered from this theory. Supported by the National Science Foundation of China under Grant No. 11371244 and the Applied Mathematical Subject of SSPU under Grant No. XXKPY1604
Toward electroweak scale cold dark matter with local dark gauge symmetry and beyond the DM EFT
NASA Astrophysics Data System (ADS)
Ko, Pyungwon
2016-06-01
In this talk, I describe a class of electroweak (EW) scale dark matter (DM) models where its stability or longevity are the results of underlying dark gauge symmetries: stable due to unbroken local dark gauge symmetry or topology, or long-lived due to the accidental global symmetry of dark gauge theories. Compared with the usual phenomenological dark matter models (including DM EFT or simplified DM models), DM models with local dark gauge symmetries include dark gauge bosons, dark Higgs bosons and sometimes excited dark matter. And dynamics among these fields are completely fixed by local gauge principle. The idea of singlet portals including the Higgs portal can thermalize these hidden sector dark matter very efficiently, so that these DM could be easily thermal DM. I also discuss the limitation of the usual DM effective field theory or simplified DM models without the full SM gauge symmetry, and emphasize the importance of the full SM gauge symmetry and renormalizability especially for collider searches for DM.
Projected Entangled Pair States with non-Abelian gauge symmetries: An SU(2) study
NASA Astrophysics Data System (ADS)
Zohar, Erez; Wahl, Thorsten B.; Burrello, Michele; Cirac, J. Ignacio
2016-11-01
Over the last years, Projected Entangled Pair States have demonstrated great power for the study of many body systems, as they naturally describe ground states of gapped many body Hamiltonians, and suggest a constructive way to encode and classify their symmetries. The PEPS study is not only limited to global symmetries, but has also been extended and applied for local symmetries, allowing to use them for the description of states in lattice gauge theories. In this paper we discuss PEPS with a local, SU(2) gauge symmetry, and demonstrate the use of PEPS features and techniques for the study of a simple family of many body states with a non-Abelian gauge symmetry. We present, in particular, the construction of fermionic PEPS able to describe both two-color fermionic matter and the degrees of freedom of an SU(2) gauge field with a suitable truncation.
Self-assembled fibre optoelectronics with discrete translational symmetry
Rein, Michael; Levy, Etgar; Gumennik, Alexander; Abouraddy, Ayman F.; Joannopoulos, John; Fink, Yoel
2016-01-01
Fibres with electronic and photonic properties are essential building blocks for functional fabrics with system level attributes. The scalability of thermal fibre drawing approach offers access to large device quantities, while constraining the devices to be translational symmetric. Lifting this symmetry to create discrete devices in fibres will increase their utility. Here, we draw, from a macroscopic preform, fibres that have three parallel internal non-contacting continuous domains; a semiconducting glass between two conductors. We then heat the fibre and generate a capillary fluid instability, resulting in the selective transformation of the cylindrical semiconducting domain into discrete spheres while keeping the conductive domains unchanged. The cylindrical-to-spherical expansion bridges the continuous conducting domains to create ∼104 self-assembled, electrically contacted and entirely packaged discrete spherical devices per metre of fibre. The photodetection and Mie resonance dependent response are measured by illuminating the fibre while connecting its ends to an electrical readout. PMID:27698454
Self-assembled fibre optoelectronics with discrete translational symmetry.
Rein, Michael; Levy, Etgar; Gumennik, Alexander; Abouraddy, Ayman F; Joannopoulos, John; Fink, Yoel
2016-10-04
Fibres with electronic and photonic properties are essential building blocks for functional fabrics with system level attributes. The scalability of thermal fibre drawing approach offers access to large device quantities, while constraining the devices to be translational symmetric. Lifting this symmetry to create discrete devices in fibres will increase their utility. Here, we draw, from a macroscopic preform, fibres that have three parallel internal non-contacting continuous domains; a semiconducting glass between two conductors. We then heat the fibre and generate a capillary fluid instability, resulting in the selective transformation of the cylindrical semiconducting domain into discrete spheres while keeping the conductive domains unchanged. The cylindrical-to-spherical expansion bridges the continuous conducting domains to create ∼10(4) self-assembled, electrically contacted and entirely packaged discrete spherical devices per metre of fibre. The photodetection and Mie resonance dependent response are measured by illuminating the fibre while connecting its ends to an electrical readout.
Self-assembled fibre optoelectronics with discrete translational symmetry
NASA Astrophysics Data System (ADS)
Rein, Michael; Levy, Etgar; Gumennik, Alexander; Abouraddy, Ayman F.; Joannopoulos, John; Fink, Yoel
2016-10-01
Fibres with electronic and photonic properties are essential building blocks for functional fabrics with system level attributes. The scalability of thermal fibre drawing approach offers access to large device quantities, while constraining the devices to be translational symmetric. Lifting this symmetry to create discrete devices in fibres will increase their utility. Here, we draw, from a macroscopic preform, fibres that have three parallel internal non-contacting continuous domains; a semiconducting glass between two conductors. We then heat the fibre and generate a capillary fluid instability, resulting in the selective transformation of the cylindrical semiconducting domain into discrete spheres while keeping the conductive domains unchanged. The cylindrical-to-spherical expansion bridges the continuous conducting domains to create ~104 self-assembled, electrically contacted and entirely packaged discrete spherical devices per metre of fibre. The photodetection and Mie resonance dependent response are measured by illuminating the fibre while connecting its ends to an electrical readout.
Families of Quintic Calabi Yau 3 Folds with Discrete Symmetries
NASA Astrophysics Data System (ADS)
Doran, Charles; Greene, Brian; Judes, Simon
2008-06-01
At special loci in their moduli spaces, Calabi Yau manifolds are endowed with discrete symmetries. Over the years, such spaces have been intensely studied and have found a variety of important applications. As string compactifications they are phenomenologically favored, and considerably simplify many important calculations. Mathematically, they provided the framework for the first construction of mirror manifolds, and the resulting rational curve counts. Thus, it is of significant interest to investigate such manifolds further. In this paper, we consider several unexplored loci within familiar families of Calabi Yau hypersurfaces that have large but unexpected discrete symmetry groups. By deriving, correcting, and generalizing a technique similar to that of Candelas, de la Ossa and Rodriguez Villegas, we find a calculationally tractable means of finding the Picard Fuchs equations satisfied by the periods of all 3 forms in these families. To provide a modest point of comparison, we then briefly investigate the relation between the size of the symmetry group along these loci and the number of nonzero Yukawa couplings. We include an introductory exposition of the mathematics involved, intended to be accessible to physicists, in order to make the discussion self contained.
Breaking discrete symmetries in the effective field theory of inflation
Cannone, Dario; Gong, Jinn-Ouk; Tasinato, Gianmassimo
2015-08-03
We study the phenomenon of discrete symmetry breaking during the inflationary epoch, using a model-independent approach based on the effective field theory of inflation. We work in a context where both time reparameterization symmetry and spatial diffeomorphism invariance can be broken during inflation. We determine the leading derivative operators in the quadratic action for fluctuations that break parity and time-reversal. Within suitable approximations, we study their consequences for the dynamics of linearized fluctuations. Both in the scalar and tensor sectors, we show that such operators can lead to new direction-dependent phases for the modes involved. They do not affect the power spectra, but can have consequences for higher correlation functions. Moreover, a small quadrupole contribution to the sound speed can be generated.
Breaking discrete symmetries in the effective field theory of inflation
Cannone, Dario; Gong, Jinn-Ouk; Tasinato, Gianmassimo E-mail: jinn-ouk.gong@apctp.org
2015-08-01
We study the phenomenon of discrete symmetry breaking during the inflationary epoch, using a model-independent approach based on the effective field theory of inflation. We work in a context where both time reparameterization symmetry and spatial diffeomorphism invariance can be broken during inflation. We determine the leading derivative operators in the quadratic action for fluctuations that break parity and time-reversal. Within suitable approximations, we study their consequences for the dynamics of linearized fluctuations. Both in the scalar and tensor sectors, we show that such operators can lead to new direction-dependent phases for the modes involved. They do not affect the power spectra, but can have consequences for higher correlation functions. Moreover, a small quadrupole contribution to the sound speed can be generated.
Gauge symmetry and Virasoro algebra in quantum charged rigid membrane: A first order formalism
NASA Astrophysics Data System (ADS)
Paul, Biswajit
2013-02-01
The quantum charged rigid membrane model, which is a higher derivative theory, has been considered to explore its gauge symmetries using a recently developed first order formalism [R. Banerjee , J. High Energy Phys. 08 (2011) 085JHEPFG1029-8479]. Hamiltonian analysis has been performed and the gauge symmetry of the model is identified as reparametrization symmetry. First class constraints are shown to have a truncated Virasoro algebraic structure. An exact correspondence between the higher derivative theory and the first order formalism has been shown from the point of view of equations of motion.
Gauging the twisted Poincare symmetry as a noncommutative theory of gravitation
Chaichian, M.; Tureanu, A.; Oksanen, M.; Zet, G.
2009-02-15
Einstein's theory of general relativity was formulated as a gauge theory of Lorentz symmetry by Utiyama in 1956, while the Einstein-Cartan gravitational theory was formulated by Kibble in 1961 as the gauge theory of Poincare transformations. In this framework, we propose a formulation of the gravitational theory on canonical noncommutative space-time by covariantly gauging the twisted Poincare symmetry, in order to fulfil the requirement of covariance under the general coordinate transformations, an essential ingredient of the theory of general relativity. It appears that the twisted Poincare symmetry cannot be gauged by generalizing the Abelian twist to a covariant non-Abelian twist, nor by introducing a more general covariant twist element. The advantages of such a formulation as well as the related problems are discussed and possible ways out are outlined.
Kagome Chiral Spin Liquid as a Gauged U(1) Symmetry Protected Topological Phase.
He, Yin-Chen; Bhattacharjee, Subhro; Pollmann, Frank; Moessner, R
2015-12-31
While the existence of a chiral spin liquid (CSL) on a class of spin-1/2 kagome antiferromagnets is by now well established numerically, a controlled theoretical path from the lattice model leading to a low-energy topological field theory is still lacking. This we provide via an explicit construction starting from reformulating a microscopic model for a CSL as a lattice gauge theory and deriving the low-energy form of its continuum limit. A crucial ingredient is the realization that the bosonic spinons of the gauge theory exhibit a U(1) symmetry protected topological (SPT) phase, which upon promoting its U(1) global symmetry to a local gauge structure ("gauging"), yields the CSL. We suggest that such an explicit lattice-based construction involving gauging of a SPT phase can be applied more generally to understand topological spin liquids.
On a discrete symmetry of the Bremsstrahlung function in {N} = 4 SYM
NASA Astrophysics Data System (ADS)
Beccaria, Matteo; Macorini, Guido
2013-07-01
We consider the quark anti-quark potential on the three sphere in planar {N} = 4 SYM and the associated vacuum potential in the near BPS limit with L units of R-charge. The associated Bremsstrahlung function B L has been recently computed analytically by means of the Thermodynamical Bethe Ansatz. We discuss it at strong coupling by computing it at large but finite L. We provide strong support to a special symmetry of the Bremsstrahlung function under the formal discrete {{{Z}}_2} symmetry L → -1 - L. In this context, it is the counterpart of the reciprocity invariance discovered in the past in the spectrum of various gauge invariant composite operators. The {{{Z}}_2} symmetry has remarkable consequences in the scaling limit where L is taken to be large with fixed ratio to the 't Hooft coupling. This limit organizes in inverse powers of the coupling and resembles the semiclassical expansion of the dual string theory which is indeed known to capture the leading classical term. We show that the various higher-order contributions to the Bremsstrahlung function obey several constraints and, in particular, the next-to-leading term, formally associated with the string one-loop correction, is completely determined by the classical contribution. The large L limit at strong coupling is also discussed.
A short review on Noether’s theorems, gauge symmetries and boundary terms
NASA Astrophysics Data System (ADS)
Bañados, Max; Reyes, Ignacio
2016-06-01
This review is dedicated to some modern applications of the remarkable paper written in 1918 by E. Noether. On a single paper, Noether discovered the crucial relation between symmetries and conserved charges as well as the impact of gauge symmetries on the equations of motion. Almost a century has gone since the publication of this work and its applications have permeated modern physics. Our focus will be on some examples that have appeared recently in the literature. This review aims at students, not researchers. The main three topics discussed are (i) global symmetries and conserved charges (ii) local symmetries and gauge structure of a theory (iii) boundary conditions and algebra of asymptotic symmetries. All three topics are discussed through examples.
NASA Astrophysics Data System (ADS)
Ma, Li-Yuan; Zhu, Zuo-Nong
2016-08-01
In this paper, we try to understand the geometry for a nonlocal nonlinear Schrödinger equation (nonlocal NLS) and its discrete version introduced by Ablowitz and Musslimani, Phys. Rev. Lett. 110, 064105 (2013); Phys. Rev. E 90, 042912 (2014). We show that, under the gauge transformations, the nonlocal focusing NLS and the nonlocal defocusing NLS are, respectively, gauge equivalent to a Heisenberg-like equation and a modified Heisenberg-like equation, and their discrete versions are, respectively, gauge equivalent to a discrete Heisenberg-like equation and a discrete modified Heisenberg-like equation. Although the geometry related to the nonlocal NLS and its discrete version is not very clear, from the gauge equivalence, we can see that the properties between the nonlocal NLS and its discrete version and NLS and discrete NLS have significant difference. By constructing the Darboux transformation for discrete nonlocal NLS equations including the cases of focusing and defocusing, we derive their discrete soliton solutions, which differ from the ones obtained by using the inverse scattering transformation.
Weakly Isolated horizons: first order actions and gauge symmetries
NASA Astrophysics Data System (ADS)
Corichi, Alejandro; Reyes, Juan D.; Vukašinac, Tatjana
2017-04-01
The notion of Isolated Horizons has played an important role in gravitational physics, being useful from the characterization of the endpoint of black hole mergers to (quantum) black hole entropy. With an eye towards a canonical formulation we consider general relativity in terms of connection and vierbein variables and their corresponding first order actions. We focus on two main issues: (i) The role of the internal gauge freedom that exists, in the consistent formulations of the action principle, and (ii) the role that a 3 + 1 canonical decomposition has in the allowed internal gauge freedom. More concretely, we clarify in detail how the requirement of having well posed variational principles compatible with general weakly isolated horizons (WIHs) as internal boundaries does lead to a partial gauge fixing in the first order descriptions used previously in the literature. We consider the standard Hilbert–Palatini action together with the Holst extension (needed for a consistent 3 + 1 decomposition), with and without boundary terms at the horizon. We show in detail that, for the complete configuration space—with no gauge fixing—, while the Palatini action is differentiable without additional surface terms at the inner WIH boundary, the more general Holst action is not. The introduction of a surface term at the horizon—that renders the action for asymptotically flat configurations differentiable—does make the Holst action differentiable, but only if one restricts the configuration space and partially reduces the internal Lorentz gauge. For the second issue at hand, we show that upon performing a 3 + 1 decomposition and imposing the time gauge, there is a further gauge reduction of the Hamiltonian theory in terms of Ashtekar–Barbero variables to a U(1)-gauge theory on the horizon. We also extend our analysis to the more restricted boundary conditions of (strongly) isolated horizons as inner boundary. We show that even when
PREFACE: DISCRETE '08: Symposium on Prospects in the Physics of Discrete Symmetries
NASA Astrophysics Data System (ADS)
Bernabéu, José; Botella, Francisco J.; Mavromatos, Nick E.; Mitsou, Vasiliki A.
2009-07-01
The Symposium DISCRETE'08 on Prospects in the Physics of Discrete Symmetries was held at the Instituto de Física Corpuscular (IFIC) in Valencia, Spain from 11 to 16 December 2008. IFIC is a joint centre of the Consejo Superior de Investigaciones Científicas (CSIC) and the Universitat de València (UVEG). The aim of the Symposium was to bring together experts on the field of Discrete Symmetries in order to discuss its prospects on the eve of the LHC era. The general state of the art for CP, T and CPT symmetries was reviewed and their interplay with Baryogenesis, Early Cosmology, Quantum Gravity, String Theory and the Dark Sector of the Universe was emphasised. Connections with physics beyond the Standard Model, in particular Supersymmetry, were investigated. Experimental implications in current and proposed facilities received particular attention. The scientific programme consisted of 24 invited Plenary Talks and 93 contributions selected among the submitted papers. Young researchers, in particular, were encouraged to submit an abstract. The Special Lecture on ''CERN and the Future of Particle Physics'', given by the CERN Director General Rolf-Dieter Heuer to close the Symposium, was of particular relevance. On the last day of the Symposium, an open meeting took place between Professor Heuer and the Spanish community of particle physics. The Symposium covered recent developments on the subject of Discrete Symmetries in the following topics: Quantum Vacuum Entanglement, Symmetrisation Principle CPT in Quantum Gravity and String Theory, Decoherence, Lorentz Violation Ultra-high-energy Messengers Time Reversal CP violation in the SM and beyond Neutrino Mass, Mixing and CP Baryogenesis, Leptogenesis Family Symmetries Supersymmetry and other searches Experimental Prospects: LHC, Super-B Factories, DAΦNE-2, Neutrino Beams The excellence of most of the presentations during the Symposium was pointed out by many participants. The broad spectrum of topics under the
PREFACE: DISCRETE 2012 - Third Symposium on Prospects in the Physics of Discrete Symmetries
NASA Astrophysics Data System (ADS)
Branco, G. C.; Emmanuel-Costa, D.; González Felipe, R.; Joaquim, F. R.; Lavoura, L.; Palomares-Ruiz, S.; Rebelo, M. N.; Romão, J. C.; Silva, J. P.
2013-07-01
The Third Symposium on Prospects in the Physics of Discrete Symmetries (DISCRETE 2012) was held at Instituto Superior Técnico, Portugal, from 3-7 December 2012 and was organised by Centro de Física Teórica de Partículas (CFTP) of Instituto Superior Técnico, Universidade Técnica de Lisboa. This is the sequel to the Symposia that was successfully organised in Valéncia in 2008 and in Rome in 2010. The topics covered included: T, C, P, CP symmetries CPT symmetry, decoherence, Lorentz symmetry breaking Discrete symmetries and models of flavour mixing Baryogenesis, leptogenesis Neutrino physics Electroweak symmetry breaking and physics beyond the Standard Model Accidental symmetries (B, L conservation) Experimental prospects at LHC Dark matter searches Super flavour factories, and other new experimental facilities The Symposium was organised in plenary sessions with a total of 24 invited talks, and parallel sessions with a total of 70 talks, including both invited and selected contributions from the submitted abstracts. The speakers of the plenary sessions were: Ignatios Antoniadis, Abdelhak Djouadi, Rabindra Mohapatra, André Rubbia, Alexei Yu Smirnov, José Bernabéu, Marco Cirelli, Apostolos Pilaftsis, Antonio Di Domenico, Robertus Potting, João Varela, Frank Rathmann, Michele Gallinaro, Dumitru Ghilencea, Neville Harnew, John Walsh, Patrícia Conde Muíño, Juan Aguilar-Saavedra, Nick Mavromatos, Ulrich Nierste, Ferruccio Feruglio, Vasiliki Mitsou, Masanori Yamauchi, and Marcello Giorgi. The Symposium was attended by about 140 participants. Among the social events, there was a social dinner in the historical Associação Comercial de Lisboa, which included a musical performance of 'Fado', the traditional music from Lisbon. The next symposium of the series will be organised by King's College, London University, UK, from 1-5 December 2014. Guest Editors G C Branco, D Emmanuel-Costa, R González Felipe, F R Joaquim, L Lavoura, S Palomares-Ruiz, M N Rebelo, J C
Multi-Higgs model with Abelian and non-Abelian discrete symmetries
NASA Astrophysics Data System (ADS)
Machado, A. C. B.; Pleitez, V.
2008-11-01
-handed fermions, singlet under the gauge symmetry, transforming as triplet or singlet of A4. The predictive power is a consequence of the discrete symmetries imposed to the model: A4 otimes Z3 otimes Z'3 otimes Z''3. In conclusions, the mass matrices obtained, which arise because of the symmetry of the model, give appropriate insight concerning the solution of the flavor problem. Of course, it is necessary to explain how these symmetries are realized from a more fundamental theory.
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.
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.
Spontaneously Broken Gauge Symmetry in a Bose Gas with Constant Particle Number
NASA Astrophysics Data System (ADS)
Schelle, A.
The interplay between spontaneously broken gauge symmetries and Bose-Einstein condensation has long been controversially discussed in science, since the equations of motion are invariant under phase transformations. Within the present model, it is illustrated that spontaneous symmetry breaking appears as a non-local process in position space, but within disjoint subspaces of the underlying Hilbert space. Numerical simulations show that it is the symmetry of the relative phase distribution between condensate and non-condensate quantum fields which is spontaneously broken when passing the critical temperature for Bose-Einstein condensation. Since the total number of gas particles remains constant over time, the global U(1)-gauge symmetry of the system is preserved.
PREFACE: DISCRETE 2010: Symposium on Prospects in the Physics of Discrete Symmetries
NASA Astrophysics Data System (ADS)
Di Domenico, Antonio; Bini, Cesare; Bloise, Caterina; Bossi, Fabio; Faccini, Riccardo; Gauzzi, Paolo; Isidori, Gino; Lipari, Paolo; Ludovici, Lucio; Silvestrini, Luca
2011-12-01
The Symposium DISCRETE2010 on Prospects in the Physics of Discrete Symmetries was held at the Sapienza Universitàa di Roma, Italy from 6-11 December 2010. This second edition, after the successful one in Valencia in 2008, covered all theoretical and experimental progress in the field, and aimed at a thorough discussion on the latest developments. The topics covered included: T, C, P, CP symmetries; accidental symmetries (B, L conservation); CPT symmetry, decoherence, Lorentz symmetry breaking; neutrino mass and mixing; cosmology and astroparticles, dark matter searches; experimental prospects at LHC, Super flavor factories, and new facilities. The Symposium was organized in plenary sessions with a total of 23 invited talks, and parallel sessions with a total of 80 talks including both invited and selected contributions from the submitted abstracts. The speakers of the plenary sessions were: Achille Stocchi, Andreas Weiler, Kevin Pitts, Tim Gershon, Marco Sozzi, Neal Weiner, Vasiliki Mitsou, Bernard Sadoulet, Gianfranco Bertone, J. Eric Grove, Mauro Mezzetto, Alexei Yu Smirnov, Oliviero Cremonesi, Antonio Riotto, Reno Mandolesi, Brett Altschul, Jose Bernabeu, Lawrence Hall, Marco Grassi, Yannis K. Semertzidis, Riccardo Barbieri, Gigi Rolandi, Luciano Maiani. The Symposium venue was the CNR (Consiglio Nazionale delle Ricerche) headquarter building, close to the Sapienza University. At the end of the Symposium a special open session, devoted to a wider audience, was held at the Pontifical University of the Holy Cross, in the historical center of Rome. The symposium was attended by about 140 participants, about half coming from Italy, and the rest mainly from other European countries and United States. Among the social events was a concert at the Aula Magna of the Sapienza University, and a social dinner in the historical Palazzo Pallavicini-Rospigliosi on the Quirinale Hill. The next symposium of the series will be organised by IST, Universidade Tàecnica de Lisboa
SVD for imaging systems with discrete rotational symmetry.
Clarkson, Eric; Palit, Robin; Kupinski, Matthew A
2010-11-22
The singular value decomposition (SVD) of an imaging system is a computationally intensive calculation for tomographic imaging systems due to the large dimensionality of the system matrix. The computation often involves memory and storage requirements beyond those available to most end users. We have developed a method that reduces the dimension of the SVD problem towards the goal of making the calculation tractable for a standard desktop computer. In the presence of discrete rotational symmetry we show that the dimension of the SVD computation can be reduced by a factor equal to the number of collection angles for the tomographic system. In this paper we present the mathematical theory for our method, validate that our method produces the same results as standard SVD analysis, and finally apply our technique to the sensitivity matrix for a clinical CT system. The ability to compute the full singular value spectra and singular vectors will augment future work in system characterization, image-quality assessment and reconstruction techniques for tomographic imaging systems.
NASA Astrophysics Data System (ADS)
Xiao, C. W.; Ozpineci, A.; Oset, E.
2015-10-01
Using a coupled channel unitary approach, combining the heavy quark spin symmetry and the dynamics of the local hidden gauge, we investigate the meson-meson interaction with hidden beauty. We obtain several new states of isospin I = 0: six bound states, and weakly bound six more possible states which depend on the influence of the coupled channel effects.
Matrix product operators for symmetry-protected topological phases: Gauging and edge theories
NASA Astrophysics Data System (ADS)
Williamson, Dominic J.; Bultinck, Nick; Mariën, Michael; Şahinoǧlu, Mehmet B.; Haegeman, Jutho; Verstraete, Frank
2016-11-01
Projected entangled pair states (PEPS) provide a natural ansatz for the ground states of gapped, local Hamiltonians in which global characteristics of a quantum state are encoded in properties of local tensors. We develop a framework to describe onsite symmetries, as occurring in systems exhibiting symmetry-protected topological (SPT) quantum order, in terms of virtual symmetries of the local tensors expressed as a set of matrix product operators (MPOs) labeled by distinct group elements. These MPOs describe the possibly anomalous symmetry of the edge theory, whose local degrees of freedom are concretely identified in a PEPS. A classification of SPT phases is obtained by studying the obstructions to continuously deforming one set of MPOs into another, recovering the results derived for fixed-point models [Chen et al., Phys. Rev. B 87, 155114 (2013), 10.1103/PhysRevB.87.155114]. Our formalism accommodates perturbations away from fixed-point models, opening the possibility of studying phase transitions between different SPT phases. We also demonstrate that applying the recently developed quantum state gauging procedure to a SPT PEPS yields a PEPS with topological order determined by the initial symmetry MPOs. The MPO framework thus unifies the different approaches to classifying SPT phases, via fixed-point models, boundary anomalies, or gauging the symmetry, into the single problem of classifying inequivalent sets of matrix product operator symmetries that are defined purely in terms of a PEPS.
NASA Astrophysics Data System (ADS)
Low, Catherine I.; Volkas, Raymond R.
2003-08-01
Neutrino oscillation experiments (excluding the Liquid Scintillator Neutrino Detector experiment) suggest a tribimaximal form for the lepton mixing matrix. This form indicates that the mixing matrix is probably independent of the lepton masses, and suggests the action of an underlying discrete family symmetry. Using these hints, we conjecture that the contrasting forms of the quark and lepton mixing matrices may both be generated by such a discrete family symmetry. This idea is that the diagonalization matrices out of which the physical mixing matrices are composed have large mixing angles, which cancel out due to a symmetry when the CKM matrix is computed, but do not do so in the MNS case. However, in the cases where the Higgs bosons are singlets under the symmetry, and the family symmetry commutes with SU(2)L, we prove a no-go theorem: no discrete unbroken family symmetry can produce the required mixing patterns. We then suggest avenues for future research.
Classification of static plane symmetric spacetime via Noether gauge symmetries
NASA Astrophysics Data System (ADS)
Jhangeer, Adil; Iftikhar, Nazish; Naz, Tayyaba
2016-07-01
In this paper, general static plane symmetric spacetime is classified with respect to Noether operators. For this purpose, Noether theorem is used which yields a set of linear partial differential equations (PDEs) with unknown radial functions A(r), B(r) and F(r). Further, these PDEs are solved by taking different possibilities of radial functions. In the first case, all radial functions are considered same, while two functions are taken proportional to each other in second case, which further discussed by taking four different relationships between A(r), B(r) and F(r). For all cases, different forms of unknown functions of radial factor r are reported for nontrivial Noether operators with non-zero gauge term. At the end, a list of conserved quantities for each Noether operator Tables 1-4 is presented.
Cost of seven-brane gauge symmetry in a quadrillion F-theory compactifications
NASA Astrophysics Data System (ADS)
Halverson, James; Tian, Jiahua
2017-01-01
We study seven-branes in O (1 015) four-dimensional F-theory compactifications where seven-brane moduli must be tuned in order to achieve non-Abelian gauge symmetry. The associated compact spaces B are the set of all smooth weak Fano toric threefolds. By a study of fine-star-regular triangulations of three-dimensional reflexive polytopes, the number of such spaces is estimated to be 5.8 ×1 014≲Nbases≲1.8 ×1 017 . Typically hundreds or thousands of moduli must be tuned to achieve symmetry for h11(B )<10 , but the average number drops sharply into the range O (25 )- O (200 ) as h11(B ) increases. For some low-rank groups, such as S U (2 ) and S U (3 ), there exist examples where only a few moduli must be tuned in order to achieve seven-brane gauge symmetry.
Symmetry breaking of localized discrete matter waves induced by spin-orbit coupling
NASA Astrophysics Data System (ADS)
Salerno, M.; Abdullaev, F. Kh.
2015-10-01
We study localized nonlinear excitations of a dilute Bose-Einstein condensate (BEC) with spin-orbit coupling in a deep optical lattice (OL). For this we introduce a tight-binding model that includes the spin-orbit coupling (SOC) at the discrete level in the form of a generalized discrete nonlinear Schrödinger equation. Existence and stability of discrete solitons of different symmetry types is demonstrated. Quite interestingly, we find three distinctive regions in which discrete solitons undergo spontaneously symmetry breaking, passing from on-site to inter-site and to asymmetric, simply by varying the interatomic interactions. Existence ranges of discrete solitons with inter-site symmetry depend on SOC and shrink to zero as the SOC parameter is increased. Asymmetric discrete solitons appear as novel excitations specific of the SOC. Possible experimental implementation of these results is briefly discussed.
Universality of spontaneous chiral symmetry breaking in gauge theories
NASA Astrophysics Data System (ADS)
Gies, Holger; Wetterich, Christof
2004-01-01
We investigate one-flavor QCD with an additional chiral scalar field. For a large domain in the space of coupling constants, this model belongs to the same universality class as QCD, and the effects of the scalar become unobservable. This is connected to a “bound-state fixed point” of the renormalization flow for which all memory of the microscopic scalar interactions is lost. The QCD domain includes a microscopic scalar potential with minima at a nonzero field. On the other hand, for a scalar mass term m2 below a critical value m2c, the universality class is characterized by perturbative spontaneous chiral symmetry breaking which renders the quarks massive. Our renormalization group analysis shows how this universality class is continuously connected with the QCD universality class.
Weyl gauge-vector and complex dilaton scalar for conformal symmetry and its breaking
NASA Astrophysics Data System (ADS)
Ohanian, Hans C.
2016-03-01
Instead of the scalar "dilaton" field that is usually adopted to construct conformally invariant Lagrangians for gravitation, we here propose a hybrid construction, involving both a complex dilaton scalar and a Weyl gauge-vector, in accord with Weyl's original concept of a non-Riemannian conformal geometry with a transport law for length and time intervals, for which this gauge vector is required. Such a hybrid construction permits us to avoid the wrong sign of the dilaton kinetic term (the ghost problem) that afflicts the usual construction. The introduction of a Weyl gauge-vector and its interaction with the dilaton also has the collateral benefit of providing an explicit mechanism for spontaneous breaking of the conformal symmetry, whereby the dilaton and the Weyl gauge-vector acquire masses somewhat smaller than {m}_{P} by the Coleman-Weinberg mechanism. Conformal symmetry breaking is assumed to precede inflation, which occurs later by a separate GUT or electroweak symmetry breaking, as in inflationary models based on the Higgs boson.
Novel symmetries in Weyl-invariant gravity with massive gauge field
NASA Astrophysics Data System (ADS)
Abhinav, K.; Shukla, A.; Panigrahi, P. K.
2016-11-01
The background field method is used to linearize the Weyl-invariant scalar-tensor gravity, coupled with a Stückelberg field. For a generic background metric, this action is found not to be invariant, under both a diffeomorphism and generalized Weyl symmetry, the latter being a combination of gauge and Weyl transformations. Interestingly, the quadratic Lagrangian, emerging from a background of Minkowski metric, respects both transformations independently. The Becchi-Rouet-Stora-Tyutin symmetry of scalar-tensor gravity coupled with a Stückelberg-like massive gauge particle, possessing a diffeomorphism and generalized Weyl symmetry, reveals that in both cases negative-norm states with unphysical degrees of freedom do exist. We then show that, by combining diffeomorphism and generalized Weyl symmetries, all the ghost states decouple, thereby removing the unphysical redundancies of the theory. During this process, the scalar field does not represent any dynamic mode, yet modifies the usual harmonic gauge condition through non-minimal coupling with gravity.
Dirac or Inverse Seesaw Neutrino Masses from Gauged B - L Symmetry
NASA Astrophysics Data System (ADS)
Ma, Ernest; Srivastava, Rahul
The gauged B - L symmetry is one of the simplest and well studied extension of standard model. In the conventional case, addition of three singlet right-handed neutrinos each transforming as -1 under the B - L symmetry renders it anomaly free. It is usually assumed that the B - L symmetry is spontaneously broken by a singlet scalar having two units of B - L charge, resulting in a natural implementation of Majorana seesaw mechanism for neutrinos. However, as we discuss in this proceeding, there is another simple anomaly free solution which leads to Dirac or inverse seesaw masses for neutrinos. These new possibilities are explored along with an application to neutrino mixing with S3 flavour symmetry.
Discrete and continuous symmetries in multi-Higgs-doublet models
Ferreira, P. M.; Silva, Joao P.
2008-12-01
We consider the Higgs sector of multi-Higgs-doublet models in the presence of simple symmetries relating the various fields. We construct basis-invariant observables which may in principle be used to detect these symmetries for any number of doublets. A categorization of the symmetries into classes is required, which we perform in detail for the case of two and three Higgs doublets.
BPS states in type IIB SUGRA with SO(4) × SO(2)gauged symmetry
NASA Astrophysics Data System (ADS)
Donos, Aristomenis
2007-05-01
We present an extension of our construction (hep-th/0606199) exhibiting SO(4) × SO(2) symmetry. We extend the previously presented ansatz by introducing a U(1) gauge field. The presence of the gauge field allows for more general values of the Killing spinor U(1) charge. One more time we identify a four dimensional Kahler structure and a Monge-Ampere type of equation parametrized by the U(1) Killing spinor charge. In addition we identify 2 scalars that parametrize the supersymmetric solutions, one of which is the Kahler potential.
Enhanced symmetries of gauge theory and resolving the spectrum of local operators
NASA Astrophysics Data System (ADS)
Kimura, Yusuke; Ramgoolam, Sanjaye
2008-12-01
Enhanced global non-Abelian symmetries at zero coupling in Yang Mills theory play an important role in diagonalizing the two-point functions of multimatrix operators. Generalized Casimirs constructed from the iterated commutator action of these enhanced symmetries resolve all the multiplicity labels of the bases of matrix operators which diagonalize the two-point function. For the case of U(N) gauge theory with a single complex matrix in the adjoint of the gauge group we have a U(N)×4 global symmetry of the scaling operator at zero coupling. Different choices of commuting sets of Casimirs, for the case of a complex matrix, lead to the restricted Schur basis previously studied in connection with string excitations of giant gravitons and the Brauer basis studied in connection with brane-antibrane systems. More generally these remarks can be extended to the diagonalization for any global symmetry group G. Schur-Weyl duality plays a central role in connecting the enhanced symmetries and the diagonal bases.
Constitutive modelling of magnetic shape memory alloys with discrete and continuous symmetries
Haldar, K.; Lagoudas, D. C.
2014-01-01
A free energy-based constitutive formulation is considered for magnetic shape memory alloys. Internal state variables are introduced whose evolution describes the transition from reference state to the deformed and transformed one. We impose material symmetry restrictions on the Gibbs free energy and on the evolution equations of the internal state variables. Discrete symmetry is considered for single crystals, whereas continuous symmetry is considered for polycrystalline materials. PMID:25197247
Constitutive modelling of magnetic shape memory alloys with discrete and continuous symmetries.
Haldar, K; Lagoudas, D C
2014-09-08
A free energy-based constitutive formulation is considered for magnetic shape memory alloys. Internal state variables are introduced whose evolution describes the transition from reference state to the deformed and transformed one. We impose material symmetry restrictions on the Gibbs free energy and on the evolution equations of the internal state variables. Discrete symmetry is considered for single crystals, whereas continuous symmetry is considered for polycrystalline materials.
Monopole operators and mirror symmetry in three-dimensional gauge theories
NASA Astrophysics Data System (ADS)
Borokhov, Vadim A.
Many gauge theories in three dimensions flow to interacting conformal field theories in the infrared. We define a new class of local operators in these conformal field theories that are not polynomial in the fundamental fields and create topological disorder. They can be regarded as higher-dimensional analogs of twist and winding-state operators in free 2-D CFTs. We call them monopole operators for reasons explained in the text. The importance of monopole operators is that in the Higgs phase, they create Abrikosov-Nielsen-Olesen vortices. We study properties of these operators in three-dimensional gauge theories using large Nf expansion. For non-supersymmetric gauge theories we show that monopole operators belong to representations of the conformal group whose primaries have dimension of order N f. We demonstrate that these monopole operators transform non-trivially under the flavor symmetry group. We also consider topology-changing operators in the infrared limits of N = 2 and N = 4 supersymmetric QED as well as N = 4 SU(2) gauge theory in three dimensions. Using large N f expansion and operator-state isomorphism of the resulting superconformal field theories, we construct monopole operators that are primaries of short representation of the superconformal algebra and compute their charges under the global symmetries. Predictions of three-dimensional mirror symmetry for the quantum numbers of these monopole operators are verified. Furthermore, we argue that some of our large-Nf results are exact. This implies, in particular, that certain monopole operators in N = 4 d = 3 SQED with Nf = 1 are free fields. This amounts to a proof of 3-D mirror symmetry in these special cases.
Noether’s second theorem and Ward identities for gauge symmetries
Avery, Steven G.; Schwab, Burkhard U. W.
2016-02-04
Recently, a number of new Ward identities for large gauge transformations and large diffeomorphisms have been discovered. Some of the identities are reinterpretations of previously known statements, while some appear to be genuinely new. We present and use Noether’s second theorem with the path integral as a powerful way of generating these kinds of Ward identities. We reintroduce Noether’s second theorem and discuss how to work with the physical remnant of gauge symmetry in gauge fixed systems. We illustrate our mechanism in Maxwell theory, Yang-Mills theory, p-form field theory, and Einstein-Hilbert gravity. We comment on multiple connections between Noether’s secondmore » theorem and known results in the recent literature. Finally, our approach suggests a novel point of view with important physical consequences.« less
Noether’s second theorem and Ward identities for gauge symmetries
Avery, Steven G.; Schwab, Burkhard U. W.
2016-02-04
Recently, a number of new Ward identities for large gauge transformations and large diffeomorphisms have been discovered. Some of the identities are reinterpretations of previously known statements, while some appear to be genuinely new. We present and use Noether’s second theorem with the path integral as a powerful way of generating these kinds of Ward identities. We reintroduce Noether’s second theorem and discuss how to work with the physical remnant of gauge symmetry in gauge fixed systems. We illustrate our mechanism in Maxwell theory, Yang-Mills theory, p-form field theory, and Einstein-Hilbert gravity. We comment on multiple connections between Noether’s second theorem and known results in the recent literature. Finally, our approach suggests a novel point of view with important physical consequences.
Nilpotent Symmetries for Matter Fields in Non-Abelian Gauge Theory:
NASA Astrophysics Data System (ADS)
Malik, R. P.
In the framework of superfield approach to Becchi-Rouet-Stora-Tyutin (BRST) formalism, the derivation of the BRST and anti-BRST nilpotent symmetry transformations for the matter fields, present in any arbitrary interacting gauge theory, has been a long-standing problem. In our present investigation, the local, covariant, continuous and off-shell nilpotent (anti-)BRST symmetry transformations for the Dirac fields (ψ ,bar ψ ) are derived in the framework of the augmented superfield formulation where the four (3 + 1)-dimensional (4D) interacting non-Abelian gauge theory is considered on the six (4 + 2)-dimensional supermanifold parametrized by the four even space-time coordinates xμ and a couple of odd elements (θ and bar θ ) of the Grassmann algebra. The requirement of the invariance of the matter (super)currents and the horizontality condition on the (super)manifolds leads to the derivation of the nilpotent symmetries for the matter fields as well as the gauge and the (anti)ghost fields of the theory in the general scheme of augmented superfield formalism.
Non-Abelian discrete flavor symmetries of 10D SYM theory with magnetized extra dimensions
NASA Astrophysics Data System (ADS)
Abe, Hiroyuki; Kobayashi, Tatsuo; Ohki, Hiroshi; Sumita, Keigo; Tatsuta, Yoshiyuki
2014-06-01
We study discrete flavor symmetries of the models based on a ten-dimensional supersymmetric Yang-Mills (10D SYM) theory compactified on magnetized tori. We assume non-vanishing non-factorizable fluxes as well as the orbifold projections. These setups allow model-building with more various flavor structures. Indeed, we show that there exist various classes of non-Abelian discrete flavor symmetries. In particular, we find that S 3 flavor symmetries can be realized in the framework of the magnetized 10D SYM theory for the first time.
Dirac dark matter and b →s ℓ+ℓ- with U(1) gauge symmetry
NASA Astrophysics Data System (ADS)
Celis, Alejandro; Feng, Wan-Zhe; Vollmann, Martin
2017-02-01
We revisit the possibility of a Dirac fermion dark matter candidate in the light of current b →s ℓ+ℓ- anomalies by investigating a minimal extension of the Standard Model with a horizontal U(1 ) ' local symmetry. Dark matter stability is protected by a remnant Z2 symmetry arising after spontaneous symmetry breaking of U(1 ) '. The associated Z' gauge boson can accommodate current hints of new physics in b →s ℓ+ℓ- decays, and acts as a vector portal between dark matter and the visible sector. We find that the model is severely constrained by a combination of precision measurements at flavor factories, LHC searches for dilepton resonances, as well as direct and indirect dark matter searches. Despite this, viable regions of the parameter space accommodating the observed dark matter relic abundance and the b →s ℓ+ℓ-anomalies still persist for dark matter and Z ' masses in the TeV range.
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)
Non-Abelian Gauge Symmetry in the Causal Epstein-Glaser Approach
NASA Astrophysics Data System (ADS)
Hurth, Tobias
Non-Abelian gauge symmetry in (3 + 1)-dimensional space-time is analyzed in the causal Epstein-Glaser framework. In this formalism, the technical details concerning the well-known UV and IR problem in quantum field theory are separated and reduced to well-defined problems, namely the causal splitting and the adiabatic switching of operator-valued distributions. Non-Abelian gauge invariance in perturbation theory is completely discussed in the well-defined Fock space of free asymptotic fields. The LSZ formalism is not used in this construction. The linear operator condition of asymptotic gauge invariance is sufficient for the unitarity of the S matrix in the physical subspace and the usual Slavnov-Taylor identities. We explicitly derive the most general specific coupling compatible with this condition. By analyzing only tree graphs in the second order of perturbation theory we show that the well-known Yang-Mills couplings with anticommuting ghosts are the only ones which are compatible with asymptotic gauge invariance. The required generalizations for linear gauges are given.
NASA Astrophysics Data System (ADS)
Kholodnyi, V. A.
2002-05-01
Although symmetries play a major role in physics, their use in finance is relatively new and, to the best of our knowledge, can be traced to 1995 when Kholodnyi introduced the beliefs-preferences gauge symmetry. One of the main outcomes of the beliefs-preferences gauge symmetry is that it allows for the valuation and dynamic replication of contingent claims in a general market environment, that is, in the case of a general, not necessarily diffusion Markov process for the prices of underlying securities. This valuation and dynamic replication is based on the novel ideas of symmetry in contrast to the standard approach which uses stochastic analysis. The practical applications of the beliefs-preferences gauge symmetry range from the detection of a new type of true arbitrage to the beliefs-preferences-independent valuation and dynamic replication of contingent claims in a general market environment.
Peccei-Quinn invariant singlet extended SUSY with anomalous U(1) gauge symmetry
NASA Astrophysics Data System (ADS)
Im, Sang Hui; Seo, Min-Seok
2015-05-01
Recent discovery of the SM-like Higgs boson with m h ≃ 125 GeV motivates an extension of the minimal supersymmetric standard model (MSSM), which involves a singlet Higgs superfield with a sizable Yukawa coupling to the doublet Higgs superfields. We examine such singlet-extended SUSY models with a Peccei-Quinn (PQ) symmetry that originates from an anomalous U(1) A gauge symmetry. We focus on the specific scheme that the PQ symmetry is spontaneously broken at an intermediate scale v PQ ˜ m SUSY M Pl by an interplay between Planck scale suppressed operators and tachyonic soft scalar mass induced dominantly by the U(1) A D-term D A . This scheme also results in spontaneous SUSY breaking in the PQ sector, generating the gaugino masses when it is transmitted to the MSSM sector by the conventional gauge mediation mechanism. As a result, the MSSM soft parameters in this scheme are induced mostly by the U(1) A D-term and the gauge mediated SUSY breaking from the PQ sector, so that the sparticle masses can be near the present experimental bounds without causing the SUSY flavor problem. The scheme is severely constrained by the condition that a phenomenologically viable form of the low energy operators of the singlet and doublet Higgs superfields is generated by the PQ breaking sector in a way similar to the Kim-Nilles solution of the μ problem, and the resulting Higgs mass parameters allow the electroweak symmetry breaking with small tan β. We find two minimal models with two singlet Higgs superfields, satisfying this condition with a relatively simple form of the PQ breaking sector, and briefly discuss some phenomenological aspects of the model.
Kim, Jihn E.
2007-09-01
It is known that the kinetic mixing of a photon and another U(1){sub ex} gauge boson can introduce millicharged particles. Millicharged particles f of mass 0.1 eV can explain the PVLAS experiment. I suggest a temperature dependent gauge symmetry breaking of U(1){sub ex} for this idea to be consistent with astrophysical and cosmological constraints.
Integrability test for discrete equations via generalized symmetries
Levi, D.; Yamilov, R. I.
2010-12-23
In this article we present some integrability conditions for partial difference equations obtained using the formal symmetries approach. We apply them to find integrable partial difference equations contained in a class of equations obtained by the multiple scale analysis of the general multilinear dispersive difference equation defined on the square.
Conditions for the emergence of gauge bosons from spontaneous Lorentz symmetry breaking
NASA Astrophysics Data System (ADS)
Escobar, C. A.; Urrutia, L. F.
2015-07-01
The emergence of gauge particles (e.g., photons and gravitons) as Goldstone bosons arising from spontaneous symmetry breaking is an interesting hypothesis which would provide a dynamical setting for the gauge principle. We investigate this proposal in the framework of a general SO (N ) non-Abelian Nambu model (NANM), effectively providing spontaneous Lorentz symmetry breaking in terms of the corresponding Goldstone bosons. Using a nonperturbative Hamiltonian analysis, we prove that the SO (N ) Yang-Mills (YM) theory is equivalent to the corresponding NANM, after both current conservation and the Gauss laws are imposed as initial conditions for the latter. This equivalence is independent of any gauge fixing in the YM theory. A substantial conceptual and practical improvement in the analysis arises by choosing a particular parametrization that solves the nonlinear constraint defining the NANM. This choice allows us to show that the relation between the NANM canonical variables and the corresponding ones of the YM theory, Aia and Eb j , is given by a canonical transformation. In terms of the latter variables, the NANM Hamiltonian has the same form as the YM Hamiltonian, except that the Gauss laws do not arise as first-class constraints. The dynamics of the NANM further guarantees that it is sufficient to impose them only as initial conditions, in order to recover the full equivalence. It is interesting to observe that this particular parametrization exhibits the NANM as a regular theory, thus providing a substantial simplification in the calculations.
BOOK REVIEW: Discrete Symmetries and CP Violation: From Experiment to Theory (Oxford Graduate Texts)
NASA Astrophysics Data System (ADS)
Fösel, A.
2009-03-01
Discrete Symmetries and CP Violation: From Experiment to Theory by Marco Sozzi discusses C(harge conjugation), P(arity) and T(ime reversal) discrete symmetries and of course CP symmetry in microscopic (atomic, nuclear and particle) physics. It includes a detailed description of key or representative experiments, and major achievements and recent developments are also mentioned. Though lots of excellent textbooks already exist which cover the basics of discrete symmetries and CP violation in theory and experiment, Sozzi has fully achieved the goal of presenting a book that describes the basics of this subject in detail, from an experimental point of view as well as from theory. He also succeeds in finding links between experiments and theory, leading to a better understanding of the subject. Besides, as an experimentalist, discrete symmetries and CP violation appear to the author as ideal subjects to convey the depth and excitement of experimental `beautiful' physics, which Marco S Sozzi - in my opinion - has managed to do brilliantly. Though mainly addressed to graduate students, the book may also be useful to undergraduates (by skipping some of the more advanced sections and utilizing the brief introduction to some topics in the appendices) and to young researchers looking for a wider modern overview of the issues related to CP symmetry. At the end of each chapter, further reading sections are conveniently provided for the reader to find relevant literature for further studies. Problems to solve at the end of each chapter act as 'little tests'. Unfortunately, their solutions are currently absent: perhaps a publication that includes them is planned in the near future. To conclude, the book succeeds in being a complete and self-consistent text describing in up-to-date detail the investigation of discrete symmetries in sub-atomic physics. It also emphasizes the concepts and ingenuity behind many delicate, careful, and by all means 'beautiful' experiments.
Gauged B-L symmetry and baryogenesis via leptogenesis at TeV scale
Sahu, Narendra; Yajnik, Urjit A.
2005-01-15
It is shown that the requirement of preservation of baryon asymmetry does not rule out a scale for leptogenesis as low as 10 TeV. The conclusions are compatible with see-saw mechanism if, for example, the pivot mass scale for neutrinos is {approx_equal}10{sup -2} that of the charged leptons. We explore the parameter space m-tilde{sub 1}- M{sub 1} of relevant light and heavy neutrino masses by solving Boltzmann equations. A viable scenario for obtaining baryogenesis in this way is presented in the context of gauged B-L symmetry.
Gravitational matter-antimatter asymmetry and four-dimensional Yang-Mills gauge symmetry
NASA Technical Reports Server (NTRS)
Hsu, J. P.
1981-01-01
A formulation of gravity based on the maximum four-dimensional Yang-Mills gauge symmetry is studied. The theory predicts that the gravitational force inside matter (fermions) is different from that inside antimatter. This difference could lead to the cosmic separation of matter and antimatter in the evolution of the universe. Moreover, a new gravitational long-range spin-force between two fermions is predicted, in addition to the usual Newtonian force. The geometrical foundation of such a gravitational theory is the Riemann-Cartan geometry, in which there is a torsion. The results of the theory for weak fields are consistent with previous experiments.
Discrete-time quantum walks: Continuous limit and symmetries
NASA Astrophysics Data System (ADS)
di Molfetta, G.; Debbasch, F.
2012-12-01
The continuous limit of one-dimensional discrete-time quantum walks with time-and space-dependent coefficients is investigated. A given quantum walk does not generally admit a continuous limit but some families (1-jets) of quantum walks do. All families (1-jets) admitting a continuous limit are identified. The continuous limit is described by a Dirac-like equation or, alternately, a couple of Klein-Gordon equations. Variational principles leading to these equations are also discussed, together with local invariance properties.
Gauged R-symmetry and its anomalies in 4D N=1 supergravity and phenomenological implications
NASA Astrophysics Data System (ADS)
Antoniadis, I.; Ghilencea, D. M.; Knoops, R.
2015-02-01
We consider a class of models with gauged U(1) R symmetry in 4D N=1 super-gravity that have, at the classical level, a metastable ground state, an infinitesimally small (tunable) positive cosmological constant and a TeV gravitino mass. We analyse if these properties are maintained under the addition of visible sector (MSSM-like) and hidden sector state(s), where the latter may be needed for quantum consistency. We then discuss the anomaly cancellation conditions in supergravity as derived by Freedman, Elvang and Körs and apply their results to the special case of a U(1) R symmetry, in the presence of the Fayet-Iliopoulos term ( ξ) and Green-Schwarz mechanism(s). We investigate the relation of these anomaly cancellation conditions to the "naive" field theory approach in global SUSY, in which case U(1) R cannot even be gauged. We show the two approaches give similar conditions. Their induced constraints at the phenomenological level, on the above models, remain strong even if one lifted the GUT-like conditions for the MSSM gauge couplings. In an anomaly-free model, a tunable, TeV-scale gravitino mass may remain possible provided that the U(1) R charges of additional hidden sector fermions (constrained by the cubic anomaly alone) do not conflict with the related values of U(1) R charges of their scalar superpartners, constrained by existence of a stable ground state. This issue may be bypassed by tuning instead the coefficients of the Kahler connection anomalies ( b K , b CK ).
NASA Astrophysics Data System (ADS)
Moskal, P.; Alfs, D.; Bednarski, T.; Białas, P.; Curceanu, C.; Czerwiński, E.; Dulski, K.; Gajos, A.; Głowacz, B.; Gupta-Sharma, N.; Gorgol, M.; Hiesmayr, B. C.; Jasińska, B.; Kamińska, D.; Khreptak, O.; Korcyl, G.; Kowalski, P.; Krzemień, W.; Krawczyk, N.; Kubicz, E.; Mohammed, M.; Niedźwiecki, Sz.; Pawlik-Niedńwiecka, M.; Raczyński, L.; Rudy, Z.; Silarski, M.; Smyrski, J.; Wieczorek, A.; Wiślicki, W.; Zgardzińska, B.; Zieliński, M.
2016-11-01
Discrete symmetries such as parity (P), charge-conjugation (C) and time reversal (T) are of fundamental importance in physics and cosmology. Breaking of charge conjugation symmetry (C) and its combination with parity (CP) constitute necessary conditions for the existence of the asymmetry between matter and antimatter in the observed Universe. The presently known sources of discrete symmetries violations can account for only a tiny fraction of the excess of matter over antimatter. So far CP and T symmetries violations were observed only for systems involving quarks and they were never reported for the purely leptonic objects. In this article we describe briefly an experimental proposal for the test of discrete symmetries in the decays of positronium atom which is made exclusively of leptons. The experiments are conducted by means of the Jagiellonian Positron Emission Tomograph (J-PET) which is constructed from strips of plastic scintillators enabling registration of photons from the positronium annihilation. J-PET tomograph together with the positronium target system enable to measure expectation values for the discrete symmetries odd operators constructed from (i) spin vector of the ortho-positronium atom, (ii) momentum vectors of photons originating from the decay of positronium, and (iii) linear polarization direction of annihilation photons. Linearly polarized positronium will be produced in the highly porous aerogel or polymer targets, exploiting longitudinally polarized positrons emitted by the sodium 22Na isotope. Information about the polarization vector of orthopositronium will be available on the event by event basis and will be reconstructed from the known position of the positron source and the reconstructed position of the orthopositronium annihilation. In 2016 the first tests and calibration runs are planned, and the data collection with high statistics will commence in the year 2017.
Dark matter, {mu} problem, and neutrino mass with gauged R symmetry
Choi, Ki-Young; Chun, Eung Jin; Lee, Hyun Min
2010-11-15
We show that the {mu} problem and the strong CP problem can be resolved in the context of the gauged U(1){sub R} symmetry, realizing an automatic Peccei-Quinn symmetry. In this scheme, right-handed neutrinos can be introduced to explain small Majorana or Dirac neutrino mass. The U(1){sub R} D-term mediated supersymmetry (SUSY) breaking, called the U(1){sub R} mediation, gives rise to a specific form of the flavor-conserving superpartner masses. For the given solution to the {mu} problem, electroweak symmetry breaking condition requires the superpartners of the standard model at low energy to be much heavier than the gravitino. Thus, the dark matter candidate can be either gravitino or right-handed sneutrino. In the Majorana neutrino case, only gravitino is a natural dark matter candidate. On the other hand, in the Dirac neutrino case, the right-handed sneutrino can be also a dark matter candidate as it gets mass only from SUSY breaking. We discuss the non-thermal production of our dark matter candidates from the late decay of stau and find that the constraints from the big bang nucleosynthesis can be evaded for a TeV-scale stau mass.
NASA Astrophysics Data System (ADS)
Brading, Katherine; Castellani, Elena
2010-01-01
Preface; Copyright acknowledgements; List of contributors; 1. Introduction; Part I. Continuous Symmetries: 2. Classic texts: extracts from Weyl and Wigner; 3. Review paper: On the significance of continuous symmetry to the foundations of physics C. Martin; 4. The philosophical roots of the gauge principle: Weyl and transcendental phenomenological idealism T. Ryckman; 5. Symmetries and Noether's theorems K. A. Brading and H. R. Brown; 6. General covariance, gauge theories, and the Kretschmann objection J. Norton; 7. The interpretation of gauge symmetry M. Redhead; 8. Tracking down gauge: an ode to the constrained Hamiltonian formalism J. Earman; 9. Time-dependent symmetries: the link between gauge symmetries and indeterminism D. Wallace; 10. A fourth way to the Aharanov-Bohm effect A. Nounou; Part II. Discrete Symmetries: 11. Classic texts: extracts from Lebniz, Kant and Black; 12. Review paper: Understanding permutation symmetry S. French and D. Rickles; 13. Quarticles and the identity of discernibles N. Hugget; 14. Review paper: Handedness, parity violation, and the reality of space O. Pooley; 15. Mirror symmetry: what is it for a relational space to be orientable? N. Huggett; 16. Physics and Leibniz's principles S. Saunders; Part III. Symmetry Breaking: 17: Classic texts: extracts from Curie and Weyl; 18. Extract from G. Jona-Lasinio: Cross-fertilization in theoretical physics: the case of condensed matter and particle physics G. Jona-Lasinio; 19. Review paper: On the meaning of symmetry breaking E. Castellani; 20. Rough guide to spontaneous symmetry breaking J. Earman; 21. Spontaneous symmetry breaking: theoretical arguments and philosophical problems M. Morrison; Part IV. General Interpretative Issues: 22. Classic texts: extracts from Wigner; 23. Symmetry as a guide to superfluous theoretical structure J. Ismael and B. van Fraassen; 24. Notes on symmetries G. Belot; 25. Symmetry, objectivity, and design P. Kosso; 26. Symmetry and equivalence E. Castellani.
Residual Z 2 symmetries and leptonic mixing patterns from finite discrete subgroups of U(3)
NASA Astrophysics Data System (ADS)
Joshipura, Anjan S.; Patel, Ketan M.
2017-01-01
We study embedding of non-commuting Z 2 and Z m , m ≥ 3 symmetries in discrete subgroups (DSG) of U(3) and analytically work out the mixing patterns implied by the assumption that Z 2 and Z m describe the residual symmetries of the neutrino and the charged lepton mass matrices respectively. Both Z 2 and Z m are assumed to be subgroups of a larger discrete symmetry group G f possessing three dimensional faithful irreducible representation. The residual symmetries predict the magnitude of a column of the leptonic mixing matrix U PMNS which are studied here assuming G f as the DSG of SU(3) designated as type C and D and large number of DSG of U(3) which are not in SU(3). These include the known group series Σ(3 n 3), T n ( m), Δ(3 n 2, m), Δ(6 n 2, m) and Δ'(6 n 2, j, k). It is shown that the predictions for a column of | U PMNS| in these group series and the C and D types of groups are all contained in the predictions of the Δ(6 N 2) groups for some integer N. The Δ(6 N 2) groups therefore represent a sufficient set of G f to obtain predictions of the residual symmetries Z 2 and Z m .
Einstein-vector gravity, emerging gauge symmetry, and de Sitter bounce
NASA Astrophysics Data System (ADS)
Geng, Wei-Jian; Lü, H.
2016-02-01
We construct a class of Einstein-vector theories where the vector field couples bilinearly to the curvature polynomials of arbitrary order in such a way that only the Riemann tensor rather than its derivative enters the equations of motion. The theories can thus be ghost free. The U (1 ) gauge symmetry may emerge in the vacuum and also in some weak-field limit. We focus on the two-derivative theory and study a variety of applications. We find that in this theory, the energy-momentum tensor of dark matter provides a position-dependent gauge-violating term to the Maxwell field. We also use the vector as an inflaton and construct cosmological solutions. We find that the expansion can accelerate without a bare cosmological constant, indicating a new candidate for dark energy. Furthermore, we obtain exact solutions of de Sitter bounce, generated by the vector which behaves like a Maxwell field at later times. We also obtain a few new exact black holes that are asymptotic to flat and Lifshitz spacetimes. In addition, we construct exact wormholes and Randall-Sundrum II domain walls.
Boundaries, mirror symmetry, and symplectic duality in 3d N=4 gauge theory
NASA Astrophysics Data System (ADS)
Bullimore, Mathew; Dimofte, Tudor; Gaiotto, Davide; Hilburn, Justin
2016-10-01
We introduce several families of N=(2, 2) UV boundary conditions in 3d N=4 gaugetheoriesandstudytheirIRimagesinsigma-modelstotheHiggsandCoulomb branches. In the presence of Omega deformations, a UV boundary condition defines a pair of modules for quantized algebras of chiral Higgs- and Coulomb-branch operators, respec-tively, whose structure we derive. In the case of abelian theories, we use the formalism of hyperplane arrangements to make our constructions very explicit, and construct a half-BPS interface that implements the action of 3d mirror symmetry on gauge theories and boundary conditions. Finally, by studying two-dimensional compactifications of 3d N=4 gauge theories and their boundary conditions, we propose a physical origin for symplectic duality — an equivalence of categories of modules associated to families of Higgs and Coulomb branches that has recently appeared in the mathematics literature, and generalizes classic results on Koszul duality in geometric representation theory. We make several predictions about the structure of symplectic duality, and identify Koszul duality as a special case of wall crossing.
NASA Astrophysics Data System (ADS)
Wang, Juven; Gu, Zheng-Cheng; Wen, Xiao-Gang
The challenge of identifying symmetry-protected topological states (SPTs) is due to their lack of symmetry-breaking order parameters and intrinsic topological orders. For this reason, it is impossible to formulate SPTs under Ginzburg-Landau theory or probe SPTs via fractionalized bulk excitations and topology-dependent ground state degeneracy. However, the partition functions from path integrals with various symmetry twists are universal SPT invariants, fully characterizing SPTs. In this work, we use gauge fields to represent those symmetry twists in closed spacetimes of any dimensionality and arbitrary topology. This allows us to express the SPT invariants in terms of continuum field theory. We show that SPT invariants of pure gauge actions describe the SPTs predicted by group cohomology, while the mixed gauge-gravity actions describe the beyond-group-cohomology SPTs, recently observed by Kapustin. We find new examples of mixed gauge-gravity actions for U(1) SPTs in 3+1D and 4+1D via the Stiefel-Whitney class and the gravitational Chern-Simons term. [Work based on Phys. Rev. Lett. 114, 031601 (2015) arXiv:1405.7689
Alternative schemes of predicting lepton mixing parameters from discrete flavor and C P symmetry
NASA Astrophysics Data System (ADS)
Lu, Jun-Nan; Ding, Gui-Jun
2017-01-01
We suggest two alternative schemes to predict lepton mixing angles as well as C P violating phases from a discrete flavor symmetry group combined with C P symmetry. In the first scenario, the flavor and C P symmetry is broken to the residual groups of the structure Z2×C P in the neutrino and charged lepton sectors. The resulting lepton mixing matrix depends on two free parameters θν and θl. This type of breaking pattern is extended to the quark sector. In the second scenario, an Abelian subgroup of the flavor group is preserved by the charged lepton mass matrix and the neutrino mass matrix is invariant under a single remnant C P transformation, all lepton mixing parameters are determined in terms of three free parameters θ1 ,2 ,3. We derive the most general criterion to determine whether two distinct residual symmetries lead to the same mixing pattern if the redefinition of the free parameters θν ,l and θ1 ,2 ,3 is taken into account. We have studied the lepton mixing patterns arising from the flavor group S4 and C P symmetry which are subsequently broken to all of the possible residual symmetries discussed in this work.
NASA Astrophysics Data System (ADS)
He, Huan; Zheng, Yunqin; von Keyserlingk, Curt
2017-01-01
Dijkgraaf-Witten (DW) theories are of recent interest to the condensed matter community, in part because they represent topological phases of matter, but also because they characterize the response theory of certain symmetry protected topological (SPT) phases. However, as yet there has not been a comprehensive treatment of the spectra of these models in the field theoretic setting even for Abelian gauge groups, the goal of this work is to fill the gap in the literature, especially for a selection of DW models with Abelian gauge groups but non-Abelian topological order. Particularly, we focus on the appearance of non-Abelian statistics in type-III twisted DW theories with Abelian gauge groups Z2⊗3. There are only 22 distinguishable line operators, and their fusion rules and correlation functions are calculated. The flux insertion operators have quantum dimension 2, which clearly demonstrates the non-Abelian topological order of type-III twisted DW theories.
Kasamatsu, Kenichi; Ichinose, Ikuo; Matsui, Tetsuo
2013-09-13
Recently, the possibility of quantum simulation of dynamical gauge fields was pointed out by using a system of cold atoms trapped on each link in an optical lattice. However, to implement exact local gauge invariance, fine-tuning the interaction parameters among atoms is necessary. In the present Letter, we study the effect of violation of the U(1) local gauge invariance by relaxing the fine-tuning of the parameters and showing that a wide variety of cold atoms is still a faithful quantum simulator for a U(1) gauge-Higgs model containing a Higgs field sitting on sites. The clarification of the dynamics of this gauge-Higgs model sheds some light upon various unsolved problems, including the inflation process of the early Universe. We study the phase structure of this model by Monte Carlo simulation and also discuss the atomic characteristics of the Higgs phase in each simulator.
Theory of the Lattice Boltzmann Equation: Symmetry properties of Discrete Velocity Sets
NASA Technical Reports Server (NTRS)
Rubinstein, Robert; Luo, Li-Shi
2007-01-01
In the lattice Boltzmann equation, continuous particle velocity space is replaced by a finite dimensional discrete set. The number of linearly independent velocity moments in a lattice Boltzmann model cannot exceed the number of discrete velocities. Thus, finite dimensionality introduces linear dependencies among the moments that do not exist in the exact continuous theory. Given a discrete velocity set, it is important to know to exactly what order moments are free of these dependencies. Elementary group theory is applied to the solution of this problem. It is found that by decomposing the velocity set into subsets that transform among themselves under an appropriate symmetry group, it becomes relatively straightforward to assess the behavior of moments in the theory. The construction of some standard two- and three-dimensional models is reviewed from this viewpoint, and procedures for constructing some new higher dimensional models are suggested.
Flocking with discrete symmetry: The two-dimensional active Ising model.
Solon, A P; Tailleur, J
2015-10-01
We study in detail the active Ising model, a stochastic lattice gas where collective motion emerges from the spontaneous breaking of a discrete symmetry. On a two-dimensional lattice, active particles undergo a diffusion biased in one of two possible directions (left and right) and align ferromagnetically their direction of motion, hence yielding a minimal flocking model with discrete rotational symmetry. We show that the transition to collective motion amounts in this model to a bona fide liquid-gas phase transition in the canonical ensemble. The phase diagram in the density-velocity parameter plane has a critical point at zero velocity which belongs to the Ising universality class. In the density-temperature "canonical" ensemble, the usual critical point of the equilibrium liquid-gas transition is sent to infinite density because the different symmetries between liquid and gas phases preclude a supercritical region. We build a continuum theory which reproduces qualitatively the behavior of the microscopic model. In particular, we predict analytically the shapes of the phase diagrams in the vicinity of the critical points, the binodal and spinodal densities at coexistence, and the speeds and shapes of the phase-separated profiles.
On the vacuum Einstein equations along curves with a discrete local rotation and reflection symmetry
Korzyński, Mikołaj; Bentivegna, Eloisa E-mail: ian.hinder@aei.mpg.de
2015-08-01
We discuss the possibility of a dimensional reduction of the Einstein equations in S{sup 3} black-hole lattices. It was reported in previous literature that the evolution of spaces containing curves of local, discrete rotation and reflection symmetry (LDRRS) can be carried out via a system of ODEs along these curves. However, 3+1 Numerical Relativity computations demonstrate that this is not the case, and we show analytically that this is due to the presence of a tensorial quantity which is not suppressed by the symmetry. We calculate the term analytically, and verify numerically for an 8-black-hole lattice that it fully accounts for the anomalous results, and thus quantify its magnitude in this specific case. The presence of this term prevents the exact evolution of these spaces via previously-reported methods which do not involve a full 3+1 integration of Einstein's equation.
Baksic, Alexandre; Ciuti, Cristiano
2014-05-02
We explore theoretically the physics of a collection of two-level systems coupled to a single-mode bosonic field in the nonstandard configuration where each (artificial) atom is coupled to both field quadratures of the boson mode. We show that such an unusual coupling scheme can be implemented in circuit QED systems, where artificial Josephson atoms are coupled both capacitively and inductively to a superconducting resonator. We demonstrate that it is possible to pass from a discrete, paritylike Z(2) symmetry to a continuous U(1) with the appearance of photonic Goldstone and amplitude modes above a critical point even in the ultrastrong coupling regime (where the rotating wave approximation for the interaction between field and two-level systems is no longer applicable). We determine the rich phase diagram showing "superradiant" phases with different symmetries and phase boundaries of both first and second order.
Discrete flavor symmetries for degenerate solar neutrino pair and their predictions
NASA Astrophysics Data System (ADS)
Joshipura, Anjan S.; Patel, Ketan M.
2014-08-01
Flavor symmetries appropriate for describing a neutrino spectrum with degenerate solar pair and a third massive or massless neutrino are discussed. We demand that the required residual symmetries of the leptonic mass matrices be subgroups of some discrete symmetry group Gf. Gf can be a subgroup of SU(3) if the third neutrino is massive and we derive general results on the mixing angle predictions for various discrete subgroups of SU(3) divided into the two classes, called type C and D in Miller et al. [Theory and Applications of Finite Groups (John Wiley & Sons, New York, 1916)]. The main results are (a) All the SU(3) subgroups of type C fail in simultaneously giving correct θ13 and θ23. (b) All the groups of type D can predict a relation cos2θ13sin2θ23=1/3 among the mixing angles which appears to be a good zeroth order approximation. Among these, various Δ(6n2) groups with n ≥8 can simultaneously lead also to sin2θ13 in agreement with global fit at 3σ. (c) The group Σ(168)≅PSL(2,7) predicts near to the best fit value for θ13 and θ23 within the 1σ range. All discrete subgroups of U(3) with order <512 and having three-dimensional irreducible representation are considered as possible Gf when the third neutrino is massless. Only seven of them are shown to be viable and three of these can correctly predict θ13 and/or θ23. The solar angle remains undetermined at the leading order in all the cases due to degeneracy in the masses. A class of general perturbations which can correctly reproduce all the observables is discussed in the context of several groups which offer good leading order predictions.
Origin of Abelian gauge symmetries in heterotic/F-theory duality
Cvetič, Mirjam; Grassi, Antonella; Klevers, Denis; Poretschkin, Maximilian; Song, Peng
2016-04-07
Here, we study aspects of heterotic/F-theory duality for compactifications with Abelian gauge symmetries. We consider F-theory on general Calabi-Yau manifolds with a rank one Mordell-Weil group of rational sections. By rigorously performing the stable degeneration limit in a class of toric models, and also derive both the Calabi-Yau geometry and the spectral cover describing the vector bundle in the heterotic dual theory. We carefully investigate the spectral cover employing the group law on the elliptic curve in the heterotic theory. We find in explicit examples that there are three different classes of heterotic duals that have U(1) factors in their low energy effective theories: split spectral covers describing bundles with S(U(m) x U(1)) structure group, spectral covers containing torsional sections that seem to give rise to bundles with SU(m) x Z_k structure group and bundles with purely non-Abelian structure groups having a centralizer in E_8 containing a U(1) factor. In the former two cases, it is required that the elliptic fibration on the heterotic side has a non-trivial Mordell-Weil group. And while the number of geometrically massless U(1)'s is determined entirely by geometry on the F-theory side, on the heterotic side the correct number of U(1)'s is found by taking into account a Stuckelberg mechanism in the lower-dimensional effective theory. Finally, in geometry, this corresponds to the condition that sections in the two half K3 surfaces that arise in the stable degeneration limit of F-theory can be glued together globally.
Origin of Abelian gauge symmetries in heterotic/F-theory duality
Cvetič, Mirjam; Grassi, Antonella; Klevers, Denis; ...
2016-04-07
Here, we study aspects of heterotic/F-theory duality for compactifications with Abelian gauge symmetries. We consider F-theory on general Calabi-Yau manifolds with a rank one Mordell-Weil group of rational sections. By rigorously performing the stable degeneration limit in a class of toric models, and also derive both the Calabi-Yau geometry and the spectral cover describing the vector bundle in the heterotic dual theory. We carefully investigate the spectral cover employing the group law on the elliptic curve in the heterotic theory. We find in explicit examples that there are three different classes of heterotic duals that have U(1) factors in theirmore » low energy effective theories: split spectral covers describing bundles with S(U(m) x U(1)) structure group, spectral covers containing torsional sections that seem to give rise to bundles with SU(m) x Z_k structure group and bundles with purely non-Abelian structure groups having a centralizer in E_8 containing a U(1) factor. In the former two cases, it is required that the elliptic fibration on the heterotic side has a non-trivial Mordell-Weil group. And while the number of geometrically massless U(1)'s is determined entirely by geometry on the F-theory side, on the heterotic side the correct number of U(1)'s is found by taking into account a Stuckelberg mechanism in the lower-dimensional effective theory. Finally, in geometry, this corresponds to the condition that sections in the two half K3 surfaces that arise in the stable degeneration limit of F-theory can be glued together globally.« less
Gauge and global symmetries of the candidate partially massless bimetric gravity
NASA Astrophysics Data System (ADS)
Apolo, Luis; Hassan, S. F.; Lundkvist, Anders
2016-12-01
In this paper we investigate a particular ghost-free bimetric theory that exhibits the partially massless (PM) symmetry at quadratic order. At this order the global S O (1 ,4 ) symmetry of the theory is enhanced to S O (1 ,5 ). We show that this global symmetry becomes inconsistent at cubic order, in agreement with a previous calculation. Furthermore, we find that the PM symmetry of this theory cannot be extended beyond cubic order in the PM field. More importantly, it is shown that the PM symmetry cannot be extended to quartic order in any theory with one massless and one massive spin-2 fields.
Interplay between Fano resonance and PT symmetry in non-Hermitian discrete systems
NASA Astrophysics Data System (ADS)
Zhu, Baogang; Lü, Rong; Chen, Shu
2015-04-01
We study the effect of PT -symmetric complex potentials on the transport properties of non-Hermitian systems, which consist of an infinite linear chain and two side-coupled defect points with PT -symmetric complex on-site potentials. By analytically solving the scattering problem of two typical models, which display standard Fano resonances in the absence of non-Hermitian terms, we find that the PT -symmetric imaginary potentials can lead to some pronounced effects on transport properties of our systems, including changes from the perfect reflection to perfect transmission, and rich behaviors for the absence or existence of the perfect reflection at one and two resonant frequencies. Our study can help us to understand the interplay between the Fano resonance and PT symmetry in non-Hermitian discrete systems, which may be realizable in optical waveguide experiments.
Discrete symmetry enhancement in non-Abelian models and the existence of asymptotic freedom
NASA Astrophysics Data System (ADS)
Patrascioiu, Adrian; Seiler, Erhard
2001-09-01
We study the universality between a discrete spin model with icosahedral symmetry and the O(3) model in two dimensions. For this purpose we study numerically the renormalized two-point functions of the spin field and the four point coupling constant. We find that those quantities seem to have the same continuum limits in the two models. This has far reaching consequences, because the icosahedron model is not asymptotically free in the sense that the coupling constant proposed by Lüscher, Weisz, and Wolff [Nucl. Phys. B359, 221 (1991)] does not approach zero in the short distance limit. By universality this then also applies to the O(3) model, contrary to the predictions of perturbation theory.
Simplified DM models with the full SM gauge symmetry: the case of t-channel colored scalar mediators
NASA Astrophysics Data System (ADS)
Ko, P.; Natale, Alexander; Park, Myeonghun; Yokoya, Hiroshi
2017-01-01
The general strategy for dark matter (DM) searches at colliders currently relies on simplified models. In this paper, we propose a new t-channel UV-complete simplified model that improves the existing simplified DM models in two important respects: (i) we impose the full SM gauge symmetry including the fact that the left-handed and the right-handed fermions have two independent mediators with two independent couplings, and (ii) we include the renormalization group evolution when we derive the effective Lagrangian for DM-nucleon scattering from the underlying UV complete models by integrating out the t-channel mediators. The first improvement will introduce a few more new parameters compared with the existing simplified DM models. In this study we look at the effect this broader set of free parameters has on direct detection and the mono- X + MET ( X=jet, W,Z) signatures at 13TeV LHC while maintaining gauge invariance of the simplified model under the full SM gauge group. We find that the direct detection constraints require DM masses less than 10 GeV in order to produce phenomenologically interesting collider signatures. Additionally, for a fixed mono-W cross section it is possible to see very large differences in the mono-jet cross section when the usual simplified model assumptions are loosened and isospin violation between RH and LH DM-SM quark couplings are allowed.
NASA Astrophysics Data System (ADS)
Bandos, Igor A.; Ortín, Tomás
2016-08-01
We review and investigate different aspects of scalar fields in supergravity theories both when they parametrize symmetric spaces and when they parametrize spaces of special holonomy which are not necessarily symmetric (Kähler and Quaternionic-Kähler spaces): their rôle in the definition of derivatives of the fermions covariant under the R-symmetry group and (in gauged supergravities) under some gauge group, their dualization into ( d - 2)-forms, their role in the supersymmetry transformation rules (via fermion shifts, for instance) etc. We find a general definition of momentum map that applies to any manifold admitting a Killing vector and coincides with those of the holomorphic and tri-holomorphic momentum maps in Kähler and quaternionic-Kähler spaces and with an independent definition that can be given in symmetric spaces. We show how the momen-tum map occurs ubiquitously: in gauge-covariant derivatives of fermions, in fermion shifts, in the supersymmetry transformation rules of ( d - 2)-forms etc. We also give the general structure of the Noether-Gaillard-Zumino conserved currents in theories with fields of different ranks in any dimension.
Gauge Symmetry of the N-body Problem in the Hamilton-Jacobi Approach
2006-05-31
Mechanics. Springer- Verlag, NY. [29] Subbotin, M. F. 1958. ” Leonhard Euler and the Astronomical Problems of his Time.” In: Voprosy Istorii...space. It coincides with the regular Lagrange gauge when the perturbation is velocity-independent. 1 Euler and Lagrange 1.1 The history The planetary...exerted upon one another by Saturn and Jupiter. In the publication on the Lunar motion, dated by 1753, Euler derived the equations for the longitude of the
Single field inflation in supergravity with a U(1) gauge symmetry
Heurtier, L.; Khalil, S.; Moursy, A. E-mail: skhalil@zewailcity.edu.eg
2015-10-01
A single field inflation based on a supergravity model with a shift symmetry and U(1) extension of the MSSM is analyzed. We show that one of the real components of the two U(1) charged scalar fields plays the role of inflaton with an effective scalar potential similar to the ''new chaotic inflation'' scenario. Both non-anomalous and anomalous (with Fayet-Iliopoulos term) U(1) are studied. We show that the non-anomalous U(1) scenario is consistent with data of the cosmic microwave background and recent astrophysical measurements. A possible kinetic mixing between U(1) and U(1){sub B−L} is considered in order to allow for natural decay channels of the inflaton, leading to a reheating epoch. Upper limits on the reheating temperature thus turn out to favour an intermediate (∼ O(10{sup 13}) GeV) scale B−L symmetry breaking.
Single field inflation in supergravity with a U(1) gauge symmetry
Heurtier, L.; Khalil, S.; Moursy, A.
2015-10-19
A single field inflation based on a supergravity model with a shift symmetry and U(1) extension of the MSSM is analyzed. We show that one of the real components of the two U(1) charged scalar fields plays the role of inflaton with an effective scalar potential similar to the “new chaotic inflation” scenario. Both non-anomalous and anomalous (with Fayet-Iliopoulos term) U(1) are studied. We show that the non-anomalous U(1) scenario is consistent with data of the cosmic microwave background and recent astrophysical measurements. A possible kinetic mixing between U(1) and U(1){sub B−L} is considered in order to allow for natural decay channels of the inflaton, leading to a reheating epoch. Upper limits on the reheating temperature thus turn out to favour an intermediate (∼O(10{sup 13}) GeV) scale B−L symmetry breaking.
7D bosonic higher spin gauge theory: symmetry algebra and linearized constraints
NASA Astrophysics Data System (ADS)
Sezgin, E.; Sundell, P.
2002-07-01
We construct the minimal bosonic higher spin extension of the 7D AdS algebra SO(6,2), which we call hs(8 ∗) . The generators, which have spin s=1,3,5,… , are realized as monomials in Grassmann even spinor oscillators. Irreducibility, in the form of tracelessness, is achieved by modding out an infinite-dimensional ideal containing the traces. In this a key role is played by the tree bilinear traces which form an SU(2) K algebra. We show that gauging of hs(8 ∗) yields a spectrum of physical fields with spin s=0,2,4,… which make up a UIR of hs(8 ∗) isomorphic to the symmetric tensor product of two 6D scalar doubletons. The scalar doubleton is the unique SU(2) K invariant 6D doubleton. The spin s⩾2 sector comes from an hs(8 ∗) -valued one-form which also contains the auxiliary gauge fields required for writing the curvature constraints in covariant form. The physical spin s=0 field arises in a separate zero-form in a 'quasi-adjoint' representation of hs(8 ∗) . This zero-form also contains the spin s⩾2 Weyl tensors, i.e., the curvatures which are non-vanishing on-shell. We suggest that the hs(8 ∗) gauge theory describes the minimal bosonic, massless truncation of M-theory on AdS7× S4 in an unbroken phase where the holographic dual is given by N free (2,0) tensor multiplets for large N.
TeV-scale gauged B-L symmetry with inverse seesaw mechanism
Khalil, Shaaban
2010-10-01
We propose a modified version of the TeV-scale B-L extension of the standard model, where neutrino masses are generated through the inverse seesaw mechanism. We show that heavy neutrinos in this model can be accessible via clean signals at the LHC. The search for the extra gauge boson Z{sub B-L}{sup '} through the decay into dileptons or two dileptons plus missing energy is studied. We also show that the B-L extra Higgs boson can be directly probed at the LHC via a clean dilepton and missing energy signal.
The gauge sector of the SME with Lorentz-symmetry violation by symplectic projector method
NASA Astrophysics Data System (ADS)
Belich, H.; Santos, M. A.; Orlando, M. T. D.
2015-09-01
We propose to analyze a modified electromagnetism inspired from the gauge sector of the Standard Model extension (SME). From the point of view of a canonical formulation, we carried out the usual analysis on the constraints structure of the odd sector (Carroll-Field-Jackiw term) and a Maxwell term with an effective metric. This effective metric is obtained by a vectorial decomposition of the CPT-even term, that is absorbed in the ordinary Maxwell term. Using symplectic projector method (SPM), we obtain the dispersions relations and we have verified conditions of stability to determine the valid spectrum.
NASA Astrophysics Data System (ADS)
Tarantino, Nicolas; Fidkowski, Lukasz
2016-09-01
We construct exactly solved commuting projector Hamiltonian lattice models for all known (2+1)-dimensional (2+1D) fermionic symmetry protected topological phases (SPTs) with on-site unitary symmetry group Gf=G ×Z2f , where G is finite and Z2f is the fermion parity symmetry. In particular, our models transcend the class of group supercohomology models, which realize some, but not all, fermionic SPTs in 2+1D. A natural ingredient in our construction is a discrete form of the spin structure of the 2D spatial surface M on which our model is defined, namely a "Kasteleyn" orientation of a certain graph associated with the lattice. As a special case, our construction yields commuting projector models for all eight members of the Z8 classification of 2D fermionic SPTs with G =Z2 .
Multi-Higgs doublet models with local U(1){sub H} gauge symmetry and neutrino physics therein
Ko, P.; Yu, Chaehyun; Omura, Yuji
2014-01-01
Multi-Higgs doublet models appear in many interesting extensions of the standard model (SM). But they suffer from Higgs-mediated flavor changing neutral current (FCNC) problem which is very generic. In this talk, I describe that this problem can be resolved or mitigated if we introduce local U(1){sub H} Higgs flavor gauge symmetry. As examples, I describe chiral U(1){sub H} models where the right-handed up-type quarks also carry U(1){sub H} charges and discuss the top forward-backward asymmetry (FBA) and B → D{sup (*)}τν puzzle. Next I describe the two-Higgs doublet models where the usual Z₂ symmetry is implemented to U(1){sub H} and show how the Type-I and Type-II models are extended. One possible extension of Type-II has the same fermion contents with the leptophobic E₆Z´ model by Rosner, and I discuss the neutrino sector in this model briefly.
Gauging spacetime symmetries on the worldsheet and the geometric Langlands program — II
NASA Astrophysics Data System (ADS)
Tan, Meng-Chwan
2008-09-01
We generalise the analysis carried out in [1], and find that our previous results can be extended beyond the case of SL (N,C). In particular, we show that an equivalence — at the level of the holomorphic chiral algebra — between a bosonic string on a smooth coset manifold G/B and a B-gauged version of itself on G, will imply an isomorphism of classical Script W-algebras and a level relation which underlie a geometric Langlands correspondence for the simply-laced, complex ADE-groups. In addition, as opposed to line operators and branes of an open topological sigma-model, the Hecke operators and Hecke eigensheaves, can, instead, be physically interpreted in terms of the correlation functions of local operators in the holomorphic chiral algebra of a closed, quasi-topological sigma-model. Our present results thus serve as an alternative physical interpretation — to that of an electric-magnetic duality of four-dimensional gauge theory demonstrated earlier by Kapustin and Witten in [2]—of the geometric Langlands correspondence for complex ADE-groups. The cases with tame and mild ``ramifications'' are also discussed.
Gauging spacetime symmetries on the worldsheet and the geometric Langlands program
NASA Astrophysics Data System (ADS)
Tan, Meng-Chwan
2008-03-01
We study the two-dimensional twisted (0, 2) sigma-model on various smooth complex flag manifolds G/B, and explore its relevance to the geometric Langlands program. We find that an equivalence—at the level of the holomorphic chiral algebra—between a bosonic string on G/B and a B-gauged version of itself on G, will imply an isomorphism of classical Script W-algebras and a level relation which underlie a geometric Langlands correspondence for G = SL(N, C). This furnishes an alternative physical interpretation of the geometric Langlands correspondence for G = SL(N, C), to that demonstrated earlier by Kapustin and Witten via an electric-magnetic duality of four-dimensional gauge theory. Likewise, the Hecke operators and Hecke eigensheaves will have an alternative physical interpretation in terms of the correlation functions of local operators in the holomorphic chiral algebra of a quasi-topological sigma-model without boundaries. A forthcoming paper will investigate the interpretation of a ``quantum'' geometric Langlands correspondence for G = SL(N, C) in a similar setting, albeit with fluxes of the sigma-model moduli which induce a ``quantum'' deformation of the relevant classical algebras turned on.
Stokes' theorem, gauge symmetry and the time-dependent Aharonov-Bohm effect
Macdougall, James Singleton, Douglas
2014-04-15
Stokes' theorem is investigated in the context of the time-dependent Aharonov-Bohm effect—the two-slit quantum interference experiment with a time varying solenoid between the slits. The time varying solenoid produces an electric field which leads to an additional phase shift which is found to exactly cancel the time-dependent part of the usual magnetic Aharonov-Bohm phase shift. This electric field arises from a combination of a non-single valued scalar potential and/or a 3-vector potential. The gauge transformation which leads to the scalar and 3-vector potentials for the electric field is non-single valued. This feature is connected with the non-simply connected topology of the Aharonov-Bohm set-up. The non-single valued nature of the gauge transformation function has interesting consequences for the 4-dimensional Stokes' theorem for the time-dependent Aharonov-Bohm effect. An experimental test of these conclusions is proposed.
Generalizing twisted gauge invariance
Duenas-Vidal, Alvaro; Vazquez-Mozo, Miguel A.
2009-05-01
We discuss the twisting of gauge symmetry in noncommutative gauge theories and show how this can be generalized to a whole continuous family of twisted gauge invariances. The physical relevance of these twisted invariances is discussed.
Natural Electroweak Breaking from a Mirror Symmetry
Chacko, Z.; Goh, Hock-Seng; Harnik, Roni
2006-06-16
We present ''twin Higgs models,'' simple realizations of the Higgs boson as a pseudo Goldstone boson that protect the weak scale from radiative corrections up to scales of order 5-10 TeV. In the ultraviolet these theories have a discrete symmetry which interchanges each standard model particle with a corresponding particle which transforms under a twin or a mirror standard model gauge group. In addition, the Higgs sector respects an approximate global symmetry. When this global symmetry is broken, the discrete symmetry tightly constrains the form of corrections to the pseudo Goldstone Higgs potential, allowing natural electroweak symmetry breaking. Precision electroweak constraints are satisfied by construction. These models demonstrate that, contrary to the conventional wisdom, stabilizing the weak scale does not require new light particles charged under the standard model gauge groups.
NASA Astrophysics Data System (ADS)
Konstantinou, Georgios; Moulopoulos, Konstantinos
2016-11-01
Due to the importance of gauge symmetry in all fields of physics, and motivated by an article written almost three decades ago that warns against a naive handling of gauge transformations in the Landau level problem (a quantum electron moving in a spatially uniform magnetic field), we point out a proper use of the generators of dynamical symmetries combined with gauge transformation methods to easily obtain exact analytical solutions for all Landau level-wavefunctions in arbitrary gauge. Our method is different from the old argument and provides solutions in an easier manner and in a broader set of geometries and gauges; in so doing, it eliminates the need for extra procedures (i.e. a change of basis) pointed out as a necessary step in the old literature, and gives back the standard simple result, provided that an appropriate use is made of the dynamical symmetries of the system and their generators. In this way the present work will at least be useful for university-level education, i.e. in advanced classes in quantum mechanics and condensed matter physics. In addition, it clarifies the actual role of the gauge in the Landau level problem, which often appears confusing in the usual derivations provided in textbooks. Finally, we go further by showing that a similar methodology can be made to apply to the more difficult case of a spatially non-uniform magnetic field (where closed analytical results are rare), in which case the various generators (pseudomomentum and pseudo-angular momentum) appear as line integrals of the inhomogeneous magnetic field; we give closed analytical solutions for all cases, and show how the old and rather forgotten Bawin-Burnel gauge shows up naturally as a ‘reference gauge’ in all solutions.
SU(3) gauge symmetry for collective rotational states in deformed nuclei
NASA Astrophysics Data System (ADS)
Rosensteel, George; Sparks, Nick
2016-09-01
How do deformed nuclei rotate? The qualitative answer is that a velocity-dependent interaction causes a strong coupling between the angular momentum and the vortex momentum (or Kelvin circulation). To achieve a quantitative explanation, we propose a significant extension of the Bohr-Mottelson legacy model in which collective wave functions are vector-valued in an irreducible representation of SU(3). This SU(3) is not the usual Elliott choice, but rather describes internal vorticity in the rotating frame. The circulation values C of an SU(3) irreducible representation, say the (8,0) for 20Ne, are C = 0, 2, 4, 6, 8, which is the same as the angular momentum spectrum in the Elliott model; the reason is a reciprocity theorem in the symplectic model. The differential geometry of Yang-Mills theory provides a natural mathematical framework to solve the angular-vortex coupling riddle. The requisite strong coupling is a ``magnetic-like'' interaction arising from the covariant derivative and the bundle connection. The model builds on prior work about the Yang-Mills SO(3) gauge group model.
NASA Astrophysics Data System (ADS)
Greschner, S.; Piraud, M.; Heidrich-Meisner, F.; McCulloch, I. P.; Schollwöck, U.; Vekua, T.
2016-12-01
We study the quantum phases of bosons with repulsive contact interactions on a two-leg ladder in the presence of a uniform Abelian gauge field. The model realizes many interesting states, including Meissner phases, vortex fluids, vortex lattices, charge density waves, and the biased-ladder phase. Our work focuses on the subset of these states that breaks a discrete symmetry. We use density matrix renormalization group simulations to demonstrate the existence of three vortex-lattice states at different vortex densities and we characterize the phase transitions from these phases into neighboring states. Furthermore, we provide an intuitive explanation of the chiral-current reversal effect that is tied to some of these vortex lattices. We also study a charge-density-wave state that exists at 1/4 particle filling at large interaction strengths and flux values close to half a flux quantum. By changing the system parameters, this state can transition into a completely gapped vortex-lattice Mott-insulating state. We elucidate the stability of these phases against nearest-neighbor interactions on the rungs of the ladder relevant for experimental realizations with a synthetic lattice dimension. A charge-density-wave state at 1/3 particle filling can be stabilized for flux values close to half a flux quantum and for very strong on-site interactions in the presence of strong repulsion on the rungs. Finally, we analytically describe the emergence of these phases in the low-density regime, and, in particular, we obtain the boundaries of the biased-ladder phase, i.e., the phase that features a density imbalance between the legs. We make contact with recent quantum-gas experiments that realized related models and discuss signatures of these quantum states in experimentally accessible observables.
NASA Astrophysics Data System (ADS)
Armitage, N. P.
2014-07-01
Optical spectroscopies are most often used to probe dynamical correlations in materials, but they are also a probe of symmetry. Polarization anisotropies are of course sensitive to structural anisotropies, but have been much less used as a probe of more exotic symmetry breakings in ordered states. In this paper, a Jones transfer matrix formalism is discussed to infer the existence of exotic broken symmetry states of matter from their electrodynamic response for a full complement of possible broken symmetries including reflection, rotation, rotation reflection, inversion, and time reversal. A specific condition to distinguish the case of macroscopic time-reversal symmetry breaking is particularly important as in a dynamical experiment like optics, one must distinguish reciprocity from time-reversal symmetry as dissipation violates strict time-reversal symmetry of an experiment. Different forms of reciprocity can be distinguished, but only one is a sufficient (but not necessary) condition for macroscopic time-reversal symmetry breaking. I show the constraints that a Jones matrix develops under the presence or absence of such symmetries. These constraints typically appear in the form of an algebra relating matrix elements or overall constraints (transposition, unitarity, hermiticity, normality, etc.) on the form of the Jones matrix. I work out a number of examples including the trivial case of a ferromagnet and the less trivial cases of magnetoelectrics and vector and scalar spin "chiral" states. I show that the formalism can be used to demonstrate that Kerr rotation must be absent in time-reversal symmetric chiral materials. The formalism here is discussed with an eye towards its use in time-domain terahetrz spectroscopy in transmission, but with small modifications it is more generally applicable.
Fendley, Paul; Moore, Joel E; Xu, Cenke
2007-05-01
We study a constrained statistical-mechanical model in two dimensions that has three useful descriptions. They are (i) the Ising model on the honeycomb lattice, constrained to have three up spins and three down spins on every hexagon, (ii) the three-color and fully packed loop model on the links of the honeycomb lattice, with loops around a single hexagon forbidden, and (iii) three Ising models on interleaved triangular lattices, with domain walls of the different Ising models not allowed to cross. Unlike the three-color model, the configuration space on the sphere or plane is connected under local moves. On higher-genus surfaces there are infinitely many dynamical sectors, labeled by a noncontractible set of nonintersecting loops. We demonstrate that at infinite temperature the transfer matrix admits an unusual structure related to a gauge symmetry for the same model on an anisotropic lattice. This enables us to diagonalize the original transfer matrix for up to 36 sites, finding an entropy per plaquette S/k{B} approximately 0.3661 ... centered and substantial evidence that the model is not critical. We also find the striking property that the eigenvalues of the transfer matrix on an anisotropic lattice are given in terms of Fibonacci numbers. We comment on the possibility of a topological phase, with infinite topological degeneracy, in an associated two-dimensional quantum model.
NASA Astrophysics Data System (ADS)
Dartora, C. A.; Cabrera, G. G.; Nobrega, K. Z.; Montagner, V. F.; Matielli, Marina H. K.; de Campos, Fillipi Klos Rodrigues; Filho, Horacio Tertuliano S.
2011-01-01
In the context of the paraxial regime, usually valid for optical frequencies and also in the microwave spectrum of guided waves, the propagation of electromagnetic fields can be analyzed through a paraxial wave equation, which is analogous to the nonrelativistic Schrödinger equation of quantum mechanics but replacing time t with spatial coordinate z. Considering that, here it is shown that for lossless media in optical frequencies it is possible to construct a Lagrangian operator with an one-to-one correspondence with nonrelativistic quantum mechanics, which allows someone to use the same mathematical methods and techniques for solving problems. To demonstrate that, we explore a few applications in optics with increasing levels of complexity. In the spirit of a Hamiltonian formulation, the ray-tracing trajectories of geometric optics in paraxial regime are obtained in a clear manner. Following that, the gauge symmetries of the optical-field Lagrangian density is discussed in a detailed way, leading to the general form of the interaction Hamiltonian. Through the use of perturbation theory, we discuss a classical analog for a quantum not gate, making use of mode coupling in an isotropic chiral medium. At last, we explore the optical spin Hall effect and its possible applications using an effective geometric optics equation derived from an interaction Hamiltonian for the optical fields. We also predict within the framework of paraxial optics a spin Hall effect of light induced by gravitational fields.
Dartora, C. A.; Matielli, Marina H. K.; Klos Rodrigues de Campos, Fillipi; Filho, Horacio Tertuliano S.; Cabrera, G. G.; Nobrega, K. Z.; Montagner, V. F.
2011-01-15
In the context of the paraxial regime, usually valid for optical frequencies and also in the microwave spectrum of guided waves, the propagation of electromagnetic fields can be analyzed through a paraxial wave equation, which is analogous to the nonrelativistic Schroedinger equation of quantum mechanics but replacing time t with spatial coordinate z. Considering that, here it is shown that for lossless media in optical frequencies it is possible to construct a Lagrangian operator with an one-to-one correspondence with nonrelativistic quantum mechanics, which allows someone to use the same mathematical methods and techniques for solving problems. To demonstrate that, we explore a few applications in optics with increasing levels of complexity. In the spirit of a Hamiltonian formulation, the ray-tracing trajectories of geometric optics in paraxial regime are obtained in a clear manner. Following that, the gauge symmetries of the optical-field Lagrangian density is discussed in a detailed way, leading to the general form of the interaction Hamiltonian. Through the use of perturbation theory, we discuss a classical analog for a quantum not gate, making use of mode coupling in an isotropic chiral medium. At last, we explore the optical spin Hall effect and its possible applications using an effective geometric optics equation derived from an interaction Hamiltonian for the optical fields. We also predict within the framework of paraxial optics a spin Hall effect of light induced by gravitational fields.
NASA Astrophysics Data System (ADS)
Bakke, K.; Belich, H.
2015-11-01
We discuss the appearance of geometric quantum phases for a Dirac neutral particle in the context of relativistic quantum mechanics based on possible scenarios of the Lorentz symmetry violation tensor background in the CPT-even gauge sector of Standard Model Extension. We assume that the Lorentz symmetry breaking is determined by a tensor background given by (KF)μναβ, then, relativistic analogues of the Anandan quantum phase [J. Anandan, Phys. Lett. A 138, 347 (1989)] are obtained based on the parity-even and parity-odd sectors of the tensor (KF)μναβ.
NASA Astrophysics Data System (ADS)
Hiesmayr, Beatrix C.
2015-07-01
About 50 years ago John St. Bell published his famous Bell theorem that initiated a new field in physics. This contribution discusses how discrete symmetries relate to the big open questions of quantum mechanics, in particular: (i) how correlations stronger than those predicted by theories sharing randomness (Bell's theorem) relate to the violation of the CP symmetry and the P symmetry; and its relation to the security of quantum cryptography, (ii) how the measurement problem (“why do we observe no tables in superposition?”) can be polled in weakly decaying systems, (iii) how strongly and weakly interacting quantum systems are affected by Newton's self gravitation. These presented preliminary results show that the meson-antimeson systems and the hyperon- antihyperon systems are a unique laboratory to tackle deep fundamental questions and to contribute to the understand what impact the violation of discrete symmetries has.
Theory of the lattice Boltzmann equation: symmetry properties of discrete velocity sets.
Rubinstein, Robert; Luo, Li-Shi
2008-03-01
The lattice Boltzmann equation replaces continuous particle velocity space by a finite set; the velocity distribution function then varies over a finite-dimensional vector space instead of over an infinite-dimensional function space. The number of linearly independent moments of the distribution function in a lattice Boltzmann model cannot exceed the number of velocities; finite dimensionality therefore necessarily induces linear dependences among the moments that do not exist in a continuous theory. Given a finite velocity set, it is important to know which moments are free of these dependences. Elementary group theory is applied to the solution of this problem. It is found that decomposing the velocity set into subsets that transform among themselves under an appropriate symmetry group makes it straightforward to uncover linear dependences among the moments. The construction of some standard two- and three-dimensional models is reviewed from this viewpoint, and procedures for constructing higher-dimensional models are suggested.
NASA Astrophysics Data System (ADS)
Paliathanasis, A.; Krishnakumar, K.; Leach, P. G. L.
2016-04-01
We discuss the relationship between the Noether point symmetries of the geodesic Lagrangian, in a (pseudo)Riemannian manifold, with the elements of the Homothetic algebra of the space. We observe that the classification problem of the Noether symmetries for the geodesic Lagrangian is equivalent with the classification of the Homothetic algebra of the space, which in the case of a Friedmann-Lemaître-Robertson-Walker spacetime is a well-known result in the literature.
Spontaneous CP Violation in E6 GUT with horizontal symmetry
NASA Astrophysics Data System (ADS)
Maekawa, Nobuhiro
2010-02-01
We consider spontaneous CP violation in E6 grand unified theory (GUT) with horizontal symmetry and anomalous U(1)A gauge symmetry in order to solve the SUSY CP problem. To realize the sufficiently small phases of SUSY Higgs mass μ and mixing parameter B, an additional discrete symmetry is introduced. The discrete symmetry plays multiple roles in explaining various things. By the symmetry, the up-type Yukawa couplings become real, which is important in satisfying the Chromo-EDM constraints to the imaginary part of the off-diagonal elements of squark mass matrices, and the down-type Yukawa couplings become complex, which is important in obtaining the Kobayashi-Maskawa phase. Moreover, this symmetry improves the smallness of up quark mass, and reduces the number of O(1) coefficients. One of the interesting predictions is Vub˜γ4, which is quite good agreement with the measured value. This talk is based on the works in Ref. [1].
NASA Astrophysics Data System (ADS)
Lee, D. H.; Joannopoulos, J. D.; Negele, J. W.; Landau, D. P.
1984-02-01
Landau-Ginzburg-Wilson symmetry analyses and Monte Carlo calculations for the classical antiferromagnetic planar (XY) model on a triangular lattice reveal a wealth of interesting critical phenomena. From this simple model arise a zero-field transition to a state of long-range order, a new mechanism for spin disordering, and a critical point associated with a possible new universality class.
E6 inspired supersymmetric models with exact custodial symmetry
NASA Astrophysics Data System (ADS)
Nevzorov, Roman
2013-01-01
The breakdown of E6 gauge symmetry at high energies may lead to supersymmetric models based on the standard model gauge group together with extra U(1)ψ and U(1)χ gauge symmetries. To ensure anomaly cancellation the particle content of these E6 inspired models involves extra exotic states that generically give rise to nondiagonal flavor transitions and rapid proton decay. We argue that a single discrete Z˜2H symmetry can be used to forbid tree-level flavor changing transitions, as well as the most dangerous baryon and lepton number violating operators. We present 5D and 6D orbifold grand unified theory constructions that lead to the E6 inspired supersymmetric models of this type. The breakdown of U(1)ψ and U(1)χ gauge symmetries that preserves E6 matter parity assignment guarantees that ordinary quarks and leptons and their superpartners, as well as the exotic states which originate from 27 representations of E6, survive to low energies. These E6 inspired models contain two dark matter candidates and must also include additional TeV scale vectorlike lepton or vectorlike down-type quark states to render the lightest exotic quark unstable. We examine gauge coupling unification in these models and discuss their implications for collider phenomenology and cosmology.
NASA Technical Reports Server (NTRS)
Gedney, Stephen D.; Lansing, Faiza
1994-01-01
It has been found that the Discrete Integral Equation (DSI)technique is a highly effective technique for the analysis of microwave circuits and devices [1,2]. The DSI is much more robust than the traditional Finite Difference Time Domain (FDTD) method in a number of ways.
BRST symmetry in the Schrödinger picture
NASA Astrophysics Data System (ADS)
Lee, Hyuk-Jae; Yee, Jae Hyung
1993-05-01
We show that the effective Lagrangian including the gauge-fixing and ghost terms of the non-Abelian gauge theories can be derived in the functional Schrödinger picture by using the residual symmetry of the gauge-fixed Lagrangian. This residual gauge symmetry is shown to be equivalent to the well-known Becchi-Rouet-Stora-Tyutin symmetry.
BOOK REVIEW: Symmetry Breaking
NASA Astrophysics Data System (ADS)
Ryder, L. H.
2005-11-01
One of the most fruitful and enduring advances in theoretical physics during the last half century has been the development of the role played by symmetries. One needs only to consider SU(3) and the classification of elementary particles, the Yang Mills enlargement of Maxwell's electrodynamics to the symmetry group SU(2), and indeed the tremendous activity surrounding the discovery of parity violation in the weak interactions in the late 1950s. This last example is one of a broken symmetry, though the symmetry in question is a discrete one. It was clear to Gell-Mann, who first clarified the role of SU(3) in particle physics, that this symmetry was not exact. If it had been, it would have been much easier to discover; for example, the proton, neutron, Σ, Λ and Ξ particles would all have had the same mass. For many years the SU(3) symmetry breaking was assigned a mathematical form, but the importance of this formulation fell away when the quark model began to be taken seriously; the reason the SU(3) symmetry was not exact was simply that the (three, in those days) quarks had different masses. At the same time, and in a different context, symmetry breaking of a different type was being investigated. This went by the name of `spontaneous symmetry breaking' and its characteristic was that the ground state of a given system was not invariant under the symmetry transformation, though the interactions (the Hamiltonian, in effect) was. A classic example is ferromagnetism. In a ferromagnet the atomic spins are aligned in one direction only—this is the ground state of the system. It is clearly not invariant under a rotation, for that would change the ground state into a (similar but) different one, with the spins aligned in a different direction; this is the phenomenon of a degenerate vacuum. The contribution of the spin interaction, s1.s2, to the Hamiltonian, however, is actually invariant under rotations. As Coleman remarked, a little man living in a ferromagnet would
Banerjee, D; Dalmonte, M; Müller, M; Rico, E; Stebler, P; Wiese, U-J; Zoller, P
2012-10-26
Using a Fermi-Bose mixture of ultracold atoms in an optical lattice, we construct a quantum simulator for a U(1) gauge theory coupled to fermionic matter. The construction is based on quantum links which realize continuous gauge symmetry with discrete quantum variables. At low energies, quantum link models with staggered fermions emerge from a Hubbard-type model which can be quantum simulated. This allows us to investigate string breaking as well as the real-time evolution after a quench in gauge theories, which are inaccessible to classical simulation methods.
NASA Astrophysics Data System (ADS)
Teyssandier, Pierre; Tucker, Robin W.
1996-01-01
We discuss the definitions of standard clocks in theories of gravitation. These definitions are motivated by the invariance of actions under different gauge symmetries. We contrast the definition of a standard Weyl clock with that of a clock in general relativity and argue that the historical criticisms of theories based on non-metric compatible connections by Einstein, Pauli and others must be considered in the context of Weyl's original gauge symmetry. We argue that standard Einsteinian clocks can be defined in non-Riemannian theories of gravitation by adopting the Weyl group as a local gauge symmetry that preserves the metric and discuss the hypothesis that atomic clocks may be adopted to measure proper time in the presence of non-Riemannian gravitational fields. These ideas are illustrated in terms of a recently developed model of gravitation based on a non-Riemannian spacetime geometry.
Discrete canonical analysis of three-dimensional gravity with cosmological constant
NASA Astrophysics Data System (ADS)
Berra-Montiel, J.; E. Rosales-Quintero, J.
2015-05-01
We discuss the interplay between standard canonical analysis and canonical discretization in three-dimensional gravity with cosmological constant. By using the Hamiltonian analysis, we find that the continuum local symmetries of the theory are given by the on-shell space-time diffeomorphisms, which at the action level, correspond to the Kalb-Ramond transformations. At the time of discretization, although this symmetry is explicitly broken, we prove that the theory still preserves certain gauge freedom generated by a constant curvature relation in terms of holonomies and the Gauss's law in the lattice approach.
Observable T{sub 7} Lepton Flavor Symmetry at the Large Hadron Collider
Cao Qinghong; Khalil, Shaaban; Ma, Ernest; Okada, Hiroshi
2011-04-01
More often than not, models of flavor symmetry rely on the use of nonrenormalizable operators (in the guise of flavons) to accomplish the phenomenologically successful tribimaximal mixing of neutrinos. We show instead how a simple renormalizable two-parameter neutrino mass model of tribimaximal mixing can be constructed with the non-Abelian discrete symmetry T{sub 7} and the gauging of B-L. This is also achieved without the addition of auxiliary symmetries and particles present in almost all other proposals. Most importantly, it is verifiable at the Large Hadron Collider.
Conformal Orbifold Partition Functions from Topologically Massive Gauge Theory
NASA Astrophysics Data System (ADS)
Castelo Ferreira, Pedro; Kogan, Ian I.; Szabo, Richard J.
2002-04-01
We continue the development of the topological membrane approach to open and unoriented string theories. We study orbifolds of topologically massive gauge theory defined on the geometry [0,1] × Σ, where Σ is a generic compact Riemann surface. The orbifold operations are constructed by gauging the discrete symmetries of the bulk three-dimensional field theory. Multi-loop bosonic string vacuum amplitudes are thereby computed as bulk correlation functions of the gauge theory. It is shown that the three-dimensional correlators naturally reproduce twisted and untwisted sectors in the case of closed worldsheet orbifolds, and Neumann and Dirichlet boundary conditions in the case of open ones. The bulk wavefunctions are used to explicitly construct the characters of the underlying extended Kac-Moody group for arbitrary genus. The correlators for both the original theory and its orbifolds give the expected modular invariant statistical sums over the characters.
Neutrinos and flavor symmetries
Tanimoto, Morimitsu
2015-07-15
We discuss the recent progress of flavor models with the non-Abelian discrete symmetry in the lepton sector focusing on the θ{sub 13} and CP violating phase. In both direct approach and indirect approach of the flavor symmetry, the non-vanishing θ{sub 13} is predictable. The flavor symmetry with the generalised CP symmetry can also predicts the CP violating phase. We show the phenomenological analyses of neutrino mixing for the typical flavor models.
Symmetry analysis of transport properties in helical superconductor junctions
NASA Astrophysics Data System (ADS)
Cheng, Qiang; Zhang, Yinhan; Zhang, Kunhua; Jin, Biao; Zhang, Changlian
2017-03-01
We study the discrete symmetries satisfied by helical p-wave superconductors with the d-vectors {{k}x}\\hat{x}+/- {{k}y}\\hat{y} or {{k}y}\\hat{x}+/- {{k}x}\\hat{y} and the transformations brought by symmetry operations to ferromagnet and spin-singlet superconductors, which show intimate associations with the transport properties in heterojunctions, including helical superconductors. In particular, the partial symmetries of the Hamiltonian under spin-rotation and gauge-rotation operations are responsible for the novel invariances of the conductance in tunnel junctions and the new selection rules for the lowest current and peculiar phase diagrams in Josephson junctions, which were reported recently. The symmetries of constructed free energies for Josephson junctions are also analyzed, and are consistent with the results from the Hamiltonian.
Symmetry analysis of transport properties in helical superconductor junctions.
Cheng, Qiang; Zhang, Yinhan; Zhang, Kunhua; Jin, Biao; Zhang, Changlian
2017-03-01
We study the discrete symmetries satisfied by helical p-wave superconductors with the d-vectors [Formula: see text] or [Formula: see text] and the transformations brought by symmetry operations to ferromagnet and spin-singlet superconductors, which show intimate associations with the transport properties in heterojunctions, including helical superconductors. In particular, the partial symmetries of the Hamiltonian under spin-rotation and gauge-rotation operations are responsible for the novel invariances of the conductance in tunnel junctions and the new selection rules for the lowest current and peculiar phase diagrams in Josephson junctions, which were reported recently. The symmetries of constructed free energies for Josephson junctions are also analyzed, and are consistent with the results from the Hamiltonian.
NASA Astrophysics Data System (ADS)
Abdi, Fatemeh; Siabi-Gerjan, Araz; Savaloni, Hadi
2012-07-01
The use of glancing angle deposition technique provides opportunities for the deposition of sculptured nanostructures of different shape. The optical properties of such nanostructures that are a function of the shape of these nanostructures may be investigated, using the discrete dipole approximation theory which is an appropriate method for solving the light scattering problem from objects of different shape and geometry. In this paper, the extinction spectra of Ag/glass-sculptured nano-flowers with threefold symmetry are modeled and calculated, while the results are compared with similar experimental observations. In modeling the nano-flower-shaped sculptured thin films, it is proposed that the nano-flower is formed as a combination of two chiral thin films with different dimensions. This structure was replaced with 1,405 electrical dipoles, and its extinction spectrum was calculated as a function of incident light angle and azimuthal angle. The extinction spectrum consists of both transverse and longitudinal modes of oscillations. The results showed that by increasing the incident angle, due to increase of amplitude of electrical oscillations, transverse oscillations shift towards longer wavelengths. It was also observed that at azimuthal angles close to nano-flower petals, where sharp points or recesses may exist, the intensity of extinction spectrum for longitudinal mode (long wavelengths in the extinction spectrum) increases.
Chiral symmetry and chiral-symmetry breaking
Peskin, M.E.
1982-12-01
These lectures concern the dynamics of fermions in strong interaction with gauge fields. Systems of fermions coupled by gauge forces have a very rich structure of global symmetries, which are called chiral symmetries. These lectures will focus on the realization of chiral symmetries and the causes and consequences of thier spontaneous breaking. A brief introduction to the basic formalism and concepts of chiral symmetry breaking is given, then some explicit calculations of chiral symmetry breaking in gauge theories are given, treating first parity-invariant and then chiral models. These calculations are meant to be illustrative rather than accurate; they make use of unjustified mathematical approximations which serve to make the physics more clear. Some formal constraints on chiral symmetry breaking are discussed which illuminate and extend the results of our more explicit analysis. Finally, a brief review of the phenomenological theory of chiral symmetry breaking is presented, and some applications of this theory to problems in weak-interaction physics are discussed. (WHK)
Some comments on unitarity gauge
NASA Astrophysics Data System (ADS)
Lopez-Osorio, M. A.; Martinez-Pascual, E.; Toscano, J. J.
2004-04-01
A pedagogical discussion on the unitarity gauge within the context of Hamiltonian path integral formalism is presented. A model based on the group O(N), spontaneously broken down to the subgroup O(N - 1), is used to illustrate the main aspects of this gauge-fixing procedure. Among the issues, discussed with some extent, are: (1) the structure of model's constraints following the Dirac's method, (2) the gauge-fixing procedure, using the unitarity gauge for the massive gauge fields and the Coulomb one for the massless gauge fields, (3) the absence of BRST symmetry in this gauge-fixing procedure and its implications on the renormalizability of the theory, and (4) the static role of the ghost and anti-ghost fields associated with the massive gauge fields and how their contributions can be eliminated by using the dimensional regularization scheme.
NASA Astrophysics Data System (ADS)
Lovelady, Benjamin C.; Wheeler, James T.
2016-04-01
According to the Coleman-Mandula theorem, any gauge theory of gravity combined with an internal symmetry based on a Lie group must take the form of a direct product in order to be consistent with basic assumptions of quantum field theory. However, we show that an alternative gauging of a simple group can lead dynamically to a spacetime with compact internal symmetry. The biconformal gauging of the conformal symmetry of n-dimensional Euclidean space doubles the dimension to give a symplectic manifold. Examining one of the Lagrangian submanifolds in the flat case, we find that in addition to the expected S O (n ) connection and curvature, the solder form necessarily becomes Lorentzian. General coordinate invariance gives rise to an S O (n -1 ,1 ) connection on the spacetime. The principal fiber bundle character of the original S O (n ) guarantees that the two symmetries enter as a direct product, in agreement with the Coleman-Mandula theorem.
NASA Technical Reports Server (NTRS)
Lee, Kimyeong; Stein-Schabes, Jaime A.; Watkins, Richard; Widrow, Lawrence M.
1988-01-01
Classical non-topological soliton configurations are considered within the theory of a complex scalar field with a gauged U symmetry. Their existence and stability against dispersion are demonstrated and some of their properties are investigated analytically and numerically. The soliton configuration is such that inside the soliton the local U symmetry is broken, the gauge field becomes massive and for a range of values of the coupling constants the soliton becomes a superconductor pushing the charge to the surface. Furthermore, because of the repulsive Coulomb force, there is a maximum size for these objects, making impossible the existence of Q-matter in bulk form. Also briefly discussed are solitons with fermions in a U gauge theory.
Twisted gauge theories in three-dimensional Walker-Wang models
NASA Astrophysics Data System (ADS)
Wang, Zitao; Chen, Xie
2017-03-01
Three-dimensional gauge theories with a discrete gauge group can emerge from spin models as a gapped topological phase with fractional point excitations (gauge charge) and loop excitations (gauge flux). It is known that 3D gauge theories can be "twisted," in the sense that the gauge flux loops can have nontrivial braiding statistics among themselves and such twisted gauge theories are realized in models discovered by Dijkgraaf and Witten. A different framework to systematically construct three-dimensional topological phases was proposed by Walker and Wang and a series of examples have been studied. Can the Walker-Wang construction be used to realize the topological order in twisted gauge theories? This is not immediately clear because the Walker-Wang construction is based on a loop condensation picture while the Dijkgraaf-Witten theory is based on a membrane condensation picture. In this paper, we show that the answer to this question is Yes, by presenting an explicit construction of the Walker-Wang models which realize both the twisted and untwisted gauge theories with gauge group Z2×Z2 . We identify the topological order of the models by performing modular transformations on the ground-state wave functions and show that the modular matrices exactly match those for the Z2×Z2 gauge theories. By relating the Walker-Wang construction to the Dijkgraaf-Witten construction, our result opens up a way to study twisted gauge theories with fermonic charges, and correspondingly strongly interacting fermionic symmetry protected topological phases and their surface states, through exactly solvable models.
Light-Front Quantization of Gauge Theories
Brodskey, Stanley
2002-12-01
Light-front wavefunctions provide a frame-independent representation of hadrons in terms of their physical quark and gluon degrees of freedom. The light-front Hamiltonian formalism provides new nonperturbative methods for obtaining the QCD spectrum and eigensolutions, including resolvant methods, variational techniques, and discretized light-front quantization. A new method for quantizing gauge theories in light-cone gauge using Dirac brackets to implement constraints is presented. In the case of the electroweak theory, this method of light-front quantization leads to a unitary and renormalizable theory of massive gauge particles, automatically incorporating the Lorentz and 't Hooft conditions as well as the Goldstone boson equivalence theorem. Spontaneous symmetry breaking is represented by the appearance of zero modes of the Higgs field leaving the light-front vacuum equal to the perturbative vacuum. I also discuss an ''event amplitude generator'' for automatically computing renormalized amplitudes in perturbation theory. The importance of final-state interactions for the interpretation of diffraction, shadowing, and single-spin asymmetries in inclusive reactions such as deep inelastic lepton-hadron scattering is emphasized.
Raduta, C. M.; Raduta, A. A.
2010-12-15
A many-body Hamiltonian involving the mean field for a projected spherical single-particle basis, the pairing interactions for alike nucleons, and the dipole-dipole proton-neutron interactions in the particle-hole (ph) channel and the ph dipole pairing potential is treated by the projected gauge fully renormalized proton-neutron quasiparticle random phase approximation approach. The resulting wave functions and energies for the mother and daughter nuclei are used to calculate the 2{nu}{beta}{beta} decay rate and the process half-life. For illustration, the formalism is applied for the decay {sup 100}Mo{yields}{sup 100}Ru. The calculated half-life is in agreement with the corresponding experimental data. The Ikeda sum rule is obeyed.
Novel symmetries in the modified version of two dimensional Proca theory
NASA Astrophysics Data System (ADS)
Bhanja, T.; Shukla, D.; Malik, R. P.
2013-08-01
By exploiting Stueckelberg's approach, we obtain a gauge theory for the two-dimensional, that is, (1+1)-dimensional (2D) Proca theory and demonstrate that this theory is endowed with, in addition to the usual Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetries, the on-shell nilpotent (anti-)co-BRST symmetries, under which the total gauge-fixing term remains invariant. The anticommutator of the BRST and co-BRST (as well as anti-BRST and anti-co-BRST) symmetries define a unique bosonic symmetry in the theory, under which the ghost part of the Lagrangian density remains invariant. To establish connections of the above symmetries with the Hodge theory, we invoke a pseudo-scalar field in the theory. Ultimately, we demonstrate that the full theory provides a field theoretic example for the Hodge theory where the continuous symmetry transformations provide a physical realization of the de Rham cohomological operators and discrete symmetries of the theory lead to the physical realization of the Hodge duality operation of differential geometry. We also mention the physical implications and utility of our present investigation.
NASA Astrophysics Data System (ADS)
Motrunich, Olexei; Geraedts, Scott
2015-03-01
We construct models realizing distinct confining phases of lattice gauge theories envisioned in a formal classification of gapped phases of gauge theories by Kapustin and Thorngreen, arXiv:1309.4721. This generalizes ideas of Symmetry-Protected Topological (SPT) phases in Condensed Matter to systems where fundamental microscopic objects are quantum lines, which is of interest in High Energy Theory. Specifically, in (3+1)D, we consider discrete ZN lattice gauge theory models, with two copies of ZN, and construct N distinct confining phases by engineering condensation of bound states of magnetic fluxes (which are quantum lines in 3d) and ZN electric field lines. In (4+1)D, we consider compact quantum electrodynamics (CQED) models, with two copies of CQED, and engineer condensation of bound states of monopoles (which are quantum lines in 4d) and U(1) electric field lines. When the bound states contain a single monopole, we find SPT-like phases of the lattice gauge theory, while when the bound states contain multiple monopoles, we find analogs of Symmetry-Enriched Topological phases, where in the present case we also have fractionalization of Faraday lines. The distinct character of these topological phases of quantum lines is revealed by unusual physics at a boundary.
Gauge invariants and correlators in flavoured quiver gauge theories
NASA Astrophysics Data System (ADS)
Mattioli, Paolo; Ramgoolam, Sanjaye
2016-10-01
In this paper we study the construction of holomorphic gauge invariant operators for general quiver gauge theories with flavour symmetries. Using a characterisation of the gauge invariants in terms of equivalence classes generated by permutation actions, along with representation theory results in symmetric groups and unitary groups, we give a diagonal basis for the 2-point functions of holomorphic and anti-holomorphic operators. This involves a generalisation of the previously constructed Quiver Restricted Schur operators to the flavoured case. The 3-point functions are derived and shown to be given in terms of networks of symmetric group branching coefficients. The networks are constructed through cutting and gluing operations on the quivers.
Dynamical Messengers for Gauge Mediation
Hook, Anson; Torroba, Gonzalo; /SLAC /Stanford U., Phys. Dept.
2011-08-17
We construct models of indirect gauge mediation where the dynamics responsible for breaking supersymmetry simultaneously generates a weakly coupled subsector of messengers. This provides a microscopic realization of messenger gauge mediation where the messenger and hidden sector fields are unified into a single sector. The UV theory is SQCD with massless and massive quarks plus singlets, and at low energies it flows to a weakly coupled quiver gauge theory. One node provides the primary source of supersymmetry breaking, which is then transmitted to the node giving rise to the messenger fields. These models break R-symmetry spontaneously, produce realistic gaugino and sfermion masses, and give a heavy gravitino.
Supersymmetry, grand unification and flavor symmetry
NASA Astrophysics Data System (ADS)
Enkhbat, Tsedenbaljir
In this thesis I have presented the findings of my research pursued during my Ph.D. study. The purpose of this thesis was to study different theoretical ideas in high energy physics model building addressed primarily towards understanding the fermion mass problem and the gauge hierarchy problem. These include: Anomalous flavor U(1) symmetry and its experimental implications, finite GUT models with discrete family symmetry, and a product GUT model in a 2D deconstructed theory space. The second and third chapters of the thesis describe our study of lepton flavor violation (LFV) and electric dipole moments (EDM) induced by a flavor-dependent anomalous U(1) gauge symmetry of string origin. The models considered also address the fermion mass hierarchy problem successfully. We have shown that the U(1) sector induces significant LFV and EDMs through the SUSY breaking parameters. These effects arise via renormalization group evolution of the parameters in the momentum regime between the string and the anomalous U(1) breaking scale. The fourth chapter of the thesis contains our work on a concrete realization of SUSY breaking using interference between the anomalous U(1) flavor gauge symmetry and a strongly coupled SU(N c), leading to the so called Split SUSY spectrum where the sfermions and the gravitino acquire masses of order 105 ÷ 108 GeV while the gauginos and the Higgsinos have masses of order 102 ÷ 103 GeV. We have calculated the leading order supergravity corrections and have presented a class of explicit models of Split SUSY which are phenomenologically consistent. In the fifth chapter I have presented models for realistic quark masses and mixings in the context of finite SU(5) GUT wherein the beta functions for the gauge and the Yukawa couplings vanish to all orders in perturbation theory. The models presented are based on non-Abelian discrete symmetries. In the case of (Z4)3 x P and A4 symmetries we have found models finite to all order of perturbation theory
Gauge natural formulation of conformal gravity
Campigotto, M.; Fatibene, L.
2015-03-15
We consider conformal gravity as a gauge natural theory. We study its conservation laws and superpotentials. We also consider the Mannheim and Kazanas spherically symmetric vacuum solution and discuss conserved quantities associated to conformal and diffeomorphism symmetries.
None
2016-07-12
âmasslessâ modes (here spin-waves), which are the ancestors of the NG bosons discussed below. Fluctuations of the order parameter (the magnetization) are described by a âmassiveâ SBS mode. - In field theory, Nambu showed that broken chiral symmetry from a spontaneous generation of hadron masses induces massless pseudoscalar modes (identified with a massless limit of pion fields). This illustrates a general phenomenon made explicit by Goldstone: massless Nambu-Goldstone (NG) bosons are a necessary concomitant of spontaneously broken continuous symmetries. Massive SBS scalars bosons describe, as in phase transitions, the fluctuations of the SBS order parameters. - In 1964, with Robert Brout, we discovered a mechanism based on SBS by which short range interactions are generated from long range ones. A similar proposal was then made independently by Higgs in a different approach. Qualitatively, our mechanism works as follows. The long range fundamental electromagnetic and gravitational interactions are governed by extended symmetries,called gauge symmetries, which were supposed to guarantee that the elementary field constituents which transmit the forces, photons or gravitons, be massless. We considered a generalization of the electromagnetic âvectorâ field, known as Yang-Mills fields, and coupled them to fields which acquire from SBS constant values in the vacuum. These fields pervade space, as did magnetization, but they have no spatial orientation: they are âscalarââ fields. The vector Yang-Mills fields which interact with the scalar fields become massive and hence the forces they mediate become short ranged. We also showed that the mechanism can survive in absence of elementary scalar fields. - Because of the extended symmetries, the nature of SBS is profoundly altered: the NG fields are absorbed into the massive vector Yang-Mills fields and restore the gauge symmetry. This has a dramatic consequence. To confront
2011-02-24
massless” modes (here spin-waves), which are the ancestors of the NG bosons discussed below. Fluctuations of the order parameter (the magnetization) are described by a “massive” SBS mode. - In field theory, Nambu showed that broken chiral symmetry from a spontaneous generation of hadron masses induces massless pseudoscalar modes (identified with a massless limit of pion fields). This illustrates a general phenomenon made explicit by Goldstone: massless Nambu-Goldstone (NG) bosons are a necessary concomitant of spontaneously broken continuous symmetries. Massive SBS scalars bosons describe, as in phase transitions, the fluctuations of the SBS order parameters. - In 1964, with Robert Brout, we discovered a mechanism based on SBS by which short range interactions are generated from long range ones. A similar proposal was then made independently by Higgs in a different approach. Qualitatively, our mechanism works as follows. The long range fundamental electromagnetic and gravitational interactions are governed by extended symmetries,called gauge symmetries, which were supposed to guarantee that the elementary field constituents which transmit the forces, photons or gravitons, be massless. We considered a generalization of the electromagnetic “vector” field, known as Yang-Mills fields, and coupled them to fields which acquire from SBS constant values in the vacuum. These fields pervade space, as did magnetization, but they have no spatial orientation: they are “scalar’’ fields. The vector Yang-Mills fields which interact with the scalar fields become massive and hence the forces they mediate become short ranged. We also showed that the mechanism can survive in absence of elementary scalar fields. - Because of the extended symmetries, the nature of SBS is profoundly altered: the NG fields are absorbed into the massive vector Yang-Mills fields and restore the gauge symmetry. This has a dramatic consequence. To confront precision experiments, the mechanism should be
Phenomenological Lagrangians, gauge models and branes
NASA Astrophysics Data System (ADS)
Zheltukhin, A. A.
2017-03-01
Phenomenological Lagrangians for physical systems with spontaneously broken symmetries are reformulated in terms of gauge field theory. Description of the Dirac p-branes in terms of the Yang-Mills- Cartan gauge multiplets interacting with gravity, is proved to be equivalent to their description as a closed dynamical system with the symmetry ISO(1, D - 1) spontaneously broken to ISO(1, p) × SO( D - p - 1).
Some global problems in gauge theories (Variations on a theme of Aharonov and Bohm)
Wilczek, F.
1989-12-01
Several situations are discussed, in which the sort of global considerations made famous by Aharonov and Bohm in their discussion of the interaction of charged particles with magnetic flux tubes have important physical implications. It is argued that discrete gauge symmetries in the continuum make sense, and manifest themselves most clearly in Aharonov-Bohm type scattering of charged particles off string singularities. The existence of such discrete symmetries has important implications for the quantum mechanics of topologically non-trivial space-times in general and black holes in particular. It is argued that in the non-abelian case essentially new features arise, most notably that the symmetry group of the homogeneous ground state generally ceases to be globally defined in the presence of a string. When continuous rather than discrete symmetries are involved, a variety of fascinating and as yet poorly understood dynamical effects occur. Perhaps the most striking is a new form of string superconductivity, that exists for purely topological reasons, and is not well modeled by regarding the string as a superconducting wire. 8 refs., 2 figs.
S-matrices and quantum group symmetry of k-deformed sigma models
NASA Astrophysics Data System (ADS)
Hollowood, Timothy J.; Miramontes, J. Luis; Schmidtt, David M.
2016-11-01
Recently, two kinds of integrable deformations of the string world sheet theory in the gauge/gravity correspondence have been constructed (Delduc et al 2014 Phys. Rev. Lett. 112 051601; Hollowood et al 2014 J. Phys. A: Math. Theor. 47 495402). One class of these, the k deformations associated to the more general q deformations but with q={{{e}}}{{i}π /k} a root of unity, has been shown to be related to a particular discrete deformation of the principal chiral models and (semi-)symmetric space sigma models involving a gauged WZW model. We conjecture a form for the exact S-matrices of the bosonic integrable field theories of this type. The S-matrices imply that the theories have a hidden infinite dimensional affine quantum group symmetry. We provide some evidence, via quantum inverse scattering techniques, that the theories do indeed possess the finite-dimensional part of this quantum group symmetry.
Supersymmetry Breaking and Gauge Mediation
NASA Astrophysics Data System (ADS)
Kitano, Ryuichiro; Ooguri, Hirosi; Ookouchi, Yutaka
2010-11-01
We review recent works on supersymmetry breaking and gauge mediation. We survey our current understanding of dynamical supersymmetry-breaking mechanisms and describe new model-building tools that use duality, metastability, and stringy construction. We discuss phenomenological constraints and their solutions, paying particular attention to gaugino masses and electroweak symmetry breaking.
Digital lattice gauge theories
NASA Astrophysics Data System (ADS)
Zohar, Erez; Farace, Alessandro; Reznik, Benni; Cirac, J. Ignacio
2017-02-01
We propose a general scheme for a digital construction of lattice gauge theories with dynamical fermions. In this method, the four-body interactions arising in models with 2 +1 dimensions and higher are obtained stroboscopically, through a sequence of two-body interactions with ancillary degrees of freedom. This yields stronger interactions than the ones obtained through perturbative methods, as typically done in previous proposals, and removes an important bottleneck in the road towards experimental realizations. The scheme applies to generic gauge theories with Lie or finite symmetry groups, both Abelian and non-Abelian. As a concrete example, we present the construction of a digital quantum simulator for a Z3 lattice gauge theory with dynamical fermionic matter in 2 +1 dimensions, using ultracold atoms in optical lattices, involving three atomic species, representing the matter, gauge, and auxiliary degrees of freedom, that are separated in three different layers. By moving the ancilla atoms with a proper sequence of steps, we show how we can obtain the desired evolution in a clean, controlled way.
NASA Astrophysics Data System (ADS)
Weisz, Peter; Majumdar, Pushan
2012-03-01
Lattice gauge theory is a formulation of quantum field theory with gauge symmetries on a space-time lattice. This formulation is particularly suitable for describing hadronic phenomena. In this article we review the present status of lattice QCD. We outline some of the computational methods, discuss some phenomenological applications and a variety of non-perturbative topics. The list of references is severely incomplete, the ones we have included are text books or reviews and a few subjectively selected papers. Kronfeld and Quigg (2010) supply a reasonably comprehensive set of QCD references. We apologize for the fact that have not covered many important topics such as QCD at finite density and heavy quark effective theory adequately, and mention some of them only in the last section "In Brief". These topics should be considered in further Scholarpedia articles.
Zero energy gauge fields and the phases of a gauge theory
Guendelman, E.I. )
1990-07-20
A new approach to the definition of the phases of a Poincare invariant gauge theory is developed. It is based on the role of gauge transformations that change the asymptotic value of the gauge fields from zero to a constant. In the context of theories without Higgs fields, this symmetry can be spontaneously broken when the gauge fields are massless particles, explicitly broken when the gauge fields develop a mass. Finally, the vacuum can be invariant under this transformation, this last case can be achieved when the theory has a violent infrared behavior, which in some theories can be connected to a confinement mechanism.
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.
Betts, Robert E.; Crawford, John F.
1989-01-01
An aging gauge comprising a container having a fixed or a variable sized t opening with a cap which can be opened to control the sublimation rate of a thermally sublimational material contained within the container. In use, the aging gauge is stored with an item to determine total heat the item is subjected to and also the maximum temperature to which the item has been exposed. The aging gauge container contains a thermally sublimational material such as naphthalene or similar material which has a low sublimation rate over the temperature range from about 70.degree. F. to about 160.degree. F. The aging products determined by analyses of a like item aged along with the aging gauge for which the sublimation amount is determined is employed to establish a calibration curve for future aging evaluation. The aging gauge is provided with a means for determining the maximum temperature exposure (i.e., a thermally indicating material which gives an irreversible color change, Thermocolor pigment). Because of the relationship of doubling reaction rates for increases of 10.degree. C., equivalency of item used in accelerated aging evaluation can be obtained by referring to a calibration curve depicting storage temperature on the abscissa scale and multiplier on the ordinate scale.
Betts, Robert E.; Crawford, John F.
1989-04-04
An aging gauge comprising a container having a fixed or a variable sized t opening with a cap which can be opened to control the sublimation rate of a thermally sublimational material contained within the container. In use, the aging gauge is stored with an item to determine total heat the item is subjected to and also the maximum temperature to which the item has been exposed. The aging gauge container contains a thermally sublimational material such as naphthalene or similar material which has a low sublimation rate over the temperature range from about 70.degree. F. to about 160.degree. F. The aging products determined by analyses of a like item aged along with the aging gauge for which the sublimation amount is determined is employed to establish a calibration curve for future aging evaluation. The aging gauge is provided with a means for determining the maximum temperature exposure (i.e., a thermally indicating material which gives an irreversible color change, Thermocolor pigment). Because of the relationship of doubling reaction rates for increases of 10.degree. C., equivalency of item used in accelerated aging evaluation can be obtained by referring to a calibration curve depicting storage temperature on the abscissa scale and multiplier on the ordinate scale.
Discrete minimal flavor violation
Zwicky, Roman; Fischbacher, Thomas
2009-10-01
We investigate the consequences of replacing the global flavor symmetry of minimal flavor violation (MFV) SU(3){sub Q}xSU(3){sub U}xSU(3){sub D}x{center_dot}{center_dot}{center_dot} by a discrete D{sub Q}xD{sub U}xD{sub D}x{center_dot}{center_dot}{center_dot} symmetry. Goldstone bosons resulting from the breaking of the flavor symmetry generically lead to bounds on new flavor structure many orders of magnitude above the TeV scale. The absence of Goldstone bosons for discrete symmetries constitute the primary motivation of our work. Less symmetry implies further invariants and renders the mass-flavor basis transformation observable in principle and calls for a hierarchy in the Yukawa matrix expansion. We show, through the dimension of the representations, that the (discrete) symmetry in principle does allow for additional {delta}F=2 operators. If though the {delta}F=2 transitions are generated by two subsequent {delta}F=1 processes, as, for example, in the standard model, then the four crystal-like groups {sigma}(168){approx_equal}PSL(2,F{sub 7}), {sigma}(72{phi}), {sigma}(216{phi}) and especially {sigma}(360{phi}) do provide enough protection for a TeV-scale discrete MFV scenario. Models where this is not the case have to be investigated case by case. Interestingly {sigma}(216{phi}) has a (nonfaithful) representation corresponding to an A{sub 4} symmetry. Moreover we argue that the, apparently often omitted, (D) groups are subgroups of an appropriate {delta}(6g{sup 2}). We would like to stress that we do not provide an actual model that realizes the MFV scenario nor any other theory of flavor.
Personal recollections on chiral symmetry breaking
NASA Astrophysics Data System (ADS)
Kobayashi, Makoto
2016-07-01
The author's work on the mass of pseudoscalar mesons is briefly reviewed. The emergence of the study of CP violation in the renormalizable gauge theory from consideration of chiral symmetry in the quark model is discussed.
A mass term for three-dimensional gauge fields
NASA Astrophysics Data System (ADS)
Schonfeld, Jonathan F.
1981-07-01
We propose the interaction Lξ≡ {1}/{2}ξɛ μνλTrA μ[∂ νA λ- {2}/{3}igA νA λ] as a mass term for gauge fields in three-dimensional spacetime. The Aμ belong to a Lie algebra (represented here in terms of matrices), ɛ μνλ is the completely antisymmetric symbol, the coupling g has units [ mass] {1}/{2}, and the parameter ξ has units [mass]. Lξ, related to the instanton current of four dimensions, is gauge invariant up to a total divergence and a topological density. (There is a supersymmetric extension with the same property.) When technical complications can be ignored, Lξ provides gauge particles with mass without breaking local symmetry and without introducing auxiliary fields. Perturbative analysis of models involving Lξ (collectively called "ξ theories") is complicated by gauge-non-invariant infrared singularities in gauge-field propagators. Nevertheless, quantized abelian ξ-theories (collectively called "ξ QED") do define gauge-invariant and infrared-finite scattering in perturbation theory. The consistency of non-abelian ξ theories is not yet established. The physics of non-relativistic charges ξ QED is, in its gross features, the same as that of the Aharanov-Bohm effect - the static field of a point charge is a non-trivial pure gauge at large distances. (We argue that in spite of the long-range fields, propagation of charges at large times is free; so that in ξ QED there should be no unexpected subtleties in the axiomatic definition of scattering amplitudes.) Compatibility of gauge invariance and mass in three dimensions is related to the existence of massive spinning representations of the Poincaré algebra with only one polarization per momentum. The massive spin-one photon of ξ QED is such a particle. (There is in fact a massive unitary representation of the three-dimensional Poincaré algebra with only one polarization for spin equal to any real number, integral multiple of one-half or otherwise. It is possible that particles
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.
Symmetry impedes symmetry discrimination.
Tjan, Bosco S; Liu, Zili
2005-12-16
Objects in the world, natural and artificial alike, are often bilaterally symmetric. The visual system is likely to take advantage of this regularity to encode shapes for efficient object recognition. The nature of encoding a symmetric shape, and of encoding any departure from it, is therefore an important matter in visual perception. We addressed this issue of shape encoding empirically, noting that a particular encoding scheme necessarily leads to a specific profile of sensitivity in perceptual discriminations. We studied symmetry discrimination using human faces and random dots. Each face stimulus was a frontal view of a three-dimensional (3-D) face model. The 3-D face model was a linearly weighted average (a morph) between the model of an original face and that of the corresponding mirror face. Using this morphing technique to vary the degree of asymmetry, we found that, for faces and analogously generated random-dot patterns alike, symmetry discrimination was worst when the stimuli were nearly symmetric, in apparent opposition to almost all studies in the literature. We analyzed the previous work and reconciled the old and new results using a generic model with a simple nonlinearity. By defining asymmetry as the minimal difference between the left and right halves of an object, we found that the visual system was disproportionately more sensitive to larger departures from symmetry than to smaller ones. We further demonstrated that our empirical and modeling results were consistent with Weber-Fechner's and Stevens's laws.
Green-Schwarz superstring on doubled-yet-gauged spacetime
NASA Astrophysics Data System (ADS)
Park, Jeong-Hyuck
2016-11-01
We construct a world-sheet action for Green-Schwarz superstring in terms of doubled-yet-gauged spacetime coordinates. For an arbitrarily curved NS-NS background, the action possesses O(10, 10) T-duality, Spin(1, 9) × Spin(9, 1) Lorentz symmetry, coordinate gauge symmetry, spacetime doubled-yet-gauged diffeomorphisms, world-sheet diffeomorphisms and Weyl symmetry. Further, restricted to flat backgrounds, it enjoys maximal spacetime supersymmetry and kappa-symmetry. After the auxiliary coordinate gauge symmetry potential being integrated out, our action can consistently reduce to the original undoubled Green-Schwarz action. Thanks to the twofold spin groups, the action is unique: it is specific choices of the NS-NS backgrounds that distinguish IIA or IIB, as well as lead to non-Riemannian or non-relativistic superstring a la Gomis-Ooguri which might deserve the nomenclature, type IIC.
Light dilaton in walking gauge theories
Appelquist, Thomas; Bai Yang
2010-10-01
We analyze the existence of a dilaton in gauge theories with approximate infrared conformal symmetry. To the extent that these theories are governed in the infrared by an approximate fixed point (walking), the explicit breaking of the conformal symmetry at these scales is vanishingly small. If confinement and spontaneous chiral-symmetry breaking set in at some infrared scale, the resultant breaking of the approximate conformal symmetry can lead to the existence of a dilaton with mass parametrically small compared to the confinement scale, and potentially observable at the LHC.
Integrable discrete PT symmetric model.
Ablowitz, Mark J; Musslimani, Ziad H
2014-09-01
An exactly solvable discrete PT invariant nonlinear Schrödinger-like model is introduced. It is an integrable Hamiltonian system that exhibits a nontrivial nonlinear PT symmetry. A discrete one-soliton solution is constructed using a left-right Riemann-Hilbert formulation. It is shown that this pure soliton exhibits unique features such as power oscillations and singularity formation. The proposed model can be viewed as a discretization of a recently obtained integrable nonlocal nonlinear Schrödinger equation.
Topological symmetry breaking by quantum wormholes
Mignemi, S.; Moss, I. )
1993-10-15
In multiply connected spacetimes which contain quantum wormholes it may be possible to break gauge symmetries without the usual Higgs fields. In a simple model, symmetry breaking is favored by the quantum effects of Dirac Fermions and leads to vector boson masses related to the wormhole separation.
Electroweak symmetry breaking: Top quard condensates
Bardeen, W.A.
1990-12-01
The fundamental mechanisms for the dynamical breaking of the electroweak gauge symmetries remain a mystery. This paper examines the possible role of heavy fermions, particularly the top quark, in generating the observed electroweak symmetry breaking, the masses of the W and Z bosons and the masses of all observed quarks and leptons. 27 refs., 10 figs., 4 tabs.
Gauge Theories of Vector Particles
DOE R&D Accomplishments Database
Glashow, S. L.; Gell-Mann, M.
1961-04-24
The possibility of generalizing the Yang-Mills trick is examined. Thus we seek theories of vector bosons invariant under continuous groups of coordinate-dependent linear transformations. All such theories may be expressed as superpositions of certain "simple" theories; we show that each "simple theory is associated with a simple Lie algebra. We may introduce mass terms for the vector bosons at the price of destroying the gauge-invariance for coordinate-dependent gauge functions. The theories corresponding to three particular simple Lie algebras - those which admit precisely two commuting quantum numbers - are examined in some detail as examples. One of them might play a role in the physics of the strong interactions if there is an underlying super-symmetry, transcending charge independence, that is badly broken. The intermediate vector boson theory of weak interactions is discussed also. The so-called "schizon" model cannot be made to conform to the requirements of partial gauge-invariance.
Symmetry enrichment in three-dimensional topological phases
NASA Astrophysics Data System (ADS)
Ning, Shang-Qiang; Liu, Zheng-Xin; Ye, Peng
2016-12-01
While two-dimensional symmetry-enriched topological phases (SETs ) have been studied intensively and systematically, three-dimensional ones are still open issues. We propose an algorithmic approach of imposing global symmetry Gs on gauge theories (denoted by GT) with gauge group Gg. The resulting symmetric gauge theories are dubbed "symmetry-enriched gauge theories" (SEG), which may be served as low-energy effective theories of three-dimensional symmetric topological quantum spin liquids. We focus on SEGs with gauge group Gg=ZN1×ZN2×⋯ and onsite unitary symmetry group Gs=ZK1×ZK2×⋯ or Gs=U (1 ) ×ZK 1×⋯ . Each SEG(Gg,Gs) is described in the path-integral formalism associated with certain symmetry assignment. From the path-integral expression, we propose how to physically diagnose the ground-state properties (i.e., SET orders) of SEGs in experiments of charge-loop braidings (patterns of symmetry fractionalization) and the mixed multiloop braidings among deconfined loop excitations and confined symmetry fluxes. From these symmetry-enriched properties, one can obtain the map from SEGs to SETs . By giving full dynamics to background gauge fields, SEGs may be eventually promoted to a set of new gauge theories (denoted by GT*). Based on their gauge groups, GT*s may be further regrouped into different classes, each of which is labeled by a gauge group Gg*. Finally, a web of gauge theories involving GT,SEG,SET, and GT* is achieved. We demonstrate the above symmetry-enrichment physics and the web of gauge theories through many concrete examples.
Asymptotically Free Gauge Theories. I
DOE R&D Accomplishments Database
Wilczek, Frank; Gross, David J.
1973-07-01
Asymptotically free gauge theories of the strong interactions are constructed and analyzed. The reasons for doing this are recounted, including a review of renormalization group techniques and their application to scaling phenomena. The renormalization group equations are derived for Yang-Mills theories. The parameters that enter into the equations are calculated to lowest order and it is shown that these theories are asymptotically free. More specifically the effective coupling constant, which determines the ultraviolet behavior of the theory, vanishes for large space-like momenta. Fermions are incorporated and the construction of realistic models is discussed. We propose that the strong interactions be mediated by a "color" gauge group which commutes with SU(3)xSU(3). The problem of symmetry breaking is discussed. It appears likely that this would have a dynamical origin. It is suggested that the gauge symmetry might not be broken, and that the severe infrared singularities prevent the occurrence of non-color singlet physical states. The deep inelastic structure functions, as well as the electron position total annihilation cross section are analyzed. Scaling obtains up to calculable logarithmic corrections, and the naive lightcone or parton model results follow. The problems of incorporating scalar mesons and breaking the symmetry by the Higgs mechanism are explained in detail.
Topological orders with global gauge anomalies
NASA Astrophysics Data System (ADS)
You, Yi-Zhuang; Xu, Cenke
2015-08-01
By definition, the physics of the d -dimensional (dim) boundary of a (d +1 ) -dim symmetry protected topological (SPT) state cannot be realized as itself on a d -dim lattice. If the symmetry of the system is unitary, then a formal way to determine whether a d -dim theory must be a boundary or not, is to couple this theory to a gauge field (or to "gauge" its symmetry), and check if there is a gauge anomaly. In this paper we discuss the following question: Can the boundary of a SPT state be driven into a fully gapped topological order which preserves all the symmetries? We argue (conjecture) that if the gauge anomaly of the boundary is "perturbative," then the boundary must remain gapless; while if the boundary only has global gauge anomaly but no perturbative anomaly, then it is possible to gap out the boundary by driving it into a topological state, when d ≥2 . We will demonstrate this conjecture with two examples: (1) the 3 d spin-1/2 chiral fermion with the well-known Witten's global anomaly [Phys. Lett. 117, 324 (1982), 10.1016/0370-2693(82)90728-6], which can be realized on the boundary of a 4 d topological superconductor with SU(2) or U (1 ) ⋊Z2 symmetry; and (2) the 4 d boundary of a 5 d topological superconductor with the same symmetry. We show that these boundary systems can be driven into a fully gapped Z2 N topological order with topological degeneracy, but this Z2 N topological order cannot be future driven into a trivial confined phase that preserves all the symmetries due to some special properties of its topological defects. Our study also leads to exotic states of matter in pure 3 d space.
NASA Astrophysics Data System (ADS)
Nucci, M. C.
2016-09-01
We review some of our recent work devoted to the problem of quantization with preservation of Noether symmetries, finding hidden linearity in superintegrable systems, and showing that nonlocal symmetries are in fact local. In particular, we derive the Schrödinger equation for the isochronous Calogero goldfish model using its relation to Darwin equation. We prove the linearity of a classical superintegrable system on a plane of nonconstant curvature. We find the Lie point symmetries that correspond to the nonlocal symmetries (also reinterpreted as λ-symmetries) of the Riccati chain.
Renormalization In Quantum Gauge Theory Using Zeta-Function Method
Chiritoiu, Viorel; Zet, Gheorghe
2009-05-22
It is possible to consider space-time symmetries (for example Poincare or de Sitter) as purely inner symmetries. A formulation of the de Sitter symmetry as purely inner symmetry defined on a fixed Minkowski space-time is presented. We define the generators of the de Sitter group and write the equations of structure using a constant deformation parameter {lambda}. Local gauge transformations and corresponding covariant derivative depending on gauge fields are obtained. The method of generalized zeta-function is used to realize the renormalization. An effective integral of action is obtained and a comparison with other results is given.
Gauge-independent Higgs mechanism and the implications for quark confinement
NASA Astrophysics Data System (ADS)
Kondo, Kei-Ichi
2017-03-01
We propose a gauge-invariant description for the Higgs mechanism by which a gauge boson acquires the mass. We do not need to assume spontaneous breakdown of gauge symmetry signaled by a non-vanishing vacuum expectation value of the scalar field. In fact, we give a manifestly gauge-invariant description of the Higgs mechanism in the operator level, which does not rely on spontaneous symmetry breaking. For concreteness, we discuss the gauge-Higgs models with U(1) and SU(2) gauge groups explicitly. This enables us to discuss the confinement-Higgs complementarity from a new perspective.
2d Affine XY-Spin Model/4d Gauge Theory Duality and Deconfinement
Anber, Mohamed M.; Poppitz, Erich; Unsal, Mithat; /SLAC /Stanford U., Phys. Dept. /San Francisco State U.
2012-08-16
We introduce a duality between two-dimensional XY-spin models with symmetry-breaking perturbations and certain four-dimensional SU(2) and SU(2) = Z{sub 2} gauge theories, compactified on a small spatial circle R{sup 1,2} x S{sup 1}, and considered at temperatures near the deconfinement transition. In a Euclidean set up, the theory is defined on R{sup 2} x T{sup 2}. Similarly, thermal gauge theories of higher rank are dual to new families of 'affine' XY-spin models with perturbations. For rank two, these are related to models used to describe the melting of a 2d crystal with a triangular lattice. The connection is made through a multi-component electric-magnetic Coulomb gas representation for both systems. Perturbations in the spin system map to topological defects in the gauge theory, such as monopole-instantons or magnetic bions, and the vortices in the spin system map to the electrically charged W-bosons in field theory (or vice versa, depending on the duality frame). The duality permits one to use the two-dimensional technology of spin systems to study the thermal deconfinement and discrete chiral transitions in four-dimensional SU(N{sub c}) gauge theories with n{sub f} {ge} 1 adjoint Weyl fermions.
Noether's therorem for local gauge transformations
Karatas, D.L.; Kowalski, K.L.
1989-05-22
The variational methods of classical field theory may be applied to any theory with an action which is invariant under local gauge transformations. What is the significance of the resulting Noether current. This paper examines such currents for both Abelian and non-Abelian gauge theories and provides an explanation for their form and limited range of physical significance on a level accessible to those with a basic knowledge of classical field theory. Several of the more subtle aspects encountered in the application of the residual local gauge symmetry found by Becchi, Rouet, Stora, and Tyutin are also considered in detail in a self-contained manner. 23 refs.
Flavor mixing in gauge-Higgs unification
Adachi, Y.; Kurahashi, N.; Lim, C. S.; Maru, N.; Tanabe, K.
2012-07-27
Gauge-Higgs unification is the fascinating scenario solving the hierarchy problem without supersymmetry. In this scenario, the Standard Model (SM) Higgs doublet is identified with extra component of the gauge field in higher dimensions and its mass becomes finite and stable under quantum corrections due to the higher dimensional gauge symmetry. On the other hand, Yukawa coupling is provided by the gauge coupling, which seems to mean that the flavor mixing and CP violation do not arise at it stands. In this talk, we discuss that the flavor mixing is originated from simultaneously non-diagonalizable bulk and brane mass matrices. Then, this mechanism is applied to various flavor changing neutral current (FCNC) processes via Kaluza-Klein (KK) gauge boson exchange at tree level and constraints for compactification scale are obtained.
Supersymmetry breaking from superstrings and the gauge hierarchy
Gaillard, M.K. California Univ., Berkeley, CA . Dept. of Physics)
1990-07-11
The gauge hierarchy problem is reviewed and a class of effective field theories obtained from superstrings is described. These are characterized by a classical symmetry, related to the space-time duality of string theory, that is responsible for the suppression of observable supersymmetry breaking effects. At the quantum level, the symmetry is broken by anomalies that provide the seed of observable supersymmetry breaking, and an acceptably large gauge hierarchy may be generated. 39 refs.
NASA Astrophysics Data System (ADS)
Loebbert, Florian
2016-08-01
In these introductory lectures we discuss the topic of Yangian symmetry from various perspectives. Forming the classical counterpart of the Yangian and an extension of ordinary Noether symmetries, first the concept of nonlocal charges in classical, two-dimensional field theory is reviewed. We then define the Yangian algebra following Drinfel’d's original motivation to construct solutions to the quantum Yang-Baxter equation. Different realizations of the Yangian and its mathematical role as a Hopf algebra and quantum group are discussed. We demonstrate how the Yangian algebra is implemented in quantum, two-dimensional field theories and how its generators are renormalized. Implications of Yangian symmetry on the two-dimensional scattering matrix are investigated. We furthermore consider the important case of discrete Yangian symmetry realized on integrable spin chains. Finally we give a brief introduction to Yangian symmetry in planar, four-dimensional super Yang-Mills theory and indicate its impact on the dilatation operator and tree-level scattering amplitudes. These lectures are illustrated by several examples, in particular the two-dimensional chiral Gross-Neveu model, the Heisenberg spin chain and { N }=4 superconformal Yang-Mills theory in four dimensions.
Discrete symmetries in covariant loop quantum gravity
NASA Astrophysics Data System (ADS)
Rovelli, Carlo; Wilson-Ewing, Edward
2012-09-01
We study time-reversal and parity—on the physical manifold and in internal space—in covariant loop gravity. We consider a minor modification of the Holst action which makes it transform coherently under such transformations. The classical theory is not affected but the quantum theory is slightly different. In particular, the simplicity constraints are slightly modified and this restricts orientation flips in a spin foam to occur only across degenerate regions, thus reducing the sources of potential divergences.
Noether symmetries and duality transformations in cosmology
NASA Astrophysics Data System (ADS)
Paliathanasis, Andronikos; Capozziello, Salvatore
2016-09-01
We discuss the relation between Noether (point) symmetries and discrete symmetries for a class of minisuperspace cosmological models. We show that when a Noether symmetry exists for the gravitational Lagrangian, then there exists a coordinate system in which a reversal symmetry exists. Moreover, as far as concerns, the scale-factor duality symmetry of the dilaton field, we show that it is related to the existence of a Noether symmetry for the field equations, and the reversal symmetry in the normal coordinates of the symmetry vector becomes scale-factor duality symmetry in the original coordinates. In particular, the same point symmetry as also the same reversal symmetry exists for the Brans-Dicke scalar field with linear potential while now the discrete symmetry in the original coordinates of the system depends on the Brans-Dicke parameter and it is a scale-factor duality when ωBD = 1. Furthermore, in the context of the O’Hanlon theory for f(R)-gravity, it is possible to show how a duality transformation in the minisuperspace can be used to relate different gravitational models.
Parity anomalies in gauge theories in 2 + 1 dimensions
Rao, S.; Yahalom, R.
1986-01-01
We show that the introduction of massless fermions in an abelian gauge theory in 2+1 dimensions does not lead to any parity anomaly despite a non-commutativity of limits in the structure function of the odd part of the vacuum polarization tensor. However, parity anomaly does exist in non-abelian theories due to a conflict between gauge invariance under large gauge transformations and the parity symmetry. 6 refs.
Generalized mixing angles in gauge theories with natural flavor conservation
Rothman, Arthur C.; Kang, Kyungsik
1981-01-01
A number of theorems, relating Natural Flavor Conservation and Calculability are proven for general gauge models of the weak and electromagnetic interactions with an unbroken U(1) symmetry. The concept of nontriviality - a necessary condition that all naturally flavor conserving gauge models must obey in order to have nontrivial mixing angles - is introduced. It is found that naturality groups guaranteeing Natural Flavor Conservation cannot generate meaningful mixing angles in any gauge model.
Discretisation errors in Landau gauge on the lattice
Frederic D.R. Bonnet; Patrick O. Bowman; Derek B. Leinweber; Anthony G. Williams; David G. Richards
1999-05-01
Lattice discretization errors in the Landau gauge condition are examined. An improved gauge fixing algorithm in which O(a{sup 2}) errors are removed is presented. O(a{sup 2}) improvement of the gauge fixing condition improves comparison with continuum Landau gauge in two ways: (1) through the elimination of O(a{sup 2}) errors and (2) through a secondary effect of reducing the size of higher-order errors. These results emphasize the importance of implementing an improved gauge fixing condition.
Vacuum stability and radiative electroweak symmetry breaking in an SO(10) dark matter model
NASA Astrophysics Data System (ADS)
Mambrini, Yann; Nagata, Natsumi; Olive, Keith A.; Zheng, Jiaming
2016-06-01
Vacuum stability in the Standard Model is problematic as the Higgs quartic self-coupling runs negative at a renormalization scale of about 1010 GeV . We consider a nonsupersymmetric SO(10) grand unification model for which gauge coupling unification is made possible through an intermediate scale gauge group, Gint=SU (3 )C⊗SU (2 )L⊗SU (2 )R⊗U (1 )B -L . Gint is broken by the vacuum expectation value of a 126 of SO(10) which not only provides for neutrino masses through the seesaw mechanism but also preserves a discrete Z2 that can account for the stability of a dark matter candidate, here taken to be the Standard Model singlet component of a bosonic 16 . We show that in addition to these features the model insures the positivity of the Higgs quartic coupling through its interactions to the dark matter multiplet and 126 . We also show that the Higgs mass squared runs negative, triggering electroweak symmetry breaking. Thus, the vacuum stability is achieved along with radiative electroweak symmetry breaking and captures two more important elements of supersymmetric models without low-energy supersymmetry. The conditions for perturbativity of quartic couplings and for radiative electroweak symmetry breaking lead to tight upper and lower limits on the dark matter mass, respectively, and this dark matter mass region (1.35-2 TeV) can be probed in future direct detection experiments.
Moubayidin, Laila; Østergaard, Lars
2015-09-01
985 I. 985 II. 986 III. 987 IV. 988 V. 989 989 References 989 SUMMARY: The development of multicellular organisms depends on correct establishment of symmetry both at the whole-body scale and within individual tissues and organs. Setting up planes of symmetry must rely on communication between cells that are located at a distance from each other within the organism, presumably via mobile morphogenic signals. Although symmetry in nature has fascinated scientists for centuries, it is only now that molecular data to unravel mechanisms of symmetry establishment are beginning to emerge. As an example we describe the genetic and hormonal interactions leading to an unusual bilateral-to-radial symmetry transition of an organ in order to promote reproduction.
Spontaneous breaking of the BRST symmetry in the ABJM theory
NASA Astrophysics Data System (ADS)
Faizal, Mir; Upadhyay, Sudhaker
2014-09-01
In this paper, we will analyze the ghost condensation in the ABJM theory. We will perform our analysis in N=1 superspace. We show that in the Delbourgo-Jarvis-Baulieu-Thierry-Mieg gauge the spontaneous breaking of BRST symmetry can occur in the ABJM theory. This spontaneous breaking of BRST symmetry is caused by ghost-anti-ghost condensation. We will also show that in the ABJM theory, the ghost-anti-ghost condensates remain present in the modified abelian gauge. Thus, the spontaneous breaking of BRST symmetry in ABJM theory can even occur in the modified abelian gauge.
Spontaneous breaking of nilpotent symmetry in boundary BLG theory
NASA Astrophysics Data System (ADS)
Upadhyay, Sudhaker
2015-09-01
We exploit boundary term to preserve the supersymmetric gauge invariance of Bagger-Lambert-Gustavsson (BLG) theory. The fermionic rigid BRST and anti-BRST symmetries are studied in linear and nonlinear gauges. Remarkably, for Delbourgo-Jarvis-Baulieu-Thierry-Mieg (DJBTM) type gauge the spontaneous breaking of BRST symmetry occurs in the BLG theory. The responsible guy for such spontaneous breaking is ghost-antighost condensation. Further, we discuss the ghost-antighost condensates in the modified maximally Abelian (MMA) gauge in the BLG theory.
Quantum Field Theory Tools:. a Mechanism of Mass Generation of Gauge Fields
NASA Astrophysics Data System (ADS)
Flores-Baez, F. V.; Godina-Nava, J. J.; Ordaz-Hernandez, G.
We present a simple mechanism for mass generation of gauge fields for the Yang-Mills theory, where two gauge SU(N)-connections are introduced to incorporate the mass term. Variations of these two sets of gauge fields compensate each other under local gauge transformations with the local gauge transformations of the matter fields, preserving gauge invariance. In this way the mass term of gauge fields is introduced without violating the local gauge symmetry of the Lagrangian. Because the Lagrangian has strict local gauge symmetry, the model is a renormalizable quantum model. This model, in the appropriate limit, comes from a class of universal Lagrangians which define a new massive Yang-Mills theories without Higgs bosons.
The role of symmetry in nuclear physics
NASA Astrophysics Data System (ADS)
Iachello, Francesco
2015-02-01
The role of discrete symmetries in nuclear physics is briefly reviewed within the context of the algebraic cluster model (ACM). The symmetries D3 (triangle) for 3α and Td (tetrahedron) for 4α are discussed and evidence shown for their occurrence in 12C (D3) and 16O (Td).
From symmetries to number theory
Tempesta, P.
2009-05-15
It is shown that the finite-operator calculus provides a simple formalism useful for constructing symmetry-preserving discretizations of quantum-mechanical integrable models. A related algebraic approach can also be used to define a class of Appell polynomials and of L series.
On lattice chiral gauge theories
NASA Technical Reports Server (NTRS)
Maiani, L.; Rossi, G. C.; Testa, M.
1991-01-01
The Smit-Swift-Aoki formulation of a lattice chiral gauge theory is presented. In this formulation the Wilson and other non invariant terms in the action are made gauge invariant by the coupling with a nonlinear auxilary scalar field, omega. It is shown that omega decouples from the physical states only if appropriate parameters are tuned so as to satisfy a set of BRST identities. In addition, explicit ghost fields are necessary to ensure decoupling. These theories can give rise to the correct continuum limit. Similar considerations apply to schemes with mirror fermions. Simpler cases with a global chiral symmetry are discussed and it is shown that the theory becomes free at decoupling. Recent numerical simulations agree with those considerations.
SU{sub {ital q}}(2) lattice gauge theory
Bimonte, G.; Stern, A.; Vitale, P.
1996-07-01
We reformulate the Hamiltonian approach to lattice gauge theories such that, at the classical level, the gauge group does not act canonically, but instead as a Poisson-Lie group. At the quantum level, the symmetry gets promoted to a quantum group gauge symmetry. The theory depends on two parameters: the deformation parameter {lambda} and the lattice spacing {ital a}. We show that the system of Kogut and Susskind is recovered when {lambda}{r_arrow}0, while QCD is recovered in the continuum limit (for any {lambda}). We, thus, have the possibility of having a two-parameter regularization of QCD. {copyright} {ital 1996 The American Physical Society.}
Sufficient symmetry conditions for Topological Quantum Order.
Nussinov, Zohar; Ortiz, Gerardo
2009-10-06
We prove sufficient conditions for Topological Quantum Order at zero and finite temperatures. The crux of the proof hinges on the existence of low-dimensional Gauge-Like Symmetries, thus providing a unifying framework based on a symmetry principle. These symmetries may be actual invariances of the system, or may emerge in the low-energy sector. Prominent examples of Topological Quantum Order display Gauge-Like Symmetries. New systems exhibiting such symmetries include Hamiltonians depicting orbital-dependent spin exchange and Jahn-Teller effects in transition metal orbital compounds, short-range frustrated Klein spin models, and p+ip superconducting arrays. We analyze the physical consequences of Gauge-Like Symmetries (including topological terms and charges) and show the insufficiency of the energy spectrum, topological entanglement entropy, maximal string correlators, and fractionalization in establishing Topological Quantum Order. General symmetry considerations illustrate that not withstanding spectral gaps, thermal fluctuations may impose restrictions on suggested quantum computing schemes. Our results allow us to go beyond standard topological field theories and engineer systems with Topological Quantum Order.
Constraints on gauge-Higgs unification models at the LHC
NASA Astrophysics Data System (ADS)
Kitazawa, Noriaki; Sakai, Yuki
2016-02-01
We examine the possibility of observing the Kaluza-Klein (KK) gluons in gauge-Higgs unification models at the LHC with the energy s=14 TeV. We consider a benchmark model with the gauge symmetry SU(3)C×SU(3)W in five-dimensional spacetime, where SU(3)C is the gauge symmetry of the strong interaction and SU(3)W is that for the electroweak interaction and a Higgs doublet field. It is natural in general to introduce SU(3)C gauge symmetry in five-dimensional spacetime as well as SU(3)W gauge symmetry in gauge-Higgs unification (GHU) models. Since the fifth dimension is compactified to S1/Z 2 orbifold, there are KK modes of gluons in low-energy effective theory in four-dimensional spacetime. We investigate the resonance contribution of the first KK gluon to dijet invariant mass distribution at the LHC, and provide signal-to-noise ratios in various cases of KK gluon masses and kinematical cuts. Although the results are given in a specific benchmark model, we discuss their application to general GHU models with KK gluons. GHU models can be verified or constrained through the physics of the strong interaction, though they are proposed to solve the naturalness problem in electroweak symmetry breaking.
Nonlinear realization and hidden local symmetries
NASA Astrophysics Data System (ADS)
Bando, Masako; Kugo, Taichiro; Yamawaki, Koichi
1988-07-01
The idea of dynamical gauge bosons of hidden local symmetries in nonlinear sigma models is reviewed. Starting with a fresh look at the Goldstone theorem and low energy theorems, we present a modern review of the general theory of nonlinear realization both in nonsupersymmetric and supersymmetric cases. We then show that any nonlinear sigma model based on the manifold G/ H is gauge equivalent to a “linear” model possessing a Gglobal × Hlocal symmetry, Hlocal being a hidden local symmetry. The corresponding supersymmetric formulation is also presented. The above gauge equivalence can be extended to a model having a larger symmetry Gglobal × Glocal. Also reviewed are dynamical calculatio ns showing that in some two-, three- and four-dimensional models, the gauge bosons of the hidden local symmetries acquire the kinetic terms via quantum effects, thus becoming “dynamical”. We suggest that such a dynamical gauge boson may be a rather common phenomenon realized in Nature. As a realistic example, we examine the QCD case where we identify the vector mesons (ϱ,ω,ф,K ∗) with the dynamical gauge bosons of the hidden U(3) v local symmetry in the U(3) L × U(3) R/U(3) V nonlinear sigma model. The totality of the vector meson phenomenology seems to support our basic idea. The axial-vector mesons are also incorporated into our framework. Also given is a brief sketch of some applications of this formalism to unified models beyond the standard model, such as technicolor, composite W/Z boson and supergravity models.
Dual technicolor with hidden local symmetry
Belitsky, A. V.
2010-08-15
We consider a dual description of the technicolor-like gauge theory within the D4/D8-brane configuration with varying confinement and electroweak symmetry breaking scales. Constructing an effective truncated model valid below a certain cutoff, we identify the particle spectrum with Kaluza-Klein modes of the model in a manner consistent with the hidden local symmetry. Integrating out heavy states, we find that the low-energy action receives nontrivial corrections stemming from the mixing between standard model and heavy gauge bosons, which results in reduction of oblique parameters.
Gauge Properties Of The Guiding Center Variational Symplectic Integrator
J. Squire, H. Qin and W. Tang
2012-03-05
Recently, variational symplectic algorithms have been developed for the long-time simulation of charged particles in magnetic fields1-3. As a direct consequence of their derivation from a discrete variational principle, these algorithms have very good long-time energy conservation, as well as exactly preserving discrete momenta. We present stability results for these algorithms, focusing on understanding how explicit variational integrators can be designed for this type of system. It is found that for explicit algorithms an instability arises because the discrete symplectic structure does not become the continuous structure in the t → 0 limit. We examine how a generalized gauge transformation can be used to put the Lagrangian in the "antisymmetric discretization gauge," in which the discrete symplectic structure has the correct form, thus eliminating the numerical instability. Finally, it is noted that the variational guiding center algorithms are not electromagnetically gauge invariant. By designing a model discrete Lagrangian, we show that the algorithms are approximately gauge invariant as long as A and are relatively smooth. A gauge invariant discrete Lagrangian is very important in a variational particle-in-cell algorithm where it ensures current continuity and preservation of Gauss's law4.
Gauge properties of the guiding center variational symplectic integrator
NASA Astrophysics Data System (ADS)
Squire, J.; Qin, H.; Tang, W. M.
2012-05-01
Variational symplectic algorithms have recently been developed for carrying out long-time simulation of charged particles in magnetic fields [H. Qin and X. Guan, Phys. Rev. Lett. 100, 035006 (2008); H. Qin, X. Guan, and W. Tang, Phys. Plasmas (2009); J. Li, H. Qin, Z. Pu, L. Xie, and S. Fu, Phys. Plasmas 18, 052902 (2011)]. As a direct consequence of their derivation from a discrete variational principle, these algorithms have very good long-time energy conservation, as well as exactly preserving discrete momenta. We present stability results for these algorithms, focusing on understanding how explicit variational integrators can be designed for this type of system. It is found that for explicit algorithms, an instability arises because the discrete symplectic structure does not become the continuous structure in the t →0 limit. We examine how a generalized gauge transformation can be used to put the Lagrangian in the "antisymmetric discretization gauge," in which the discrete symplectic structure has the correct form, thus eliminating the numerical instability. Finally, it is noted that the variational guiding center algorithms are not electromagnetically gauge invariant. By designing a model discrete Lagrangian, we show that the algorithms are approximately gauge invariant as long as A and φ are relatively smooth. A gauge invariant discrete Lagrangian is very important in a variational particle-in-cell algorithm where it ensures current continuity and preservation of Gauss's law [J. Squire, H. Qin, and W. Tang (to be published)].
Dynamical supersymmetry breaking and late-time R symmetry breaking as the origin of cosmic inflation
NASA Astrophysics Data System (ADS)
Schmitz, Kai; Yanagida, Tsutomu T.
2016-10-01
Spontaneously broken supersymmetry (SUSY) and a vanishingly small cosmological constant imply that R symmetry must be spontaneously broken at low energies. Based on this observation, we suppose that, in the sector responsible for low-energy R symmetry breaking, a discrete R symmetry remains preserved at high energies and only becomes dynamically broken at relatively late times in the cosmological evolution, i.e., after the dynamical breaking of SUSY. Prior to R symmetry breaking, the Universe is then bound to be in a quasi-de Sitter phase—which offers a dynamical explanation for the occurrence of cosmic inflation. This scenario yields a new perspective on the interplay between SUSY breaking and inflation, which neatly fits into the paradigm of high-scale SUSY: inflation is driven by the SUSY-breaking vacuum energy density, while the chiral field responsible for SUSY breaking, the Polonyi field, serves as the inflaton. Because R symmetry is broken only after inflation, slow-roll inflation is not spoiled by otherwise dangerous gravitational corrections in supergravity. We illustrate our idea by means of a concrete example, in which both SUSY and R symmetry are broken by strong gauge dynamics and in which late-time R symmetry breaking is triggered by a small inflaton field value. In this model, the scales of inflation and SUSY breaking are unified, the inflationary predictions are similar to those of F-term hybrid inflation in supergravity, reheating proceeds via gravitino decay at temperatures consistent with thermal leptogenesis, and the sparticle mass spectrum follows from pure gravity mediation. Dark matter consists of thermally produced winos with a mass in the TeV range.
Gauge invariance and radiative corrections in an extra dimensional theory
NASA Astrophysics Data System (ADS)
Novales-Sánchez, H.; Toscano, J. J.
2011-04-01
The gauge structure of the four dimensional effective theory originated in a pure five dimensional Yang-Mills theory compactified on the orbifold S1 /Z2, is discussed on the basis of the BRST symmetry. If gauge parameters propagate in the bulk, the excited Kaluza-Klein (KK) modes are gauge fields and the four dimensional theory is gauge invariant only if the compactification is carried out by using curvatures as fundamental objects. The four dimensional theory is governed by two types of gauge transformations, one determined by the KK zero modes of the gauge parameters and the other by the excited ones. Within this context, a gauge-fixing procedure to quantize the KK modes that is covariant under the first type of gauge transformations is shown and the ghost sector induced by the gauge-fixing functions is presented. If the gauge parameters are confined to the usual four dimensional space-time, the known result in the literature is reproduced with some minor variants, although it is emphasized that the excited KK modes are not gauge fields, but matter fields transforming under the adjoint representation of SU4(N). A calculation of the one-loop contributions of the excited KK modes of the SUL(2) gauge group on the off-shell W+W-V, with V a photon or a Z boson, is exhibited. Such contributions are free of ultraviolet divergences and well-behaved at high energies.
Geometric interpretations of the Discrete Fourier Transform (DFT)
NASA Technical Reports Server (NTRS)
Campbell, C. W.
1984-01-01
One, two, and three dimensional Discrete Fourier Transforms (DFT) and geometric interpretations of their periodicities are presented. These operators are examined for their relationship with the two sided, continuous Fourier transform. Discrete or continuous transforms of real functions have certain symmetry properties. The symmetries are examined for the one, two, and three dimensional cases. Extension to higher dimension is straight forward.
Diffractive Scattering and Gauge/String Duality
Tan, Chung-I [Brown University, Providence, Rhode Island, United States
2016-07-12
High-energy diffractive scattering will be discussed based on Gauge/String duality. As shown by Brower, Polchinski, Strassler and Tan, the ubiquitous Pomeron emerges naturally in gauge theories with string-theoretical descriptions. Its existence is intimately tied to gluons, and also to the energy-momentum tensor. With a confining dual background metric, the Pomeron can be interpreted as a 'massive graviton'. In a single unified step, both its infrared and ultraviolet properties are dealt with, reflecting confinement and conformal symmetry respectively. An effective field theory for high-energy scattering can be constructed. Applications based on this approach will also be described.
Gauge fixing in higher-derivative gravity
NASA Astrophysics Data System (ADS)
Bartoli, A.; Julve, J.; Sánchez, E. J.
1999-07-01
Linearized 4-derivative gravity with a general gauge-fixing term is considered. By a Legendre transform and a suitable diagonalization procedure it is cast into a second-order equivalent form where the nature of the physical degrees of freedom, the gauge ghosts, the Weyl ghosts and the intriguing `third ghosts', characteristic to higher-derivative theories, is made explicit. The symmetries of the theory and the structure of the compensating Faddeev-Popov ghost sector exhibit non-trivial peculiarities. The unitarity breaking negative-norm Weyl ghosts, already present in the diff-invariant theory, are out of the reach of the ghost cancellation BRST mechanism.
Gauge invariant actions for string models
Banks, T.
1986-06-01
String models of unified interactions are elegant sets of Feynman rules for the scattering of gravitons, gauge bosons, and a host of massive excitations. The purpose of these lectures is to describe the progress towards a nonperturbative formulation of the theory. Such a formulation should make the geometrical meaning of string theory manifest and explain the many ''miracles'' exhibited by the string Feynman rules. There are some new results on gauge invariant observables, on the cosmological constant, and on the symmetries of interacting string field theory. 49 refs.
Entanglement in weakly coupled lattice gauge theories
NASA Astrophysics Data System (ADS)
Radičević, Ðorđe
2016-04-01
We present a direct lattice gauge theory computation that, without using dualities, demonstrates that the entanglement entropy of Yang-Mills theories with arbitrary gauge group G contains a generic logarithmic term at sufficiently weak coupling e. In two spatial dimensions, for a region of linear size r, this term equals 1/2 dim( G) log( e 2 r) and it dominates the universal part of the entanglement entropy. Such logarithmic terms arise from the entanglement of the softest mode in the entangling region with the environment. For Maxwell theory in two spatial dimensions, our results agree with those obtained by dualizing to a compact scalar with spontaneous symmetry breaking.
Massless gauge bosons other than the photon
Dobrescu, Bogdan A.; /Fermilab
2004-11-01
Gauge bosons associated with unbroken gauge symmetries, under which all standard model fields are singlets, may interact with ordinary matter via higher-dimensional operators. A complete set of dimension-six operators involving a massless U(1) field, {gamma}', and standard model fields is presented. The {mu} {yields} e{gamma}' decay, primordial nucleosynthesis, star cooling and other phenomena set lower limits on the scale of chirality-flip operators in the 1-15 TeV range, if the operators have coefficients given by the corresponding Yukawa couplings. Simple renormalizable models induce {gamma}' interactions with leptons or quarks at two loops, and may provide a cold dark matter candidate.
Liu, Ke; Nissinen, Jaakko; de Boer, Josko; Slager, Robert-Jan; Zaanen, Jan
2017-02-01
The paradigm of spontaneous symmetry breaking encompasses the breaking of the rotational symmetries O(3) of isotropic space to a discrete subgroup, i.e., a three-dimensional point group. The subgroups form a rich hierarchy and allow for many different phases of matter with orientational order. Such spontaneous symmetry breaking occurs in nematic liquid crystals, and a highlight of such anisotropic liquids is the uniaxial and biaxial nematics. Generalizing the familiar uniaxial and biaxial nematics to phases characterized by an arbitrary point-group symmetry, referred to as generalized nematics, leads to a large hierarchy of phases and possible orientational phase transitions. We discuss how a particular class of nematic phase transitions related to axial point groups can be efficiently captured within a recently proposed gauge theoretical formulation of generalized nematics [K. Liu, J. Nissinen, R.-J. Slager, K. Wu, and J. Zaanen, Phys. Rev. X 6, 041025 (2016)2160-330810.1103/PhysRevX.6.041025]. These transitions can be introduced in the model by considering anisotropic couplings that do not break any additional symmetries. By and large this generalizes the well-known uniaxial-biaxial nematic phase transition to any arbitrary axial point group in three dimensions. We find in particular that the generalized axial transitions are distinguished by two types of phase diagrams with intermediate vestigial orientational phases and that the window of the vestigial phase is intimately related to the amount of symmetry of the defining point group due to inherently growing fluctuations of the order parameter. This might explain the stability of the observed uniaxial-biaxial phases as compared to the yet to be observed other possible forms of generalized nematic order with higher point-group symmetries.
NASA Astrophysics Data System (ADS)
Liu, Ke; Nissinen, Jaakko; de Boer, Josko; Slager, Robert-Jan; Zaanen, Jan
2017-02-01
The paradigm of spontaneous symmetry breaking encompasses the breaking of the rotational symmetries O(3 ) of isotropic space to a discrete subgroup, i.e., a three-dimensional point group. The subgroups form a rich hierarchy and allow for many different phases of matter with orientational order. Such spontaneous symmetry breaking occurs in nematic liquid crystals, and a highlight of such anisotropic liquids is the uniaxial and biaxial nematics. Generalizing the familiar uniaxial and biaxial nematics to phases characterized by an arbitrary point-group symmetry, referred to as generalized nematics, leads to a large hierarchy of phases and possible orientational phase transitions. We discuss how a particular class of nematic phase transitions related to axial point groups can be efficiently captured within a recently proposed gauge theoretical formulation of generalized nematics [K. Liu, J. Nissinen, R.-J. Slager, K. Wu, and J. Zaanen, Phys. Rev. X 6, 041025 (2016), 10.1103/PhysRevX.6.041025]. These transitions can be introduced in the model by considering anisotropic couplings that do not break any additional symmetries. By and large this generalizes the well-known uniaxial-biaxial nematic phase transition to any arbitrary axial point group in three dimensions. We find in particular that the generalized axial transitions are distinguished by two types of phase diagrams with intermediate vestigial orientational phases and that the window of the vestigial phase is intimately related to the amount of symmetry of the defining point group due to inherently growing fluctuations of the order parameter. This might explain the stability of the observed uniaxial-biaxial phases as compared to the yet to be observed other possible forms of generalized nematic order with higher point-group symmetries.
Strain gauge installation tool
Conard, Lisa Marie
1998-01-01
A tool and a method for attaching a strain gauge to a test specimen by maaining alignment of, and applying pressure to, the strain gauge during the bonding of the gauge to the specimen. The tool comprises rigid and compliant pads attached to a spring-loaded clamp. The pads are shaped to conform to the specimen surface to which the gauge is to be bonded. The shape of the pads permits the tool to align itself to the specimen and to maintain alignment of the gauge to the specimen during the bond curing process. A simplified method of attaching a strain gauge is provided by use of the tool.
Quantum Symmetries and Exceptional Collections
NASA Astrophysics Data System (ADS)
Karp, Robert L.
2011-01-01
We study the interplay between discrete quantum symmetries at certain points in the moduli space of Calabi-Yau compactifications, and the associated identities that the geometric realization of D-brane monodromies must satisfy. We show that in a wide class of examples, both local and compact, the monodromy identities in question always follow from a single mathematical statement. One of the simplest examples is the {{mathbb Z}_5} symmetry at the Gepner point of the quintic, and the associated D-brane monodromy identity.
ERIC Educational Resources Information Center
Attanucci, Frank J.; Losse, John
2008-01-01
In a first calculus course, it is not unusual for students to encounter the theorems which state: If f is an even (odd) differentiable function, then its derivative is odd (even). In our paper, we prove some theorems which show how the symmetry of a continuous function f with respect to (i) the vertical line: x = a or (ii) with respect to the…
Discrete Variational Optimal Control
NASA Astrophysics Data System (ADS)
Jiménez, Fernando; Kobilarov, Marin; Martín de Diego, David
2013-06-01
This paper develops numerical methods for optimal control of mechanical systems in the Lagrangian setting. It extends the theory of discrete mechanics to enable the solutions of optimal control problems through the discretization of variational principles. The key point is to solve the optimal control problem as a variational integrator of a specially constructed higher dimensional system. The developed framework applies to systems on tangent bundles, Lie groups, and underactuated and nonholonomic systems with symmetries, and can approximate either smooth or discontinuous control inputs. The resulting methods inherit the preservation properties of variational integrators and result in numerically robust and easily implementable algorithms. Several theoretical examples and a practical one, the control of an underwater vehicle, illustrate the application of the proposed approach.
Gauge engineering and propagators
NASA Astrophysics Data System (ADS)
Maas, Axel
2017-03-01
Beyond perturbation theory gauge-fixing becomes more involved due to the Gribov-Singer ambiguity: The appearance of additional gauge copies requires to define a procedure how to handle them. For the case of Landau gauge the structure and properties of these additional gauge copies will be investigated. Based on these properties gauge conditions are constructed to account for these gauge copies. The dependence of the propagators on the choice of these complete gauge-fixings will then be investigated using lattice gauge theory for Yang-Mills theory. It is found that the implications for the infrared, and to some extent mid-momentum behavior, can be substantial. In going beyond the Yang-Mills case it turns out that the influence of matter can generally not be neglected. This will be briefly discussed for various types of matter.
Kim, Hyung Do
2006-11-28
We consider gauge messenger models in which X and Y gauge bosons and gauginos are messengers of supersymmetry breaking. In simple gauge messenger models, all the soft parameters except {mu} and B{mu} are calculated in terms of a single scale parameter MSUSY which is proportional to F / MGUT. Unique prediction on dark matter in gauge messenger models is discussed. (Based on hep-ph/0601036 and hep-ph/0607169)
A Study of Confinement and Dynamical Chiral Symmetry Breaking in QED3
Sanchez, Saul; Raya, Alfredo; Bashir, Adnan
2009-04-20
We study the gauge invariance of physical observables related to confinement and dynamical chiral symmetry breaking in unquenched QED3 for a simple truncation of the corresponding Schwinger-Dyson equations in arbitrary covariant gauges. An explicit implementation of Landau-Khalatnikov-Fradkin transformations renders these observables gauge independent.
Gauged flavor, supersymmetry and grand unification
NASA Astrophysics Data System (ADS)
Mohapatra, Rabindra N.
2012-07-01
I review a recent work on gauged flavor with left-right symmetry, where all masses and all Yukawa couplings owe their origin to spontaneous flavor symmetry breaking. This is suggested as a precursor to a full understanding of flavor of quarks and leptons. An essential ingredient of this approach is the existence of heavy vector-like fermions, which is the home of flavor, which subsequently gets transmitted to the familiar quarks and leptons via the seesaw mechanism. I then discuss implications of extending this idea to include supersymmetry and finally speculate on a possible grand unified model based on the gauge group SU(5)L×SU(5)R which provides a group theoretic origin for the vector-like fermions.
Applications of chiral symmetry
Pisarski, R.D.
1995-03-01
The author discusses several topics in the applications of chiral symmetry at nonzero temperature. First, where does the rho go? The answer: up. The restoration of chiral symmetry at a temperature T{sub {chi}} implies that the {rho} and a{sub 1} vector mesons are degenerate in mass. In a gauged linear sigma model the {rho} mass increases with temperature, m{sub {rho}}(T{sub {chi}}) > m{sub {rho}}(0). The author conjectures that at T{sub {chi}} the thermal {rho} - a{sub 1}, peak is relatively high, at about {approximately}1 GeV, with a width approximately that at zero temperature (up to standard kinematic factors). The {omega} meson also increases in mass, nearly degenerate with the {rho}, but its width grows dramatically with temperature, increasing to at least {approximately}100 MeV by T{sub {chi}}. The author also stresses how utterly remarkable the principle of vector meson dominance is, when viewed from the modern perspective of the renormalization group. Secondly, he discusses the possible appearance of disoriented chiral condensates from {open_quotes}quenched{close_quotes} heavy ion collisions. It appears difficult to obtain large domains of disoriented chiral condensates in the standard two flavor model. This leads to the last topic, which is the phase diagram for QCD with three flavors, and its proximity to the chiral critical point. QCD may be very near this chiral critical point, and one might thereby generated large domains of disoriented chiral condensates.
Possible violations of spacetime symmetries
NASA Astrophysics Data System (ADS)
Urrutia, Luis
2016-10-01
The identification of symmetries has played a fundamental role in our understanding of physical phenomena. Nevertheless, in most cases such symmetries constitute only a zeroth-order approximation and they need to be broken so that the predictions of the theory are consistent with experimental observation. In particular, the almost sacred CPT and Lorentz symmetries, which are certainly part of the fundamental ideas of modern physics, need to be probed experimentally. Recently, such efforts have been intensified because different theoretical approaches aiming to understand the microstructure of space-time suggest the possibility that such symmetries could present minute violations. Up to now, and with increasing experimental sensitivities, no signs of violation have been found. Nevertheless, we observe that even the persistence of such negative results will have a profound impact. On one hand, they will provide those symmetries with a firm experimental basis. On the other, they will set stringent experimental bounds to be compared with the possible emergence of such violations in quantum gravity models based upon a discrete structure of space. We present a very general perspective of the research on Lorentz symmetry breaking, together with a review of a few specific topics.
Seiberg duality versus hidden local symmetry
NASA Astrophysics Data System (ADS)
Abel, Steven; Barnard, James
2012-05-01
It is widely believed that the emergent magnetic gauge symmetry of SQCD is analogous to a hidden local symmetry (HLS). We explore this idea in detail, deriving the entire (spontaneously broken) magnetic theory by applying the HLS formalism to spontaneously broken SU( N) SQCD. We deduce the Kähler potential in the HLS description, and show that gauge and flavour symmetry are smoothly restored along certain scaling directions in moduli space. We propose that it is these symmetry restoring directions, associated with the R-symmetry of the theory, that allow full Seiberg duality. Reconsidering the origin of the magnetic gauge bosons as the ρ-mesons of the electric theory, colour-flavour locking allows a simple determination of the parameter a. Its value continuously interpolates between a = 2 on the baryonic branch of moduli space — corresponding to "vector meson dominance" — and a = 1 on the mesonic branch. Both limiting values are consistent with previous results in the literature. The HLS formalism is further applied to SO and Sp groups, where the usual Seiberg duals are recovered, as well as adjoint SQCD. Finally we discuss some possible future applications, including (naturally) the unitarisation of composite W scattering, blended Higgs/technicolour models, real world QCD and non-supersymmetric dualities.
Geometric phase and gauge connection in polyatomic molecules.
Wittig, Curt
2012-05-14
Geometric phase is an interesting topic that is germane to numerous and varied research areas: molecules, optics, quantum computing, quantum Hall effect, graphene, and so on. It exists only when the system of interest interacts with something it perceives as exterior. An isolated system cannot display geometric phase. This article addresses geometric phase in polyatomic molecules from a gauge field theory perspective. Gauge field theory was introduced in electrodynamics by Fock and examined assiduously by Weyl. It yields the gauge field A(μ), particle-field couplings, and the Aharonov-Bohm phase, while Yang-Mills theory, the cornerstone of the standard model of physics, is a template for non-Abelian gauge symmetries. Electronic structure theory, including nonadiabaticity, is a non-Abelian gauge field theory with matrix-valued covariant derivative. Because the wave function of an isolated molecule must be single-valued, its global U(1) symmetry cannot be gauged, i.e., products of nuclear and electron functions such as χ(n)ψ(n) are forbidden from undergoing local phase transformation on R, where R denotes nuclear degrees of freedom. On the other hand, the synchronous transformations (first noted by Mead and Truhlar): ψ(n)→ψ(n)e(iζ) and simultaneously χ(n)→χ(n)e(-iζ), preserve single-valuedness and enable wave functions in each subspace to undergo phase transformation on R. Thus, each subspace is compatible with a U(1) gauge field theory. The central mathematical object is Berry's adiabatic connection i
Quenched domain wall QCD with DBW2 gauge action toward nucleon decay matrix element calculation
NASA Astrophysics Data System (ADS)
Aoki, Yasumichi
2001-10-01
The domain wall fermion action is a promising way to control chiral symmetry in lattice gauge theory. By the good chiral symmetry of this approach even at finite lattice spacing, one is able to extract hadronic matrix elements, like kaon weak matrix elements, for which the symmetry is extremely important. Ordinary fermions with poor chiral symmetry make calculation difficult because of the large mixing of operators with different chiral structure. Even though the domain wall fermion action with the simple Wilson gauge action has a good chiral symmetry, one can further improve the symmetry by using a different gauge action. We take a non-perturbatively improved action, the DBW2 action of the QCD Taro group. Hadron masses are systematically examined for a range of parameters. Application to nucleon decay matrix element is also discussed.
Light-cone gauge for 1 + 1 strings
NASA Astrophysics Data System (ADS)
Smith, Eric
1992-09-01
Explicit construction of the light-cone gauge quantum theory of bosonic strings in 1 + 1 space-time dimensions reveals unexpected structures. One is the existence of a gauge choice that gives a free action at the price of propagating ghosts and a nontrivial BRST charge. Fixing this gauge leaves a U(1) Kac-Moody algebra of residual symmetry, generated by a conformal tensor of rank two and a conformal scalar. Another is that the BRST charge made from these currents is nilpotent when the action includes a linear dilaton background, independent of the particular value of the dilaton gradient. Space-time Lorentz invariance in this theory is still elusive, however, because of the linear dilaton background and the nature of the gauge symmetries.
Cosmological properties of a gauged axion
Coriano, Claudio; Mariano, Antonio; Guzzi, Marco; Lazarides, George
2010-09-15
We analyze the most salient cosmological features of axions in extensions of the standard model with a gauged anomalous extra U(1) symmetry. The model is built by imposing the constraint of gauge invariance in the anomalous effective action, which is extended with Wess-Zumino counterterms. These generate axionlike interactions of the axions to the gauge fields and a gauged shift symmetry. The scalar sector is assumed to acquire a nonperturbative potential after inflation, at the electroweak phase transition, which induces a mixing of the Stueckelberg field of the model with the scalars of the electroweak sector, and at the QCD phase transition. We discuss the possible mechanisms of sequential misalignments which could affect the axions of these models, and generated, in this case, at both transitions. We compute the contribution of these particles to dark matter, quantifying their relic densities as a function of the Stueckelberg mass. We also show that models with a single anomalous U(1) in general do not account for the dark energy, due to the presence of mixed U(1)-SU(3) anomalies.
Unsal, Mithat
2007-03-06
We study the phase diagrams of N = {infinity} vector-like, asymptotically free gauge theories as a function of volume, on S{sup 3} x S{sup 1}. The theories of interest are the ones with fermions in two index representations [adjoint, (anti)symmetric, and bifundamental abbreviated as QCD(adj), QCD(AS/S) and QCD(BF)], and are interrelated via orbifold or orientifold projections. The phase diagrams reveal interesting phenomena such as disentangled realizations of chiral and center symmetry, confinement without chiral symmetry breaking, zero temperature chiral transitions, and in some cases, exotic phases which spontaneously break the discrete symmetries such as C, P, T as well as CPT. In a regime where the theories are perturbative, the deconfinement temperature in SYM, and QCD(AS/S/BF) coincide. The thermal phase diagrams of thermal orbifold QCD(BF), orientifold QCD(AS/S), and N = 1 SYM coincide, provided charge conjugation symmetry for QCD(AS/S) and Z{sub 2} interchange symmetry of the QCD(BF) are not broken in the phase continuously connected to R{sup 4} limit. When the S{sup 1} circle is endowed with periodic boundary conditions, the (nonthermal) phase diagrams of orbifold and orientifold QCD are still the same, however, both theories possess chirally symmetric phases which are absent in N=1 SYM. The match and mismatch of the phase diagrams depending on the spin structure of fermions along the S{sup 1} circle is naturally explained in terms of the necessary and sufficient symmetry realization conditions which determine the validity of the nonperturbative orbifold orientifold equivalence.
Compatible, energy and symmetry preserving 2D Lagrangian hydrodynamics in rz-cylindrical coordinates
Shashkov, Mikhail; Wendroff, Burton; Burton, Donald; Barlow, A; Hongbin, Guo
2009-01-01
We present a new discretization for 2D Lagrangian hydrodynamics in rz geometry (cylindrical coordinates) that is compatible, energy conserving and symmetry preserving. We describe discretization of the basic Lagrangian hydrodynamics equations.
Nilpotent symmetries in supergroup field cosmology
NASA Astrophysics Data System (ADS)
Upadhyay, Sudhaker
2015-04-01
In this paper, we study the gauge invariance of the third quantized supergroup field cosmology which is a model for multiverse. Further, we propose both the infinitesimal (usual) as well as the finite superfield-dependent BRST symmetry transformations which leave the effective theory invariant. The effects of finite superfield-dependent BRST transformations on the path integral (so-called void functional in the case of third quantization) are implemented. Within the finite superfield-dependent BRST formulation, the finite superfield-dependent BRST transformations with specific parameter switch the void functional from one gauge to another. We establish this result for the most general gauge with the help of explicit calculations which holds for all possible sets of gauge choices at both the classical and the quantum levels.
Nonintegrable semidiscrete Hirota equation: gauge-equivalent structures and dynamical properties.
Ma, Li-Yuan; Zhu, Zuo-Nong
2014-09-01
In this paper, we investigate nonintegrable semidiscrete Hirota equations, including the nonintegrable semidiscrete Hirota(-) equation and the nonintegrable semidiscrete Hirota(+) equation. We focus on the topics on gauge-equivalent structures and dynamical behaviors for the two nonintegrable semidiscrete equations. By using the concept of the prescribed discrete curvature, we show that, under the discrete gauge transformations, the nonintegrable semidiscrete Hirota(-) equation and the nonintegrable semidiscrete Hirota(+) equation are, respectively, gauge equivalent to the nonintegrable generalized semidiscrete modified Heisenberg ferromagnet equation and the nonintegrable generalized semidiscrete Heisenberg ferromagnet equation. We prove that the two discrete gauge transformations are reversible. We study the dynamical properties for the two nonintegrable semidiscrete Hirota equations. The exact spatial period solutions of the two nonintegrable semidiscrete Hirota equations are obtained through the constructions of period orbits of the stationary discrete Hirota equations. We discuss the topic regarding whether the spatial period property of the solution to the nonintegrable semidiscrete Hirota equation is preserved to that of the corresponding gauge-equivalent nonintegrable semidiscrete equations under the action of discrete gauge transformation. By using the gauge equivalent, we obtain the exact solutions to the nonintegrable generalized semidiscrete modified Heisenberg ferromagnet equation and the nonintegrable generalized semidiscrete Heisenberg ferromagnet equation. We also give the numerical simulations for the stationary discrete Hirota equations. We find that their dynamics are much richer than the ones of stationary discrete nonlinear Schrödinger equations.
P T -invariant Weyl semimetals in gauge-symmetric systems
NASA Astrophysics Data System (ADS)
Lepori, L.; Fulga, I. C.; Trombettoni, A.; Burrello, M.
2016-08-01
Weyl semimetals typically appear in systems in which either time-reversal (T ) or inversion (P ) symmetry is broken. Here we show that in the presence of gauge potentials these topological states of matter can also arise in fermionic lattices preserving both T and P . We analyze in detail the case of a cubic lattice model with π fluxes, discussing the role of gauge symmetries in the formation of Weyl points and the difference between the physical and the canonical T and P symmetries. We examine the robustness of this P T -invariant Weyl semimetal phase against perturbations that remove the chiral sublattice symmetries, and we discuss further generalizations. Finally, motivated by advances in ultracold-atom experiments and by the possibility of using synthetic magnetic fields, we study the effect of random perturbations of the magnetic fluxes, which can be compared to a local disorder in realistic scenarios.
History of electroweak symmetry breaking
NASA Astrophysics Data System (ADS)
Kibble, T. W. B.
2015-07-01
In this talk, I recall the history of the development of the unified electroweak theory, incorporating the symmetry-breaking Higgs mechanism, as I saw it from my standpoint as a member of Abdus Salam's group at Imperial College. I start by describing the state of physics in the years after the Second World War, explain how the goal of a unified gauge theory of weak and electromagnetic interactions emerged, the obstacles encountered, in particular the Goldstone theorem, and how they were overcome, followed by a brief account of more recent history, culminating in the historic discovery of the Higgs boson in 2012.
Strain gauge installation tool
Conard, L.M.
1998-06-16
A tool and a method are disclosed for attaching a strain gauge to a test specimen by maintaining alignment of, and applying pressure to, the strain gauge during the bonding of the gauge to the specimen. The tool comprises rigid and compliant pads attached to a spring-loaded clamp. The pads are shaped to conform to the specimen surface to which the gauge is to be bonded. The shape of the pads permits the tool to align itself to the specimen and to maintain alignment of the gauge to the specimen during the bond curing process. A simplified method of attaching a strain gauge is provided by use of the tool. 6 figs.
A simple example of a classical gauge transformation
NASA Technical Reports Server (NTRS)
Whitten, R. C.
1983-01-01
Attention is given to the manner in which the interaction of a gravitational field with a diffusing gas is induced by a gauge transformation. Since the gas can be thought of as a field, the diffusion process may be represented by a Lagrangian density with the symmetry property of invariance under translation. While this property is lost when the field interacts with a static gravitational field, it is formally restored when an appropriate gauge transformation is performed. This ascription of field properties to a gas offers an illuminating illustration of the coupling of matter to a gauge field within the context of classical mechanics.
Composite gauge-bosons made of fermions
NASA Astrophysics Data System (ADS)
Suzuki, Mahiko
2016-07-01
We construct a class of Abelian and non-Abelian local gauge theories that consist only of matter fields of fermions. The Lagrangian is local and does not contain an auxiliary vector field nor a subsidiary condition on the matter fields. It does not involve an extra dimension nor supersymmetry. This Lagrangian can be extended to non-Abelian gauge symmetry only in the case of SU(2) doublet matter fields. We carry out an explicit diagrammatic computation in the leading 1 /N order to show that massless spin-one bound states appear with the correct gauge coupling. Our diagram calculation exposes the dynamical features that cannot be seen in the formal auxiliary vector-field method. For instance, it shows that the s -wave fermion-antifermion interaction in the 3S1 channel (ψ ¯ γμψ ) alone cannot form the bound gauge bosons; the fermion-antifermion pairs must couple to the d -wave state too. One feature common to our class of Lagrangian is that the Noether current does not exist. Therefore it evades possible conflict with the no-go theorem of Weinberg and Witten on the formation of the non-Abelian gauge bosons.
High temperature pressure gauge
Echtler, J. Paul; Scandrol, Roy O.
1981-01-01
A high temperature pressure gauge comprising a pressure gauge positioned in fluid communication with one end of a conduit which has a diaphragm mounted in its other end. The conduit is filled with a low melting metal alloy above the diaphragm for a portion of its length with a high temperature fluid being positioned in the remaining length of the conduit and in the pressure gauge.
Discrete Time Crystals: Rigidity, Criticality, and Realizations.
Yao, N Y; Potter, A C; Potirniche, I-D; Vishwanath, A
2017-01-20
Despite being forbidden in equilibrium, spontaneous breaking of time translation symmetry can occur in periodically driven, Floquet systems with discrete time-translation symmetry. The period of the resulting discrete time crystal is quantized to an integer multiple of the drive period, arising from a combination of collective synchronization and many body localization. Here, we consider a simple model for a one-dimensional discrete time crystal which explicitly reveals the rigidity of the emergent oscillations as the drive is varied. We numerically map out its phase diagram and compute the properties of the dynamical phase transition where the time crystal melts into a trivial Floquet insulator. Moreover, we demonstrate that the model can be realized with current experimental technologies and propose a blueprint based upon a one dimensional chain of trapped ions. Using experimental parameters (featuring long-range interactions), we identify the phase boundaries of the ion-time-crystal and propose a measurable signature of the symmetry breaking phase transition.
Discrete Time Crystals: Rigidity, Criticality, and Realizations
NASA Astrophysics Data System (ADS)
Yao, N. Y.; Potter, A. C.; Potirniche, I.-D.; Vishwanath, A.
2017-01-01
Despite being forbidden in equilibrium, spontaneous breaking of time translation symmetry can occur in periodically driven, Floquet systems with discrete time-translation symmetry. The period of the resulting discrete time crystal is quantized to an integer multiple of the drive period, arising from a combination of collective synchronization and many body localization. Here, we consider a simple model for a one-dimensional discrete time crystal which explicitly reveals the rigidity of the emergent oscillations as the drive is varied. We numerically map out its phase diagram and compute the properties of the dynamical phase transition where the time crystal melts into a trivial Floquet insulator. Moreover, we demonstrate that the model can be realized with current experimental technologies and propose a blueprint based upon a one dimensional chain of trapped ions. Using experimental parameters (featuring long-range interactions), we identify the phase boundaries of the ion-time-crystal and propose a measurable signature of the symmetry breaking phase transition.
NASA Astrophysics Data System (ADS)
Babu, K. S.; Khan, S.
2015-10-01
We present a minimal renormalizable nonsupersymmetric S O (10 ) grand unified model with a symmetry breaking sector consisting of Higgs fields in the 5 4H+12 6H+1 0H representations. This model admits a single intermediate scale associated with Pati-Salam symmetry along with a discrete parity. Spontaneous symmetry breaking, the unification of gauge couplings, and proton lifetime estimates are studied in detail in this framework. Including threshold corrections self-consistently obtained from a full analysis of the Higgs potential, we show that the model is compatible with the current experimental bound on proton lifetime. The model generally predicts an upper bound of few times 1035 yr for proton lifetime, which is not too far from the present Super-Kamiokande limit of τp≳1.29 ×1034 yr . With the help of a Pecci-Quinn symmetry and the resulting axion, the model provides a suitable dark matter candidate while also solving the strong C P problem. The intermediate scale, MI≈(1013- 1014) GeV which is also the B -L scale, is of the right order for the right-handed neutrino mass which enables a successful description of light neutrino masses and oscillations. The Yukawa sector of the model consists of only two matrices in family space and leads to a predictive scenario for quark and lepton masses and mixings. The branching ratios for proton decay are calculable with the leading modes being p →e+π0 and p →ν ¯π+. Even though the model predicts no new physics within the reach of the LHC, the next-generation proton decay detectors and axion search experiments have the capability to reach a verdict on this minimal scenario.
Hidden local symmetry and beyond
NASA Astrophysics Data System (ADS)
Yamawaki, Koichi
Gerry Brown was a godfather of our hidden local symmetry (HLS) for the vector meson from the birth of the theory throughout his life. The HLS is originated from very nature of the nonlinear realization of the symmetry G based on the manifold G/H, and thus is universal to any physics based on the nonlinear realization. Here, I focus on the Higgs Lagrangian of the Standard Model (SM), which is shown to be equivalent to the nonlinear sigma model based on G/H = SU(2)L ×SU(2)R/SU(2)V with additional symmetry, the nonlinearly-realized scale symmetry. Then, the SM does have a dynamical gauge boson of the SU(2)V HLS, “SM ρ meson”, in addition to the Higgs as a pseudo-dilaton as well as the NG bosons to be absorbed in to the W and Z. Based on the recent work done with Matsuzaki and Ohki, I discuss a novel possibility that the SM ρ meson acquires kinetic term by the SM dynamics itself, which then stabilizes the skyrmion dormant in the SM as a viable candidate for the dark matter, what we call “dark SM skyrmion (DSMS)”.
Geometry and symmetries in lattice spinor gravity
Wetterich, C.
2012-09-15
Lattice spinor gravity is a proposal for regularized quantum gravity based on fermionic degrees of freedom. In our lattice model the local Lorentz symmetry is generalized to complex transformation parameters. The difference between space and time is not put in a priori, and the euclidean and the Minkowski quantum field theory are unified in one functional integral. The metric and its signature arise as a result of the dynamics, corresponding to a given ground state or cosmological solution. Geometrical objects as the vierbein, spin connection or the metric are expectation values of collective fields built from an even number of fermions. The quantum effective action for the metric is invariant under general coordinate transformations in the continuum limit. The action of our model is found to be also invariant under gauge transformations. We observe a 'geometrical entanglement' of gauge- and Lorentz-transformations due to geometrical objects transforming non-trivially under both types of symmetry transformations. - Highlights: Black-Right-Pointing-Pointer We formulate the geometrical aspects of a proposal for a lattice regularized model of quantum gravity. Black-Right-Pointing-Pointer The vierbein shows an entanglement between Lorentz symmetry and gauge symmetry. Black-Right-Pointing-Pointer Euclidean and Minkowski signatures of the collective metric and the vierbein are described within the same functional integral.
NASA Astrophysics Data System (ADS)
Cheng, Meng; Zaletel, Michael; Barkeshli, Maissam; Vishwanath, Ashvin; Bonderson, Parsa
2016-10-01
The Lieb-Schultz-Mattis theorem and its higher-dimensional generalizations by Oshikawa and Hastings require that translationally invariant 2D spin systems with a half-integer spin per unit cell must either have a continuum of low energy excitations, spontaneously break some symmetries, or exhibit topological order with anyonic excitations. We establish a connection between these constraints and a remarkably similar set of constraints at the surface of a 3D interacting topological insulator. This, combined with recent work on symmetry-enriched topological phases with on-site unitary symmetries, enables us to develop a framework for understanding the structure of symmetry-enriched topological phases with both translational and on-site unitary symmetries, including the effective theory of symmetry defects. This framework places stringent constraints on the possible types of symmetry fractionalization that can occur in 2D systems whose unit cell contains fractional spin, fractional charge, or a projective representation of the symmetry group. As a concrete application, we determine when a topological phase must possess a "spinon" excitation, even in cases when spin rotational invariance is broken down to a discrete subgroup by the crystal structure. We also describe the phenomena of "anyonic spin-orbit coupling," which may arise from the interplay of translational and on-site symmetries. These include the possibility of on-site symmetry defect branch lines carrying topological charge per unit length and lattice dislocations inducing degeneracies protected by on-site symmetry.
Continuous symmetry measures for complex symmetry group.
Dryzun, Chaim
2014-04-05
Symmetry is a fundamental property of nature, used extensively in physics, chemistry, and biology. The Continuous symmetry measures (CSM) is a method for estimating the deviation of a given system from having a certain perfect symmetry, which enables us to formulate quantitative relation between symmetry and other physical properties. Analytical procedures for calculating the CSM of all simple cyclic point groups are available for several years. Here, we present a methodology for calculating the CSM of any complex point group, including the dihedral, tetrahedral, octahedral, and icosahedral symmetry groups. We present the method and analyze its performances and errors. We also introduce an analytical method for calculating the CSM of the linear symmetry groups. As an example, we apply these methods for examining the symmetry of water, the symmetry maps of AB4 complexes, and the symmetry of several Lennard-Jones clusters.
Strong Coupling Gauge Theories in LHC ERA
NASA Astrophysics Data System (ADS)
Fukaya, H.; Harada, M.; Tanabashi, M.; Yamawaki, K.
2011-01-01
AdS/QCD, light-front holography, and the nonperturbative running coupling / Stanley J. Brodsky, Guy de Teramond and Alexandre Deur -- New results on non-abelian vortices - Further insights into monopole, vortex and confinement / K. Konishi -- Study on exotic hadrons at B-factories / Toru Iijima -- Cold compressed baryonic matter with hidden local symmetry and holography / Mannque Rho -- Aspects of baryons in holographic QCD / T. Sakai -- Nuclear force from string theory / K. Hashimoto -- Integrating out holographic QCD back to hidden local symmetry / Masayasu Harada, Shinya Matsuzaki and Koichi Yamawaki -- Holographic heavy quarks and the giant Polyakov loop / Gianluca Grignani, Joanna Karczmarek and Gordon W. Semenoff -- Effect of vector-axial-vector mixing to dilepton spectrum in hot and/or dense matter / Masayasu Harada and Chihiro Sasaki -- Infrared behavior of ghost and gluon propagators compatible with color confinement in Yang-Mills theory with the Gribov horizon / Kei-Ichi Kondo -- Chiral symmetry breaking on the lattice / Hidenori Fukaya [for JLQCD and TWQCD collaborations] -- Gauge-Higgs unification: Stable Higgs bosons as cold dark matter / Yutaka Hosotani -- The limits of custodial symmetry / R. Sekhar Chivukula ... [et al.] -- Higgs searches at the tevatron / Kazuhiro Yamamoto [for the CDF and D[symbol] collaborations] -- The top triangle moose / R. S. Chivukula ... [et al.] -- Conformal phase transition in QCD like theories and beyond / V. A. Miransky -- Gauge-Higgs unification at LHC / Nobuhito Maru and Nobuchika Okada -- W[symbol]W[symbol] scattering in Higgsless models: Identifying better effective theories / Alexander S. Belyaev ... [et al.] -- Holographic estimate of Muon g - 2 / Deog Ki Hong -- Gauge-Higgs dark matter / T. Yamashita -- Topological and curvature effects in a multi-fermion interaction model / T. Inagaki and M. Hayashi -- A model of soft mass generation / J. Hosek -- TeV physics and conformality / Thomas Appelquist -- Conformal
Symmetry, conservation laws, and theoretical particle physics
NASA Astrophysics Data System (ADS)
Krumins, Andris Visvaldis
In this work, we trace the role of symmetry throughout the history of theoretical particle physics, paying particular attention to the role of group theory, the formal mathematics of symmetry. After an analysis of the role of conservation laws and invariance in the theory of general relativity, we move on to Weyl's gauge theory of 1918, which was developed within the context of general relativity as an attempt to unify gravitation and electromagnetism. Weyl was trying to exploit an invariance of scale, and although his theory was experimentally refuted, it provided a formulation of the conservation of charge. After the advent of quantum mechanics, gauge theory was reinterpreted by London as an invariance of the wave-function. Weyl and Wigner studied group theory in the context of quantum mechanics, but the broadness of its application had yet to be appreciated. Symmetry was soon exploited in the nuclear interactions, however, and we examine the events leading to the discovery of SU(2) of isotopic spin. We analyze how the discovery of strangeness was linked to the generalization of SU(2) to SU(3), and also how it led to a differentiation between the strong interactions, which conserve isotopic spin and strangeness, and the weak interactions, which violate these conservation laws, along with the conservation of parity. Yang and Mills were impressed with gauge invariance, and in 1954, they took the bold step of imposing it upon the Lagrangian of the strong interactions, forcing the introduction of three new gauge fields. There was a problem, however, because although the short-range of the strong interactions implied that these gauge bosons should be massive, they needed to be massless in order to preserve gauge invariance. In addition, efforts were made to extend Yang-Mills theory to the weak interactions, but they also faced the same zero-mass problem. This problem was finally solved in 1967, when Weinberg and Salam showed how gauge boson masses could be generated
Gauge-invariant extensions of the Proca model in a noncommutative space-time
NASA Astrophysics Data System (ADS)
Abreu, Everton M. C.; Neto, Jorge Ananias; Fernandes, Rafael L.; Mendes, Albert C. R.
2016-09-01
The gauge invariance analysis of theories described in noncommutative (NC) space-times can lead us to interesting results since noncommutativity is one of the possible paths to investigate quantum effects in classical theories such as general relativity, for example. This theoretical possibility has motivated us to analyze the gauge invariance of the NC version of the Proca model, which is a second-class system, in Dirac’s classification, since its classical formulation (commutative space-time) has its gauge invariance broken thanks to the mass term. To obtain such gauge invariant model, we have used the gauge unfixing method to construct a first-class NC version of the Proca model. We have also questioned if the gauge symmetries of NC theories are affected necessarily or not by the NC parameter. In this way, we have calculated its respective symmetries in a standard way via Poisson brackets.
Bartholomew, M. J.
2016-01-01
To improve the quantitative description of precipitation processes in climate models, the Atmospheric Radiation Measurement (ARM) Climate Research Facility deployed rain gauges located near disdrometers (DISD and VDIS data streams). This handbook deals specifically with the rain gauges that make the observations for the RAIN data stream. Other precipitation observations are made by the surface meteorology instrument suite (i.e., MET data stream).
The new integrable symplectic map and the symmetry of integrable nonlinear lattice equation
NASA Astrophysics Data System (ADS)
Dong, Huanhe; Zhang, Yong; Zhang, Xiaoen
2016-07-01
A discrete matrix spectral problem is presented and the hierarchy of discrete integrable systems is derived. Their Hamiltonian structures are established. As to the discrete integrable system, nonlinearization of the spatial parts of the Lax pairs and the adjoint Lax pairs generate a new integrable symplectic map. Based on the theory, a new integrable symplectic map and a family of finite-dimension completely integrable systems are given. Especially, two explicit equations are obtained under the Bargmann constraint. Finally, the symmetry of the discrete equation is provided according to the recursion operator and the seed symmetry. Although the solutions of the discrete equations have been gained by many methods, there are few articles that solving the discrete equation via the symmetry. So the solution of the discrete lattice equation is obtained through the symmetry theory.
Discretization errors in particle tracking
NASA Astrophysics Data System (ADS)
Carmon, G.; Mamman, N.; Feingold, M.
2007-03-01
High precision video tracking of microscopic particles is limited by systematic and random errors. Systematic errors are partly due to the discretization process both in position and in intensity. We study the behavior of such errors in a simple tracking algorithm designed for the case of symmetric particles. This symmetry algorithm uses interpolation to estimate the value of the intensity at arbitrary points in the image plane. We show that the discretization error is composed of two parts: (1) the error due to the discretization of the intensity, bD and (2) that due to interpolation, bI. While bD behaves asymptotically like N-1 where N is the number of intensity gray levels, bI is small when using cubic spline interpolation.
Equivalence of light-cone and conformal gauges in two-dimensional quantum gravity
Ahn, G.J.; Kim, W.T.; Park, Y.J.; Kim, K.Y. )
1992-08-20
In this paper, the authors show that the light-cone and conformal gauges are equivalent in the sense that the well known SL(2,R) current structure in the light-cone gauge is obtained from the results in the conformal one under a proper coordinate transformation. This result is due to the residual symmetry of the scalar field [Phi].
Democracy of internal symmetries in supersymmetrical quantum field theory
Lopuszanski, J.T.
1981-12-01
The freedom of choice of some discrete and internal symmetries in the supersymmetric, massive, interacting quantum field theory is discussed. It is shown that the discrete symmetry consisting of changing the sign of some (not all) scalar fields is incompatible with the supersymmetric structure of the theory. It is further demonstrated that an internal symmetry which transforms only some of the fields of fixed spin leaving the other fields invariant and which acts nontrivially on the supercharges can not be admitted as a symmetry; although it can be a good internal symmetry in absence of supersymmetric covariance. Moreover, in case of a model consisting of scalar, spinor and vector fields even a symmetry which transforms all of the scalar (vector) fields leaving spinor and vector (scalar) fields unaffected is ruled out provided it acts nontrivially on some of the supercharges.
Nonlinear W∞ as asymptotic symmetry of three-dimensional higher spin AdS gravity
NASA Astrophysics Data System (ADS)
Henneaux, Marc; Rey, Soo-Jong
2010-12-01
We investigate the asymptotic symmetry algebra of (2+1)-dimensional higher spin, anti-de Sitter gravity. We use the formulation of the theory as a Chern-Simons gauge theory based on the higher spin algebra hs(1 , 1). Expanding the gauge connection around asymptotically anti-de Sitter spacetime, we specify consistent boundary conditions on the higher spin gauge fields. We then study residual gauge transformation, the corresponding surface terms and their Poisson bracket algebra. We find that the asymptotic symmetry algebra is a nonlinearly realized W ∞ algebra with classical central charges. We discuss implications of our results to quantum gravity and to various situations in string theory.
Local subsystems in gauge theory and gravity
NASA Astrophysics Data System (ADS)
Donnelly, William; Freidel, Laurent
2016-09-01
We consider the problem of defining localized subsystems in gauge theory and gravity. Such systems are associated to spacelike hypersurfaces with boundaries and provide the natural setting for studying entanglement entropy of localized subsystems. We present a general formalism to associate a gauge-invariant classical phase space to a spatial slice with boundary by introducing new degrees of freedom on the boundary. In Yang-Mills theory the new degrees of freedom are a choice of gauge on the boundary, transformations of which are generated by the normal component of the nonabelian electric field. In general relativity the new degrees of freedom are the location of a codimension-2 surface and a choice of conformal normal frame. These degrees of freedom transform under a group of surface symmetries, consisting of diffeomorphisms of the codimension-2 boundary, and position-dependent linear deformations of its normal plane. We find the observables which generate these symmetries, consisting of the conformal normal metric and curvature of the normal connection. We discuss the implications for the problem of defining entanglement entropy in quantum gravity. Our work suggests that the Bekenstein-Hawking entropy may arise from the different ways of gluing together two partial Cauchy surfaces at a cross-section of the horizon.
Modeling spontaneous breaking of time-translation symmetry
NASA Astrophysics Data System (ADS)
Sacha, Krzysztof
2015-03-01
We show that an ultracold atomic cloud bouncing on an oscillating mirror can reveal spontaneous breaking of a discrete time-translation symmetry. In many-body simulations, we illustrate the process of the symmetry breaking that can be induced by atomic losses or by a measurement of particle positions. The results pave the way for understanding and realization of the time crystal idea where crystalline structures form in the time domain due to spontaneous breaking of continuous time-translation symmetry.
Remarks on asymptotic symmetries and the subleading soft photon theorem
NASA Astrophysics Data System (ADS)
Conde, Eduardo; Mao, Pujian
2017-01-01
A deep connection has been recently established between soft theorems and symmetries at null infinity in gravity and gauge theories, recasting the former as Ward identities of the latter. In particular, different orders (in the frequency of the soft particle) in the soft theorems are believed to be controlled by different asymptotic symmetries. In this paper we argue that this need not be the case by focusing on the soft photon theorem. We argue that the subleading soft factor follows from the same symmetry responsible for the leading one, namely certain residual (large) gauge transformations of the gauge theory. In particular, expanding the associated charge in inverse powers of the radial coordinate, the (sub)leading charge yields the (sub)leading soft factor.
BRST symmetry for Regge-Teitelboim-based minisuperspace models
NASA Astrophysics Data System (ADS)
Upadhyay, Sudhaker; Paul, Biswajit
2016-07-01
The Einstein-Hilbert action in the context of higher derivative theories is considered for finding their BRST symmetries. Being a constraint system, the model is transformed in the minisuperspace language with the FRLW background and the gauge symmetries are explored. Exploiting the first order formalism developed by Banerjee et al. the diffeomorphism symmetry is extracted. From the general form of the gauge transformations of the field, the analogous BRST transformations are calculated. The effective Lagrangian is constructed by considering two gauge-fixing conditions. Further, the BRST (conserved) charge is computed, which plays an important role in defining the physical states from the total Hilbert space of states. The finite field-dependent BRST formulation is also studied in this context where the Jacobian for the functional measure is illustrated specifically.
Non-Abelian gauge field theory in scale relativity
Nottale, Laurent; Celerier, Marie-Noeelle; Lehner, Thierry
2006-03-15
Gauge field theory is developed in the framework of scale relativity. In this theory, space-time is described as a nondifferentiable continuum, which implies it is fractal, i.e., explicitly dependent on internal scale variables. Owing to the principle of relativity that has been extended to scales, these scale variables can themselves become functions of the space-time coordinates. Therefore, a coupling is expected between displacements in the fractal space-time and the transformations of these scale variables. In previous works, an Abelian gauge theory (electromagnetism) has been derived as a consequence of this coupling for global dilations and/or contractions. We consider here more general transformations of the scale variables by taking into account separate dilations for each of them, which yield non-Abelian gauge theories. We identify these transformations with the usual gauge transformations. The gauge fields naturally appear as a new geometric contribution to the total variation of the action involving these scale variables, while the gauge charges emerge as the generators of the scale transformation group. A generalized action is identified with the scale-relativistic invariant. The gauge charges are the conservative quantities, conjugates of the scale variables through the action, which find their origin in the symmetries of the ''scale-space.'' We thus found in a geometric way and recover the expression for the covariant derivative of gauge theory. Adding the requirement that under the scale transformations the fermion multiplets and the boson fields transform such that the derived Lagrangian remains invariant, we obtain gauge theories as a consequence of scale symmetries issued from a geometric space-time description.
Noel, Bruce W.; Borella, Henry M.; Cates, Michael R.; Turley, W. Dale; MaCarthur, Charles D.; Cala, Gregory C.
1991-01-01
A heat flux gauge comprising first and second thermographic phosphor layers separated by a layer of a thermal insulator. The gauge may be mounted on a surface with the first thermographic phosphor in contact with the surface. A light source is directed at the gauge, causing the phosphors to luminesce. The luminescence produced by the phosphors is collected and its spectra analyzed in order to determine the heat flux on the surface. First and second phosphor layers must be different materials to assure that the spectral lines collected will be distinguishable.
Noel, Bruce W.; Borella, Henry M.; Cates, Michael R.; Turley, W. Dale; MacArthur, Charles D.; Cala, Gregory C.
1991-01-01
A heat flux gauge comprising first and second thermographic phosphor layers separated by a layer of a thermal insulator wherein each thermographic layer comprises a plurality of respective thermographic phosphors. The gauge may be mounted on a surface with the first thermographic phosphor in contact with the surface. A light source is directed at the gauge, causing the phosphors to luminesce. The luminescence produced by the phosphors is collected and its spectra analyzed in order to determine the heat flux on the surface. First and second phosphor layers must be different materials to assure that the spectral lines collected will be distinguishable.
Noel, Bruce W.; Borella, Henry M.; Cates, Michael R.; Turley, W. Dale; MacArthur, Charles D.; Cala, Gregory C.
1991-01-01
A heat flux gauge comprising first and second thermographic phosphor layers separated by a layer of a thermal insulator, wherein each thermographic layer comprises a plurality of respective thermographic sensors in a juxtaposed relationship with respect to each other. The gauge may be mounted on a surface with the first thermographic phosphor in contact with the surface. A light source is directed at the gauge, causing the phosphors to luminesce. The luminescence produced by the phosphors is collected and its spectra analyzed in order to determine the heat flux on the surface. First and second phosphor layers must be different materials to assure that the spectral lines collected will be distinguishable.
Noel, B.W.; Borella, H.M.; Cates, M.R.; Turley, W.D.; MacArthur, C.D.; Cala, G.C.
1991-06-25
A heat flux gauge is described comprising first and second thermographic phosphor layers separated by a layer of a thermal insulator wherein each thermographic layer comprises respective thermographic phosphors. The gauge may be mounted on a surface with the first thermographic phosphor in contact with the surface. A light source is directed at the gauge, causing the phosphors to luminesce. The luminescence produced by the phosphors is collected and its spectra analyzed in order to determine the heat flux on the surface. First and second phosphor layers must be different materials to assure that the spectral lines collected will be distinguishable.
Noel, B.W.; Borella, H.M.; Cates, M.R.; Turley, W.D.; MacArthur, C.D.; Cala, G.C.
1989-06-07
A heat flux gauge comprising first and second thermographic phosphor layers separated by a layer of a thermal insulator. The gauge may be mounted on a surface with the first thermographic phosphor in contact with the surface. A light source is directed at the gauge, causing the phosphors to luminesce. The luminescence produced by the phosphors is collected and its spectra analyzed in order to determine the heat flux on the surface. First and second phosphor layers must be different materials to assure that the spectral lines collected will be distinguishable. 9 figs.
Noel, B.W.; Borella, H.M.; Cates, M.R.; Turley, W.D.; MaCarthur, C.D.; Cala, G.C.
1991-09-03
A heat flux gauge is described comprising first and second thermographic phosphor layers separated by a layer of a thermal insulator. The gauge may be mounted on a surface with the first thermographic phosphor in contact with the surface. A light source is directed at the gauge, causing the phosphors to luminesce. The luminescence produced by the phosphors is collected and its spectra analyzed in order to determine the heat flux on the surface. First and second phosphor layers must be different materials to assure that the spectral lines collected will be distinguishable. 9 figures.
Bacvinskas, W.S.; Bayer, J.E.; Davis, W.W.; Fodor, G.; Kikta, T.J.; Matchett, R.L.; Nilsen, R.J.; Wilczynski, R.
1991-12-31
The present invention is directed to a semi-automatic rod examination gauge for performing a large number of exacting measurements on radioactive fuel rods. The rod examination gauge performs various measurements underwater with remote controlled machinery of high reliability. The rod examination gauge includes instruments and a closed circuit television camera for measuring fuel rod length, free hanging bow measurement, diameter measurement, oxide thickness measurement, cladding defect examination, rod ovality measurement, wear mark depth and volume measurement, as well as visual examination. A control system is provided including a programmable logic controller and a computer for providing a programmed sequence of operations for the rod examination and collection of data.
Gauge mediation models with adjoint messengers
NASA Astrophysics Data System (ADS)
Gogoladze, Ilia; Mustafayev, Azar; Shafi, Qaisar; Ün, Cem Salih
2016-10-01
We present a class of models in the framework of gauge mediation supersymmetry breaking where the messenger fields transform in the adjoint representation of the standard model gauge symmetry. To avoid unacceptably light right-handed sleptons in the spectrum we introduce a nonzero U (1 )B-L D-term. This leads to an additional contribution to the soft supersymmetry breaking mass terms which makes the right-handed slepton masses compatible with the current experimental bounds. We show that in this framework the observed 125 GeV Higgs boson mass can be accommodated with the sleptons accessible at the LHC, while the squarks and gluinos lie in the multi-TeV range. We also discuss the issue of the fine-tuning and show that the desired relic dark matter abundance can also be accommodated.
Generalized gauge U(1) family symmetry for quarks and leptons
NASA Astrophysics Data System (ADS)
Kownacki, Corey; Ma, Ernest; Pollard, Nicholas; Zakeri, Mohammadreza
2017-03-01
If the standard model of quarks and leptons is extended to include three singlet right-handed neutrinos, then the resulting fermion structure admits an infinite number of anomaly-free solutions with just one simple constraint. Well-known examples satisfying this constraint are B- L, Lμ-Lτ, B- 3Lτ, etc. We derive this simple constraint, and discuss two new examples which offer some insights to the structure of mixing among quark and lepton families, together with their possible verification at the Large Hadron Collider.
Foliation dependence of black hole apparent horizons in spherical symmetry
NASA Astrophysics Data System (ADS)
Faraoni, Valerio; Ellis, George F. R.; Firouzjaee, Javad T.; Helou, Alexis; Musco, Ilia
2017-01-01
Numerical studies of gravitational collapse to black holes make use of apparent horizons, which are intrinsically foliation dependent. We expose the problem and discuss possible solutions using the Hawking-Hayward quasilocal mass. In spherical symmetry, we present a physically sensible approach to the problem by restricting to spherically symmetric spacetime slicings. In spherical symmetry, the apparent horizons enjoy a restricted gauge independence in any spherically symmetric foliation, but physical quantities associated with them, such as surface gravity and temperature, are fully gauge dependent. The widely used comoving and Kodama foliations, which are of particular interest, are discussed in detail as examples.
Aldrovandi, R.; Pereira, J.G.
1986-05-15
Because it acts on space-time and is not semisimple, the Poincare group cannot lead to a gauge theory of the usual kind. A candidate model is discussed which keeps itself as close as possible to the typical gauge scheme. Its field equations are the Yang-Mills equations for the Poincare group. It is shown that there exists no Lagrangian for these equations.
Local renormalizable gauge theories from nonlocal operators
Capri, M.A.L. Lemes, V.E.R. Sobreiro, R.F. Sorella, S.P. Thibes, R.
2008-03-15
The possibility that nonlocal operators might be added to the Yang-Mills action is investigated. We point out that there exists a class of nonlocal operators which lead to renormalizable gauge theories. These operators turn out to be localizable by means of the introduction of auxiliary fields. The renormalizability is thus ensured by the symmetry content exhibited by the resulting local theory. The example of the nonlocal operator Tr{integral}A{sub {mu}}1/(D{sup 2}) A{sub {mu}} is analyzed in detail. A few remarks on the possible role that these operators might have for confining theories are outlined.
Subleading soft photons and large gauge transformations
NASA Astrophysics Data System (ADS)
Campiglia, Miguel; Laddha, Alok
2016-11-01
Lysov, Pasterski and Strominger have shown how Low's subleading soft photon theorem can be understood as Ward identities of new symmetries of massless QED. In this paper we offer a different perspective and show that there exists a class of large U(1) gauge transformations such that (i) the associated (electric and magnetic) charges can be computed from first principles, (ii) their Ward identities are equivalent to Low's theorem. Our framework paves the way to analyze the sub-subleading theorem in gravity in terms of Ward identities associated to large diffeomorphisms.
Strongly broken Peccei-Quinn symmetry in the early Universe
Takahashi, Fuminobu; Yamada, Masaki E-mail: yamadam@icrr.u-tokyo.ac.jp
2015-10-01
We consider QCD axion models where the Peccei-Quinn symmetry is badly broken by a larger amount in the past than in the present, in order to avoid the axion isocurvature problem. Specifically we study supersymmetric axion models where the Peccei-Quinn symmetry is dynamically broken by either hidden gauge interactions or the SU(3){sub c} strong interactions whose dynamical scales are temporarily enhanced by the dynamics of flat directions. The former scenario predicts a large amount of self-interacting dark radiation as the hidden gauge symmetry is weakly coupled in the present Universe. We also show that the observed amount of baryon asymmetry can be generated by the QCD axion dynamics via spontaneous baryogenesis. We briefly comment on the case in which the PQ symmetry is broken by a non-minimal coupling to gravity.
Strongly broken Peccei-Quinn symmetry in the early Universe
Takahashi, Fuminobu; Yamada, Masaki
2015-10-06
We consider QCD axion models where the Peccei-Quinn symmetry is badly broken by a larger amount in the past than in the present, in order to avoid the axion isocurvature problem. Specifically we study supersymmetric axion models where the Peccei-Quinn symmetry is dynamically broken by either hidden gauge interactions or the SU(3){sub c} strong interactions whose dynamical scales are temporarily enhanced by the dynamics of flat directions. The former scenario predicts a large amount of self-interacting dark radiation as the hidden gauge symmetry is weakly coupled in the present Universe. We also show that the observed amount of baryon asymmetry can be generated by the QCD axion dynamics via spontaneous baryogenesis. We briefly comment on the case in which the PQ symmetry is broken by a non-minimal coupling to gravity.
Strongly broken Peccei-Quinn symmetry in the early Universe
NASA Astrophysics Data System (ADS)
Takahashi, Fuminobu; Yamada, Masaki
2015-10-01
We consider QCD axion models where the Peccei-Quinn symmetry is badly broken by a larger amount in the past than in the present, in order to avoid the axion isocurvature problem. Specifically we study supersymmetric axion models where the Peccei-Quinn symmetry is dynamically broken by either hidden gauge interactions or the SU(3)c strong interactions whose dynamical scales are temporarily enhanced by the dynamics of flat directions. The former scenario predicts a large amount of self-interacting dark radiation as the hidden gauge symmetry is weakly coupled in the present Universe. We also show that the observed amount of baryon asymmetry can be generated by the QCD axion dynamics via spontaneous baryogenesis. We briefly comment on the case in which the PQ symmetry is broken by a non-minimal coupling to gravity.
Geometric Representations for Discrete Fourier Transforms
NASA Technical Reports Server (NTRS)
Cambell, C. W.
1986-01-01
Simple geometric representations show symmetry and periodicity of discrete Fourier transforms (DFT's). Help in visualizing requirements for storing and manipulating transform value in computations. Representations useful in any number of dimensions, but particularly in one-, two-, and three-dimensional cases often encountered in practice.
Higher gauge theories from Lie n-algebras and off-shell covariantization
NASA Astrophysics Data System (ADS)
Carow-Watamura, Ursula; Heller, Marc Andre; Ikeda, Noriaki; Kaneko, Yukio; Watamura, Satoshi
2016-07-01
We analyze higher gauge theories in various dimensions using a supergeometric method based on a differential graded symplectic manifold, called a QP-manifold, which is closely related to the BRST-BV formalism in gauge theories. Extensions of the Lie 2-algebra gauge structure are formulated within the Lie n-algebra induced by the QP-structure. We find that in 5 and 6 dimensions there are special extensions of the gauge algebra. In these cases, a restriction of the gauge symmetry by imposing constraints on the auxiliary gauge fields leads to a covariantized theory. As an example we show that we can obtain an off-shell covariantized higher gauge theory in 5 dimensions, which is similar to the one proposed in [1].
Two-Color Gauge Theory with Novel Infrared Behavior
NASA Astrophysics Data System (ADS)
Appelquist, T.; Brower, R. C.; Buchoff, M. I.; Cheng, M.; Fleming, G. T.; Kiskis, J.; Lin, M. F.; Neil, E. T.; Osborn, J. C.; Rebbi, C.; Schaich, D.; Schroeder, C.; Syritsyn, S.; Voronov, G.; Vranas, P.; Witzel, O.; Lattice Strong Dynamics (LSD) Collaboration
2014-03-01
Using lattice simulations, we study the infrared behavior of a particularly interesting SU(2) gauge theory, with six massless Dirac fermions in the fundamental representation. We compute the running gauge coupling derived nonperturbatively from the Schrödinger functional of the theory, finding no evidence for an infrared fixed point up through gauge couplings g¯2 of order 20. This implies that the theory either is governed in the infrared by a fixed point of considerable strength, unseen so far in nonsupersymmetric gauge theories, or breaks its global chiral symmetries producing a large number of composite Nambu-Goldstone bosons relative to the number of underlying degrees of freedom. Thus either of these phases exhibits novel behavior.
Localization of Gauge Theories on the Three-Sphere
NASA Astrophysics Data System (ADS)
Yaakov, Itamar
We describe the application of localization techniques to the path integral for supersymmetric gauge theories in three dimensions. The localization procedure reduces the computation of the expectation value of BPS observables to a calculation in a matrix model. We describe the ingredients of this model for a general quiver gauge theory and the incorporation of supersymmetric deformations and observables. We use the matrix model expressions to test several duality conjectures for supersymmetric gauge theories. We perform tests of mirror symmetry of three-dimensional quiver gauge theories and of Seiberg-like dualities. Specifically, we explicitly show that the partition functions of the dual pairs, which are highly nontrivial functions of the deformations, agree. We describe extensions of these dualities which can be inferred from the form of the partition functions. We review the application of the matrix model to the study of renormalization group flow and the space of conformal field theories in three dimensions.
Generalized CP symmetries and special regions of parameter space in the two-Higgs-doublet model
Ferreira, P. M.; Haber, Howard E.; Silva, Joao P.
2009-06-01
We consider the impact of imposing generalized CP symmetries on the Higgs sector of the two-Higgs-doublet model, and identify three classes of symmetries. Two of these classes constrain the scalar potential parameters to an exceptional region of parameter space, which respects either a Z{sub 2} discrete flavor symmetry or a U(1) symmetry. We exhibit a basis-invariant quantity that distinguishes between these two possible symmetries. We also show that the consequences of imposing these two classes of CP symmetry can be achieved by combining Higgs family symmetries, and that this is not possible for the usual CP symmetry. We comment on the vacuum structure and on renormalization in the presence of these symmetries. Finally, we demonstrate that the standard CP symmetry can be used to build all the models we identify, including those based on Higgs family symmetries.
Relativistic Pseudospin Symmetry
Ginocchio, Joseph N.
2011-05-06
We show that the pseudospin symmetry that Akito Arima discovered many years ago (with collaborators) is a symmetry of the the Dirac Hamiltonian for which the sum of the scalar and vector potentials are a constant. In this paper we discuss some of the implications of this relativistic symmetry and the experimental data that support these predictions. In his original paper Akito also discussed pseudo-U(3) symmetry. We show that pseudo-U(3) symmetry is a symmetry of the Dirac Hamiltonian for which the sum of harmonic oscillator vector and scalar potentials are equal to a constant, and we give the generators of pseudo-U(3) symmetry. Going beyond the mean field we summarize new results on non relativistic shell model Hamiltonians that have pseudospin symmetry and pseudo-orbital angular momentum symmetry as a dynamical symmetries.
Scalar-tensor teleparallel wormholes by Noether symmetries
NASA Astrophysics Data System (ADS)
Bahamonde, Sebastian; Camci, Ugur; Capozziello, Salvatore; Jamil, Mubasher
2016-10-01
A gravitational theory of a scalar field nonminimally coupled with torsion and a boundary term is considered with the aim to construct Lorentzian wormholes. Geometrical parameters including shape and redshift functions are obtained for these solutions. We adopt the formalism of the Noether gauge symmetry approach in order to find symmetries, Lie brackets and invariants (conserved quantities). Furthermore by imposing specific forms of potential function, we are able to calculate metric coefficients and discuss their geometrical behavior.
An Additional Symmetry in the Weinberg-Salam Model
Bakker, B.L.G.; Veselov, A.I.; Zubkov, M.A.
2005-06-01
An additional Z{sub 6} symmetry hidden in the fermion and Higgs sectors of the Standard Model has been found recently. It has a singular nature and is connected to the centers of the SU(3) and SU(2) subgroups of the gauge group. A lattice regularization of the Standard Model was constructed that possesses this symmetry. In this paper, we report our results on the numerical simulation of its electroweak sector.
Quantum Chromodynamics -- The Perfect Yang-Mills Gauge Field Theory
NASA Astrophysics Data System (ADS)
Gross, David
David Gross: My talk today is about the most beautiful of all Yang-Mills Theories (non-Abelian gauge theories), the theory of the strong nuclear interactions, Quantum Chromodynamics, QCD. We are celebrating 60 years of the publication of a remarkable paper which introduced the concept of non-Abelian local gauge symmetries, now called the Yang-Mills theory, to physics. In the introduction to this paper it is noted that the usual principle of isotopic spin symmetry is not consistent with the concept of localized fields. This sentence has drawn attention over the years because the usual principle of isotopic spin symmetry is consistent, it is just not satisfactory. The authors, Yang and Mills, introduced a more satisfactory notion of local symmetry which did not require one to rotate (in isotopic spin space) the whole universe at once to achieve the symmetry transformation. Global symmetries are thus are similar to `action at a distance', whereas Yang-Mills theory is manifestly local...
NASA Astrophysics Data System (ADS)
Huang, Changyu; Huang, Yong-Chang; Zhou, Bao-Hua
2015-09-01
We investigate the inner structure of a general S U (2 ) [naturally including S O (3 )] symmetry system—the fermion-gauge field interaction system—and achieve naturally a set of gauge-invariant spin and orbital angular momentum operators of fermion and gauge fields by Noether's theorem in general field theory. Some new relations concerning non-Abelian field strengths are discovered, e.g., the covariant transverse condition, covariant parallel condition (i.e., non-Abelian divergence, non-Abelian curl), and simplified S U (2 ) Coulomb theorem. And we show that the condition that Chen et al. obtained to construct their gauge-invariant angular momentum operators is a result of some fundamental equations in the general field theory. The results obtained in this paper present a new perspective for looking at the overall structure of the gauge field, and provide a new viewpoint to the final resolution of the nucleon spin crisis in the general field theory. Especially, the achieved theory in this paper can calculate the strong interactions with isospin symmetry and solves the serious problem without gauge-invariant angular momenta in strong interaction systems with isospin symmetry, and then the achieved predictions in the calculations can be exactly measured by particle physics experiments due to their gauge invariant properties.
Friedberg-Lee symmetry and tribimaximal neutrino mixing in the inverse seesaw mechanism
NASA Astrophysics Data System (ADS)
Chan, Aik Hui; Low, Hwee Boon; Xing, Zhi-Zhong
2009-10-01
The inverse seesaw mechanism with three pairs of gauge-singlet neutrinos offers a natural interpretation of the tiny masses of three active neutrinos at the TeV scale. We combine this picture with the newly proposed Friedberg-Lee (FL) symmetry in order to understand the observed pattern of neutrino mixing. We show that the FL symmetry requires only two pairs of the gauge-singlet neutrinos to be massive, implying that one active neutrino must be massless. We propose a phenomenological ansatz with broken FL symmetry and exact μ-τ symmetry in the gauge-singlet neutrino sector, and obtain the tribimaximal neutrino mixing pattern by means of the inverse seesaw relation. We demonstrate that nonunitary corrections to this result can possibly reach the percent level, and a soft breaking of μ-τ symmetry can give rise to CP violation in such a TeV-scale seesaw scenario.
Residual Weyl symmetry out of conformal geometry and its BRST structure
NASA Astrophysics Data System (ADS)
François, J.; Lazzarini, S.; Masson, T.
2015-09-01
The conformal structure of second order in m-dimensions together with the so-called (normal) conformal Cartan connection, is considered as a framework for gauge theories. The dressing field scheme presented in a previous work amounts to a decoupling of both the inversion and the Lorentz symmetries such that the residual gauge symmetry is the Weyl symmetry. On the one hand, it provides straightforwardly the Riemannian parametrization of the normal conformal Cartan connection and its curvature. On the other hand, it also provides the finite transformation laws under the Weyl rescaling of the various geometric objects involved. Subsequently, the dressing field method is shown to fit the BRST differential algebra treatment of infinitesimal gauge symmetry. The dressed ghost field encoding the residual Weyl symmetry is presented. The related so-called algebraic connection supplies relevant combinations found in the literature in the algebraic study of the Weyl anomaly.
Symmetries in fluctuations far from equilibrium.
Hurtado, Pablo I; Pérez-Espigares, Carlos; del Pozo, Jesús J; Garrido, Pedro L
2011-05-10
Fluctuations arise universally in nature as a reflection of the discrete microscopic world at the macroscopic level. Despite their apparent noisy origin, fluctuations encode fundamental aspects of the physics of the system at hand, crucial to understand irreversibility and nonequilibrium behavior. To sustain a given fluctuation, a system traverses a precise optimal path in phase space. Here we show that by demanding invariance of optimal paths under symmetry transformations, new and general fluctuation relations valid arbitrarily far from equilibrium are unveiled. This opens an unexplored route toward a deeper understanding of nonequilibrium physics by bringing symmetry principles to the realm of fluctuations. We illustrate this concept studying symmetries of the current distribution out of equilibrium. In particular we derive an isometric fluctuation relation that links in a strikingly simple manner the probabilities of any pair of isometric current fluctuations. This relation, which results from the time-reversibility of the dynamics, includes as a particular instance the Gallavotti-Cohen fluctuation theorem in this context but adds a completely new perspective on the high level of symmetry imposed by time-reversibility on the statistics of nonequilibrium fluctuations. The new symmetry implies remarkable hierarchies of equations for the current cumulants and the nonlinear response coefficients, going far beyond Onsager's reciprocity relations and Green-Kubo formulas. We confirm the validity of the new symmetry relation in extensive numerical simulations, and suggest that the idea of symmetry in fluctuations as invariance of optimal paths has far-reaching consequences in diverse fields.
Symmetries in fluctuations far from equilibrium
Hurtado, Pablo I.; Pérez-Espigares, Carlos; del Pozo, Jesús J.; Garrido, Pedro L.
2011-01-01
Fluctuations arise universally in nature as a reflection of the discrete microscopic world at the macroscopic level. Despite their apparent noisy origin, fluctuations encode fundamental aspects of the physics of the system at hand, crucial to understand irreversibility and nonequilibrium behavior. To sustain a given fluctuation, a system traverses a precise optimal path in phase space. Here we show that by demanding invariance of optimal paths under symmetry transformations, new and general fluctuation relations valid arbitrarily far from equilibrium are unveiled. This opens an unexplored route toward a deeper understanding of nonequilibrium physics by bringing symmetry principles to the realm of fluctuations. We illustrate this concept studying symmetries of the current distribution out of equilibrium. In particular we derive an isometric fluctuation relation that links in a strikingly simple manner the probabilities of any pair of isometric current fluctuations. This relation, which results from the time-reversibility of the dynamics, includes as a particular instance the Gallavotti–Cohen fluctuation theorem in this context but adds a completely new perspective on the high level of symmetry imposed by time-reversibility on the statistics of nonequilibrium fluctuations. The new symmetry implies remarkable hierarchies of equations for the current cumulants and the nonlinear response coefficients, going far beyond Onsager’s reciprocity relations and Green–Kubo formulas. We confirm the validity of the new symmetry relation in extensive numerical simulations, and suggest that the idea of symmetry in fluctuations as invariance of optimal paths has far-reaching consequences in diverse fields. PMID:21493865
Improved and perfect actions in discrete gravity
Bahr, Benjamin; Dittrich, Bianca
2009-12-15
We consider the notion of improved and perfect actions within Regge calculus. These actions are constructed in such a way that they - although being defined on a triangulation - reproduce the continuum dynamics exactly, and therefore capture the gauge symmetries of general relativity. We construct the perfect action in three dimensions with a cosmological constant, and in four dimensions for one simplex. We conclude with a discussion about Regge calculus with curved simplices, which arises naturally in this context.
Poincare gauge in electrodynamics
Brittin, W.E.; Smythe, W.R.; Wyss, W.
1982-08-01
The gauge presented here, which we call the Poincare gauge, is a generalization of the well-known expressions phi = -rxE/sub 0/ and A = 1/2 B/sub 0/ x r for the scalar and vector potentials which describe static, uniform electric and magnetic fields. This gauge provides a direct method for calculating a vector potential for any given static or dynamic magnetic field. After we establish the validity and generality of this gauge, we use it to produce a simple and unambiguous method of computing the flux linking an arbitrary knotted and twisted closed circuit. The magnetic flux linking the curve bounding a Moebius band is computed as a simple example. Arguments are then presented that physics students should have the opportunity of learning early in their curriculum modern geometric approaches to physics. (The language of exterior calculus may be as important to future physics as vector calculus was to the past.) Finally, an appendix illustrates how the Poincare gauge (and others) may be derived from Poincare's lemma relating exact and closed exterior differential forms.
The Wronskian solution of the constrained discrete Kadomtsev-Petviashvili hierarchy
NASA Astrophysics Data System (ADS)
Li, Maohua; He, Jingsong
2016-05-01
From the constrained discrete Kadomtsev-Petviashvili (cdKP) hierarchy, the discrete nonlinear Schrödinger (DNLS) equations have been derived. By means of the gauge transformation, the Wronskian solution of DNLS equations have been given. The u1 of the cdKP hierarchy is a Y-type soliton solution for odd times of the gauge transformation, but it becomes a dark-bright soliton solution for even times of the gauge transformation. The role of the discrete variable n in the profile of the u1 is discussed.
NASA Astrophysics Data System (ADS)
Khan, Saki
2016-06-01
We present a minimal renormalizable non-supersymmetric S O(10) grand unified model with a symmetry breaking sector consisting of Higgs fields in the 54H + 126H + 10H representations. This model admits a single intermediate scale associated with Pati-Salam symmetry along with a discrete parity. Spontaneous symmetry breaking, the unification of gauge couplings and proton lifetime estimates are studied in detail in this framework. Including threshold corrections self-consistently, obtained from a full analysis of the Higgs potential, we show that the model is compatible with the current experimental bound on proton lifetime. The model generally predicts an upper bound of few times 1035 yrs for proton lifetime, which is not too far from the present Super-Kamiokande limit of τp ≳ 1.29 × 1034 yrs. With the help of a Pecci-Quinn symmetry and the resulting axion, the model provides a suitable dark matter candidate while also solving the strong CP problem. The intermediate scale, MI ≈ (1013 - 1014) GeV which is also the B - L scale, is of the right order for the right-handed neutrino mass which enables a successful description of light neutrino masses and oscillations. The Yukawa sector of the model consists of only two matrices in family space and leads to a predictive scenario for quark and lepton masses and mixings. The branching ratios for proton decay are calculable with the leading modes being p → e+π0 and p →v ¯π+ . Even though the model predicts no new physics within the reach of LHC, the next generation proton decay detectors and axion search experiments have the capability to pass verdict on this minimal scenario.
Flavored Peccei-Quinn symmetry
NASA Astrophysics Data System (ADS)
Ahn, Y. H.
2015-03-01
In an attempt to uncover any underlying physics in the standard model (SM), we suggest a μ - τ power law in the lepton sector, such that relatively large 13 mixing angle with bilarge ones can be derived. On the basis of this, we propose a neat and economical model for both the fermion mass hierarchy problem of the SM and a solution to the strong charge parity (C P ) problem, in a way that no domain wall problem occurs, based on A4×U (1 )X symmetry in a supersymmetric framework. Here we refer to the global U (1 )X symmetry that can explain the above problems as "flavored Peccei-Quinn symmetry." In the model, a direct coupling of the SM gauge singlet flavon fields responsible for spontaneous symmetry breaking to ordinary quarks and leptons, both of which are charged under U (1 )X, comes to pass through Yukawa interactions, and all vacuum expectation values breaking the symmetries are connected to each other. So the scale of Peccei-Quinn symmetry breaking is shown to be roughly located around the 1 012 GeV section through its connection to the fermion masses. The model predictions are shown to lie on the testable regions in the very near future through on-going experiments for neutrino oscillation, neutrinoless double beta decay, and the axion. We examine the model predictions, arisen from the μ - τ power law, on leptonic C P violation, neutrinoless double beta decay, and atmospheric mixing angle, and show that the fermion mass and mixing hierarchies are in good agreement with the present data. Interestingly, we show the model predictions on the axion mass ma≃2.53 ×1 0-5 eV and the axion coupling to photon ga γ γ≃1.33 ×1 0-15 GeV-1 . And subsequently the square of the ratio between them is shown to be one or two orders of magnitude lower than that of the conventional axion model.
Noel, B.W.; Borella, H.M.; Cates, M.R.; Turley, W.D.; MacArthur, C.D.; Cala, G.C.
1991-04-09
A heat flux gauge is disclosed comprising first and second thermographic phosphor layers separated by a layer of a thermal insulator, wherein each thermographic layer comprises a plurality of respective thermographic sensors in a juxtaposed relationship with respect to each other. The gauge may be mounted on a surface with the first thermographic phosphor in contact with the surface. A light source is directed at the gauge, causing the phosphors to luminesce. The luminescence produced by the phosphors is collected and its spectra analyzed in order to determine the heat flux on the surface. First and second phosphor layers must be different materials to assure that the spectral lines collected will be distinguishable. 9 figures.
Mirror symmetry for Enriques surfaces
NASA Astrophysics Data System (ADS)
Lakuriqi, Enkeleida
In this thesis, we investigate three separate but related projects. In the first one, we describe the geometric backgrounds of Type II string theory which are given by Enriques surfaces and their mirrors. We also study the effect of various string dualities on such backgrounds, in particular phase change in Gauged Linear Sigma Models and mirror symmetry. In the second project, we investigate special Kahler geometry in order to find canonical coordinates on the moduli of generalised Calabi-Yau spaces and the associated (2, 2) superconformal field theories. In the third project, we develop a general technique for computing the massless spectrum of (0, 2) quantum field theory compactified on a proper stack or an orbifold. We produce general formulas for the contribution of the twisted sectors and compute specific examples of compactifications on gerbes on projective spaces and Calabi-Yau threefolds.
Benini, Francesco; Dymarsky, Anatoly; Franco, Sebastian; Kachru, Shamit; Simic, Dusan; Verlinde, Herman; /Princeton, Inst. Advanced Study
2009-06-19
We discuss gravitational backgrounds where supersymmetry is broken at the end of a warped throat, and the SUSY-breaking is transmitted to the Standard Model via gauginos which live in (part of) the bulk of the throat geometry. We find that the leading effect arises from splittings of certain 'messenger mesons,' which are adjoint KK-modes of the D-branes supporting the Standard Model gauge group. This picture is a gravity dual of a strongly coupled field theory where SUSY is broken in a hidden sector and transmitted to the Standard Model via a relative of semi-direct gauge mediation.
Surface charge algebra in gauge theories and thermodynamic integrability
NASA Astrophysics Data System (ADS)
Barnich, Glenn; Compère, Geoffrey
2008-04-01
Surface charges and their algebra in interacting Lagrangian gauge field theories are constructed out of the underlying linearized theory using techniques from the variational calculus. In the case of exact solutions and symmetries, the surface charges are interpreted as a Pfaff system. Integrability is governed by Frobenius' theorem and the charges associated with the derived symmetry algebra are shown to vanish. In the asymptotic context, we provide a generalized covariant derivation of the result that the representation of the asymptotic symmetry algebra through charges may be centrally extended. Comparison with Hamiltonian and covariant phase space methods is made. All approaches are shown to agree for exact solutions and symmetries while there are differences in the asymptotic context.
Necessary Condition for Emergent Symmetry from the Conformal Bootstrap.
Nakayama, Yu; Ohtsuki, Tomoki
2016-09-23
We use the conformal bootstrap program to derive the necessary conditions for emergent symmetry enhancement from discrete symmetry (e.g., Z_{n}) to continuous symmetry [e.g., U(1)] under the renormalization group flow. In three dimensions, in order for Z_{2} symmetry to be enhanced to U(1) symmetry, the conformal bootstrap program predicts that the scaling dimension of the order parameter field at the infrared conformal fixed point must satisfy Δ_{1}>1.08. We also obtain the similar necessary conditions for Z_{3} symmetry with Δ_{1}>0.580 and Z_{4} symmetry with Δ_{1}>0.504 from the simultaneous conformal bootstrap analysis of multiple four-point functions. As applications, we show that our necessary conditions impose severe constraints on the nature of the chiral phase transition in QCD, the deconfinement criticality in Néel valence bond solid transitions, and anisotropic deformations in critical O(n) models. We prove that some fixed points proposed in the literature are unstable under the perturbation that cannot be forbidden by the discrete symmetry. In these situations, the second-order phase transition with enhanced symmetry cannot happen.
Determining triple gauge boson couplings from Higgs data.
Corbett, Tyler; Éboli, O J P; Gonzalez-Fraile, J; Gonzalez-Garcia, M C
2013-07-05
In the framework of effective Lagrangians with the SU(2)(L)×U(1)(Y) symmetry linearly realized, modifications of the couplings of the Higgs field to the electroweak gauge bosons are related to anomalous triple gauge couplings (TGCs). Here, we show that the analysis of the latest Higgs boson production data at the LHC and Tevatron give rise to strong bounds on TGCs that are complementary to those from direct TGC analysis. We present the constraints on TGCs obtained by combining all available data on direct TGC studies and on Higgs production analysis.
Symmetries in Three-Dimensional Superconformal Quantum Field Theories
NASA Astrophysics Data System (ADS)
Bashkirov, Denis
Many examples of gauge-gravity duality and quantum equivalences of different-looking three-dimensional Quantum Field Theories indicate the existence of continuous symmetries whose currents are not built from elementary, or perturbative, fields used to write down the Lagrangian. These symmetries are called hidden or nonperturbative. We describe a method for studying continuous symmetries in a large class of three-dimensional supersymmetric gauge theories which, in particular, enables one to explore nonperturbative global symmetries and supersymmetries. As an application of the method, we prove conjectured supersymmetry enhancement in strongly coupled ABJM theory from N = 6 to N = 8 and find additional nonperturbative evidence for its duality to the N = 8 U(N) SYM theory for the minimal value of the Chern-Simons coupling. Hidden supersymmetry is also shown to occur in N = 4 d = 3 SQCD with one fundamental and one adjoint hypermultiplets. An infinite family of N = 6 d = 3 ABJ theories is proved to have hidden N = 8 superconformal symmetry and hidden parity on the quantum level. We test several conjectural dualities between ABJ theories and theories proposed by Bagger and Lambert, and Gustavsson by comparing superconformal indices of these theories. Comparison of superconformal indices is also used to test dualities between N = 2 d = 3 theories proposed by Aharony, the analysis of whose chiral rings teaches some general lessons about nonperturbative chiral operators of strongly coupled 3d supersymmetric gauge theories. As another application of our method we consider examples of hidden global symmetries in a class of quiver three-dimensional N = 4 superconformal gauge theories. Finally, we point out to the relations between some basic propeties of superconformal N ≥ 6 theories and their symmetries. The results presented in this thesis were obtained in a series of papers [1, 2, 3, 4, 5].
A confining model for charmonium and new gauge-invariant field equations
NASA Astrophysics Data System (ADS)
Hsu, Jong-Ping
2014-06-01
We discuss a confining model for charmonium in which the attractive force are derived from a new type of gauge field equation with a generalized SU3 gauge symmetry. The new gauge transformations involve non-integrable phase factors with vector gauge functions ω {ω/ a }( x). These transformations reduce to the usual SU3 gauge transformations in the special case ω {μ/ a }( x) = ∂ μ ξ a ( x). Such a generalized gauge symmetry leads to the fourth-order equations for new gauge fields and to the linear confining potentials. The fourth-order field equation implies that the corresponding massless gauge boson has non-definite energy. However, the new gauge boson is permanently confined in a quark system by the linear potential. We use the empirical potentials of the Cornell group for charmonium to obtain the coupling strength f 2/(4 π) ≈ 0.19 for the strong interaction. Such a confining model of quark dynamics could be compatible with perturbation. The model can be applied to other quark-antiquark systems.
Novel symmetries in N=2 supersymmetric quantum mechanical models
Malik, R.P.; Khare, Avinash
2013-07-15
We demonstrate the existence of a novel set of discrete symmetries in the context of the N=2 supersymmetric (SUSY) quantum mechanical model with a potential function f(x) that is a generalization of the potential of the 1D SUSY harmonic oscillator. We perform the same exercise for the motion of a charged particle in the X–Y plane under the influence of a magnetic field in the Z-direction. We derive the underlying algebra of the existing continuous symmetry transformations (and corresponding conserved charges) and establish its relevance to the algebraic structures of the de Rham cohomological operators of differential geometry. We show that the discrete symmetry transformations of our present general theories correspond to the Hodge duality operation. Ultimately, we conjecture that any arbitrary N=2 SUSY quantum mechanical system can be shown to be a tractable model for the Hodge theory. -- Highlights: •Discrete symmetries of two completely different kinds of N=2 supersymmetric quantum mechanical models have been discussed. •The discrete symmetries provide physical realizations of Hodge duality. •The continuous symmetries provide the physical realizations of de Rham cohomological operators. •Our work sheds a new light on the meaning of the above abstract operators.
Singlet-stabilized minimal gauge mediation
NASA Astrophysics Data System (ADS)
Curtin, David; Tsai, Yuhsin
2011-04-01
We propose singlet-stabilized minimal gauge mediation as a simple Intriligator, Seiberg and Shih-based model of direct gauge mediation which avoids both light gauginos and Landau poles. The hidden sector is a massive s-confining supersymmetric QCD that is distinguished by a minimal SU(5) flavor group. The uplifted vacuum is stabilized by coupling the meson to an additional singlet sector with its own U(1) gauge symmetry via nonrenormalizable interactions suppressed by a higher scale ΛUV in the electric theory. This generates a nonzero vacuum expectation value for the singlet meson via the inverted hierarchy mechanism, but requires tuning to a precision ˜(Λ/ΛUV)2, which is ˜10-4. In the course of this analysis we also outline some simple model-building rules for stabilizing uplifted-ISS models, which lead us to conclude that meson deformations are required (or at least heavily favored) to stabilize the adjoint component of the magnetic meson.
Does three-dimensional electromagnetic field inherit the spacetime symmetries?
NASA Astrophysics Data System (ADS)
Cvitan, M.; Dominis Prester, P.; Smolić, I.
2016-04-01
We prove that the electromagnetic field in a (1+2)-dimensional spacetime necessarily inherits the symmetries of the spacetime metric in a large class of generalized Einstein-Maxwell theories. The Lagrangians of the studied theories have general diff-covariant gravitational part and include both the gravitational and the gauge Chern-Simons terms.
Mechanisms of chiral symmetry breaking in QCD: A lattice perspective
NASA Astrophysics Data System (ADS)
Giusti, Leonardo
2016-01-01
I briefly review two recent studies on chiral symmetry breaking in QCD: (a) a computation of the spectral density of the Dirac operator in QCD Lite, (b) a precise determination of the topological charge distribution in the SU(3) Yang-Mills theory as defined by evolving the fundamental gauge field with the Yang-Mills gradient flow equation.
Introduction to gauge theories of the strong, weak, and electromagnetic interactions
Quigg, C.
1980-07-01
The plan of these notes is as follows. Chapter 1 is devoted to a brief evocative review of current beliefs and prejudices that form the context for the discussion to follow. The idea of Gauge Invariance is introduced in Chapter 2, and the connection between conservation laws and symmetries of the Lagrangian is recalled. Non-Abelian gauge field theories are constructed in Chapter 3, by analogy with the familiar case of electromagnetism. The Yang-Mills theory based upon isospin symmetry is constructed explicitly, and the generalization is made to other gauge groups. Chapter 4 is concerned with spontaneous symmetry breaking and the phenomena that occur in the presence or absence of local gauge symmetries. The existence of massless scalar fields (Goldstone particles) and their metamorphosis by means of the Higgs mechanism are illustrated by simple examples. The Weinberg-Salam model is presented in Chapter 5, and a brief resume of applications to experiment is given. Quantum Chromodynamics, the gauge theory of colored quarks and gluons, is developed in Chapter 6. Asymptotic freedom is derived schematically, and a few simple applications of perturbative QCD ae exhibited. Details of the conjectured confinement mechanism are omitted. The strategy of grand unified theories of the strong, weak, and electromagnetic interactions is laid out in Chapter 7. Some properties and consequences of the minimal unifying group SU(5) are presented, and the gauge hierarchy problem is introduced in passing. The final chapter contains an essay on the current outlook: aspirations, unanswered questions, and bold scenarios.
Rasin, A.
1994-04-01
We discuss the idea of approximate flavor symmetries. Relations between approximate flavor symmetries and natural flavor conservation and democracy models is explored. Implications for neutrino physics are also discussed.
Rizzo, T.G.
1995-02-01
Present and future prospects for the discovery of new gauge bosons, Z{prime} and W{prime}, are reviewed. Particular attention is paid to hadron and e{sup +}e{sup {minus}} collider searches for the W{prime} of the Left-Right Symmetric Model.
D0- and D1-branes with κ- and κ+ extended symmetry
NASA Astrophysics Data System (ADS)
Moshe, Moshe; Sakai, Norisuke
2000-10-01
D0-brane (D-particle) and D1-brane actions possess first and second class constraints that result in local κ symmetry. The κ symmetry of the D-particle and the D1-brane is extended here into a larger symmetry (κ- and κ+) in a larger phase space by turning second class constraints into first class constraints. Different gauge fixings of these symmetries result in different presentations of these systems while a ``unitary'' gauge fixing of the new κ+ symmetry retrieves the original action with κ-=κ symmetry. For a D1-brane our extended phase space makes all constraints into first class constraints in the case of a vanishing world sheet electric field [namely, (0,1) string].
SL(2, z) Action on Three-Dimensional Conformal Field Theories with Abelian Symmetry
NASA Astrophysics Data System (ADS)
Witten, Edward
On the space of three-dimensional conformal field theories with U(1) symmetry and a chosen coupling to a background gauge field, there is a natural action of the group SL(2, Z). The generator S of SL(2, Z) acts by letting the background gauge field become dynamical, an operation considered recently by Kapustin and Strassler in explaining three-dimensional mirror symmetry. The other generator T acts by shifting the Chern-Simons coupling of the background field. This SL(2, Z) action in three dimensions is related by the AdS/CFT correspondence to SL(2, Z) duality of low energy U(1) gauge fields in four dimensions.
Nonlocal symmetries, spectral parameter and minimal surfaces in AdS/CFT
NASA Astrophysics Data System (ADS)
Klose, Thomas; Loebbert, Florian; Münkler, Hagen
2017-03-01
We give a general account of nonlocal symmetries in symmetric space models and their relation to the AdS/CFT correspondence. In particular, we study a master symmetry which generates the spectral parameter and acts as a level-raising operator on the classical Yangian generators. The master symmetry extends to an infinite tower of symmetries with nonlocal Casimir elements as associated conserved charges. We discuss the algebraic properties of these symmetries and establish their role in explaining the recently observed one-parameter deformation of holographic Wilson loops. Finally, we provide a numerical framework, in which discretized minimal surfaces and their master symmetry deformation can be calculated.
Polynomial Graphs and Symmetry
ERIC Educational Resources Information Center
Goehle, Geoff; Kobayashi, Mitsuo
2013-01-01
Most quadratic functions are not even, but every parabola has symmetry with respect to some vertical line. Similarly, every cubic has rotational symmetry with respect to some point, though most cubics are not odd. We show that every polynomial has at most one point of symmetry and give conditions under which the polynomial has rotational or…
Existence and Stability of Gauged Non-Topological Solitons
NASA Astrophysics Data System (ADS)
Lee, Chul H.; Yoon, Seung Un
Classical non-topological soliton configurations are considered in a theory with a local U(1) symmetry. Their existence, stability against dispersion into free particles are studied numerically. As in the case of Friedberg, Lee, and Sirlin with a global U(1) symmetry, also in this case there are two critical charges; Qc for the existence and Qs for the stability of the non-topological soliton configurations. Our numerical results show that the magnitudes of both Qc and Qs increase as the magnitude of the gauge coupling constant e is increased with the other parameters kept at fixed values.
Two-dimensional quantum gravity in the conformal gauge
Ahn, C.; Park, Y.; Kim, K.Y.; Kim, Y. ); Kim, W.; Cho, B. )
1990-08-15
Gravity coupled to a scalar field in two dimensions is analyzed in the conformal gauge. We obtain the solution of a scalar field. The residual symmetry associated with the scalar field is found from the invariance of the action and the covariance of the equation of motion of a scalar field. This symmetry is naturally related to the fact that the energy-momentum tensor satisfies the transformation rule of the usual second-rank tensor under SL(2,{ital R}){direct product}SL(2,{ital R}) group transformations for the coordinates {ital x}{sup +} and {ital x}{sup {minus}}.
Global symmetries and renormalizability of Lee-Wick theories
Chivukula, R. Sekhar; Farzinnia, Arsham; Foadi, Roshan; Simmons, Elizabeth H.
2010-08-01
In this paper we discuss the global symmetries and the renormalizability of Lee-Wick (LW) scalar QED. In particular, in the ''auxiliary-field'' formalism we identify softly broken SO(1,1) global symmetries of the theory. We introduce SO(1,1) invariant gauge-fixing conditions that allow us to show in the auxiliary-field formalism directly that the number of superficially divergent amplitudes in a LW Abelian gauge theory is finite. To illustrate the renormalizability of the theory, we explicitly carry out the one-loop renormalization program in LW scalar QED and demonstrate how the counterterms required are constrained by the joint conditions of gauge and SO(1,1) invariance. We also compute the one-loop beta functions in LW scalar QED and contrast them with those of ordinary scalar QED.
NASA Astrophysics Data System (ADS)
Anselmi, Damiano
2015-05-01
We prove the Adler-Bardeen theorem in a large class of general gauge theories, including nonrenormalizable ones. We assume that the gauge symmetries are general covariance, local Lorentz symmetry, and Abelian and non-Abelian Yang-Mills symmetries, and that the local functionals of vanishing ghost numbers satisfy a variant of the Kluberg-Stern-Zuber conjecture. We show that if the gauge anomalies are trivial at one loop, for every truncation of the theory there exists a subtraction scheme where they manifestly vanish to all orders, within the truncation. Outside the truncation the cancellation of gauge anomalies can be enforced by fine-tuning local counterterms. The framework of the proof is worked out by combining a recently formulated chiral dimensional regularization with a gauge invariant higher-derivative regularization. If the higher-derivative regularizing terms are placed well beyond the truncation, and the energy scale Λ associated with them is kept fixed, the theory is superrenormalizable and has the property that, once the gauge anomalies are canceled at one loop, they manifestly vanish from two loops onwards by simple power counting. When the Λ divergences are subtracted away and Λ is sent to infinity, the anomaly cancellation survives in a manifest form within the truncation and in a nonmanifest form outside. The standard model coupled to quantum gravity satisfies all the assumptions, so it is free of gauge anomalies to all orders.
Pöll, J S
1999-06-01
Gauges are old measures of thickness. They originated in the British iron wire industry at a time when there was no universal unit of thickness. The sizes of the gauge numbers were the result of the process of wire-drawing and the nature of iron as a substance. Gauges were measured and described in fractions of an inch during the 19th century. In the UK, one gauge was standardised and legally enforced as the Standard Wire Gauge. One important reason for the standardisation of the gauge was the convenience of craftsmen. In the 20th century, the gauge was to be replaced with the introduction of the International System of Units. However, within the field of anaesthesia at the threshold of the 21st century, the gauge seems hard to remove from the minds of craftsmen like anaesthetists.
Contact symmetries and Hamiltonian thermodynamics
Bravetti, A.; Lopez-Monsalvo, C.S.; Nettel, F.
2015-10-15
It has been shown that contact geometry is the proper framework underlying classical thermodynamics and that thermodynamic fluctuations are captured by an additional metric structure related to Fisher’s Information Matrix. In this work we analyse several unaddressed aspects about the application of contact and metric geometry to thermodynamics. We consider here the Thermodynamic Phase Space and start by investigating the role of gauge transformations and Legendre symmetries for metric contact manifolds and their significance in thermodynamics. Then we present a novel mathematical characterization of first order phase transitions as equilibrium processes on the Thermodynamic Phase Space for which the Legendre symmetry is broken. Moreover, we use contact Hamiltonian dynamics to represent thermodynamic processes in a way that resembles the classical Hamiltonian formulation of conservative mechanics and we show that the relevant Hamiltonian coincides with the irreversible entropy production along thermodynamic processes. Therefore, we use such property to give a geometric definition of thermodynamically admissible fluctuations according to the Second Law of thermodynamics. Finally, we show that the length of a curve describing a thermodynamic process measures its entropy production.
Commutation Relations and Discrete Garnier Systems
NASA Astrophysics Data System (ADS)
Ormerod, Christopher M.; Rains, Eric M.
2016-11-01
We present four classes of nonlinear systems which may be considered discrete analogues of the Garnier system. These systems arise as discrete isomonodromic deformations of systems of linear difference equations in which the associated Lax matrices are presented in a factored form. A system of discrete isomonodromic deformations is completely determined by commutation relations between the factors. We also reparameterize these systems in terms of the image and kernel vectors at singular points to obtain a separate birational form. A distinguishing feature of this study is the presence of a symmetry condition on the associated linear problems that only appears as a necessary feature of the Lax pairs for the least degenerate discrete Painlevé equations.
A Few Continuous and Discrete Dynamical Systems
NASA Astrophysics Data System (ADS)
Zhang, Yufeng; Rui, Wenjuan
2016-08-01
Starting from a 2-unimodular group, we construct its new Lie algebras for which the positive-order Lax pairs and the negative-order Lax pairs are introduced, respectively. With the help of the resulting structure equation of the group we generate some partial differential equations including the well-known MKdV equation, the sine-Gordon equation, the hyperbolic sine-Gordon equation and other new nonlinear evolution equations. With the aid of the Tu scheme combined with the given Lax pairs, we obtain the isospectral and nonisospectral hierarchies of evolution equations, from which we generate two sets of symmetries of a generalized nonlinear Schrödinger (gNLS) equation. Finally, we discretize the Lax pairs to obtain a set of coupled semi-discrete equations. As their reduction, we produce the semi-discrete MKdV equation and semi-discrete NLS equation.
Finite field-dependent symmetries in perturbative quantum gravity
Upadhyay, Sudhaker
2014-01-15
In this paper we discuss the absolutely anticommuting nilpotent symmetries for perturbative quantum gravity in general curved spacetime in linear and non-linear gauges. Further, we analyze the finite field-dependent BRST (FFBRST) transformation for perturbative quantum gravity in general curved spacetime. The FFBRST transformation changes the gauge-fixing and ghost parts of the perturbative quantum gravity within functional integration. However, the operation of such symmetry transformation on the generating functional of perturbative quantum gravity does not affect the theory on physical ground. The FFBRST transformation with appropriate choices of finite BRST parameter connects non-linear Curci–Ferrari and Landau gauges of perturbative quantum gravity. The validity of the results is also established at quantum level using Batalin–Vilkovisky (BV) formulation. -- Highlights: •The perturbative quantum gravity is treated as gauge theory. •BRST and anti-BRST transformations are developed in linear and non-linear gauges. •BRST transformation is generalized by making it finite and field dependent. •Connection between linear and non-linear gauges is established. •Using BV formulation the results are established at quantum level also.
Extended Nambu-Jona-Lasinio model and hidden local symmetry of low energy QCD
NASA Astrophysics Data System (ADS)
Wakamatsu, M.
1996-11-01
Using the standard auxiliary field method, we derive from the extended Nambu-Jona-Lasinio model an effective meson action containing vector and axial-vector mesons in addition to Goldstone bosons. The vector and axial-vector mesons in this effective action transform as gauge fields of hidden local symmetry Glocal=[U(n)L×U(n)R]local. Here, the realization of enlarged hidden local symmetry is accomplished via the introduction of two kinds of ``compensating'' fields. For obtaining the intrinsic-parity-violating part of the action, we generalize the standard gauged Wess-Zumino-Witten action such that it also contains two kinds of ``compensators'' in addition to the usual Goldstone bosons as well as the vector and axial-vector mesons. This generalized gauged Wess-Zumino-Witten action turns out to have Gglobal×Glocal symmetry, where Gglobal is the usual U(n)L×U(n)R global chiral symmetry while Glocal is the U(n)L×U(n)R hidden local symmetry. This means that Glocal has no gauge anomaly and its associated vector and axial-vector mesons can be regarded as gauge bosons of Glocal. The introduction of the coupling with the external electroweak fields requires us to gauge some appropriate subgroup of Gglobal. To make it consistent with the anomaly structure of QCD is a nontrivial problem. We explain how this can be done, following the recent suggestion by several authors.
A new family of gauges in linearized general relativity
NASA Astrophysics Data System (ADS)
Esposito, Giampiero; Stornaiolo, Cosimo
2000-05-01
For vacuum Maxwell theory in four dimensions, a supplementary condition exists (due to Eastwood and Singer) which is invariant under conformal rescalings of the metric, in agreement with the conformal symmetry of the Maxwell equations. Thus, starting from the de Donder gauge, which is not conformally invariant but is the gravitational counterpart of the Lorenz gauge, one can consider, led by formal analogy, a new family of gauges in general relativity, which involve fifth-order covariant derivatives of metric perturbations. The admissibility of such gauges in the classical theory is first proven in the cases of linearized theory about flat Euclidean space or flat Minkowski spacetime. In the former, the general solution of the equation for the fulfillment of the gauge condition after infinitesimal diffeomorphisms involves a 3-harmonic 1-form and an inverse Fourier transform. In the latter, one needs instead the kernel of powers of the wave operator, and a contour integral. The analysis is also used to put restrictions on the dimensionless parameter occurring in the DeWitt supermetric, while the proof of admissibility is generalized to a suitable class of curved Riemannian backgrounds. Eventually, a non-local construction of the tensor field is obtained which makes it possible to achieve conformal invariance of the above gauges.
Dark matter and vectorlike leptons from gauged lepton number
NASA Astrophysics Data System (ADS)
Schwaller, Pedro; Tait, Tim M. P.; Vega-Morales, Roberto
2013-08-01
We investigate a simple model where lepton number is promoted to a local U(1)L gauge symmetry which is then spontaneously broken, leading to a viable thermal dark matter (DM) candidate and vectorlike leptons as a byproduct. The dark matter arises as part of the exotic lepton sector required by the need to satisfy anomaly cancellation and is a Dirac electroweak (mostly) singlet neutrino. It is stabilized by an accidental global symmetry of the renormalizable Lagrangian which is preserved even after the gauged lepton number is spontaneously broken and can annihilate efficiently to give the correct thermal relic abundance. We examine the ability of this model to give a viable DM candidate and discuss both direct and indirect detection implications. We also examine some of the LHC phenomenology of the associated exotic lepton sector and in particular its effects on Higgs decays.
Duality invariance in Fayet-Iliopoulos gauged supergravity
NASA Astrophysics Data System (ADS)
Cacciatori, Sergio L.; Klemm, Dietmar; Rabbiosi, Marco
2016-09-01
We propose a geometric method to study the residual symmetries in N = 2, d = 4 U(1) Fayet-Iliopoulos (FI) gauged supergravity. It essentially involves the stabilization of the symplectic vector of gauge couplings (FI parameters) under the action of the U-duality symmetry of the ungauged theory. In particular we are interested in those transformations that act non-trivially on the solutions and produce scalar hair and dyonic black holes from a given seed. We illustrate the procedure for finding this group in general and then show how it works in some specific models. For the prepotential F = - iX 0 X 1, we use our method to add one more parameter to the rotating Chow-Compère solution, representing scalar hair.
Phases of N=1 Supersymmetric Chiral Gauge Theories
Craig, Nathaniel; Essig, Rouven; Hook, Anson; Torroba, Gonzalo; /SLAC /Stanford U., Phys. Dept.
2012-02-17
We analyze the phases of supersymmetric chiral gauge theories with an antisymmetric tensor and (anti)fundamental flavors, in the presence of a classically marginal superpotential deformation. Varying the number of flavors that appear in the superpotential reveals rich infrared chiral dynamics and novel dualities. The dualities are characterized by an infinite family of magnetic duals with arbitrarily large gauge groups describing the same fixed point, correlated with arbitrarily large classical global symmetries that are truncated nonperturbatively. At the origin of moduli space, these theories exhibit a phase with confinement and chiral symmetry breaking, an interacting nonabelian Coulomb phase, and phases where an interacting sector coexists with a sector that either s-confines or is in a free magnetic phase. Properties of these intriguing 'mixed phases' are studied in detail using duality and a-maximization, and the presence of superpotential interactions provides further insights into their formation.
Spontaneous parity violation and SUSY strong gauge theory
Haba, Naoyuki; Ohki, Hiroshi
2012-07-27
We suggest simple models of spontaneous parity violation in supersymmetric strong gauge theory. We focus on left-right symmetric model and investigate vacuum with spontaneous parity violation. Non-perturbative effects are calculable in supersymmetric gauge theory, and we suggest new models. Our models show confinement, so that we try to understand them by using a dual description of the theory. The left-right symmetry breaking and electroweak symmetry breaking are simultaneously occurred with the suitable energy scale hierarchy. This structure has several advantages compared to the MSSM. The scale of the Higgs mass (left-right breaking scale) and that of VEVs are different, so the SUSY little hierarchy problems are absent. The second model also induces spontaneous supersymmetry breaking.
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.
Symmetry and Evolution in Quantum Gravity
NASA Astrophysics Data System (ADS)
Gryb, Sean; Thébaault, Karim
2014-03-01
We propose an operator constraint equation for the wavefunction of the Universe that admits genuine evolution. While the corresponding classical theory is equivalent to the canonical decomposition of General Relativity, the quantum theory contains an evolution equation distinct from standard Wheeler-DeWitt cosmology. Furthermore, the local symmetry principle—and corresponding observables—of the theory have a direct interpretation in terms of a conventional gauge theory, where the gauge symmetry group is that of spatial conformal diffeomorphisms (that preserve the spatial volume of the Universe). The global evolution is in terms of an arbitrary parameter that serves only as an unobservable label for successive states of the Universe. Our proposal follows unambiguously from a suggestion of York whereby the independently specifiable initial data in the action principle of General Relativity is given by a conformal geometry and the spatial average of the York time on the spacelike hypersurfaces that bound the variation. Remarkably, such a variational principle uniquely selects the form of the constraints of the theory so that we can establish a precise notion of both symmetry and evolution in quantum gravity.
Variational contact symmetries of constrained Lagrangians
NASA Astrophysics Data System (ADS)
Terzis, Petros A.; Dimakis, N.; Christodoulakis, T.; Paliathanasis, Andronikos; Tsamparlis, Michael
2016-03-01
The investigation of contact symmetries of re-parametrization invariant Lagrangians of finite degrees of freedom and quadratic in the velocities is presented. The main concern of the paper is those symmetry generators which depend linearly in the velocities. A natural extension of the symmetry generator along the lapse function N(t) , with the appropriate extension of the dependence in N ˙ (t) of the gauge function, is assumed; this action yields new results. The central finding is that the integrals of motion are either linear or quadratic in velocities and are generated, respectively by the conformal Killing vector fields and the conformal Killing tensors of the configuration space metric deduced from the kinetic part of the Lagrangian (with appropriate conformal factors). The freedom of re-parametrization allows one to appropriately scale N(t) , so that the potential becomes constant; in this case the integrals of motion can be constructed from the Killing fields and Killing tensors of the scaled metric. A rather interesting result is the non-necessity of the gauge function in Noether's theorem due to the presence of the Hamiltonian constraint.
Pinsky, Mark; Casanova, David; Alemany, Pere; Alvarez, Santiago; Avnir, David; Dryzun, Chaim; Kizner, Ziv; Sterkin, Alexander
2008-01-30
We introduce a new mathematical tool for quantifying the symmetry contents of molecular structures: the Symmetry Operation Measures. In this approach, we measure the minimal distance between a given structure and the structure which is obtained after applying a selected symmetry operation on it. If the given operation is a true symmetry operation for the structure, this distance is zero; otherwise it gives an indication of how different the transformed structure is from the original one. Specifically, we provide analytical solutions for measures of all the improper rotations, S n p, including mirror symmetry and inversion, as well as for all pure rotations, C n p. These measures provide information complementary to the Continuous Symmetry Measures (CSM) that evaluate the distance between a given structure and the nearest structure which belongs to a selected symmetry point-group.
Gauge-invariant masses through Schwinger-Dyson equations
Bashir, A.; Raya, A.
2007-02-27
Schwinger-Dyson equations (SDEs) are an ideal framework to study non-perturbative phenomena such as dynamical chiral symmetry breaking (DCSB). A reliable truncation of these equations leading to gauge invariant results is a challenging problem. Constraints imposed by Landau-Khalatnikov-Fradkin transformations (LKFT) can play an important role in the hunt for physically acceptable truncations. We present these constrains in the context of dynamical mass generation in QED in 2 + 1-dimensions.
Semistrict higher gauge theory
NASA Astrophysics Data System (ADS)
Jurčo, Branislav; Sämann, Christian; Wolf, Martin
2015-04-01
We develop semistrict higher gauge theory from first principles. In particular, we describe the differential Deligne cohomology underlying semistrict principal 2-bundles with connective structures. Principal 2-bundles are obtained in terms of weak 2-functors from the Čech groupoid to weak Lie 2-groups. As is demonstrated, some of these Lie 2-groups can be differentiated to semistrict Lie 2-algebras by a method due to Ševera. We further derive the full description of connective structures on semistrict principal 2-bundles including the non-linear gauge transformations. As an application, we use a twistor construction to derive superconformal constraint equations in six dimensions for a non-Abelian tensor multiplet taking values in a semistrict Lie 2-algebra.
Cuzinatto, R.R. . E-mail: rodrigo@ift.unesp.br; Melo, C.A.M. de . E-mail: cassius.anderson@gmail.com; Pompeia, P.J. . E-mail: pompeia@ift.unesp.br
2007-05-15
A gauge theory of second order in the derivatives of the auxiliary field is constructed following Utiyama's program. A novel field strength G = {partial_derivative}F + fAF arises besides the one of the first order treatment, F = {partial_derivative}A - {partial_derivative}A + fAA. The associated conserved current is obtained. It has a new feature: topological terms are determined from local invariance requirements. Podolsky Generalized Eletrodynamics is derived as a particular case in which the Lagrangian of the gauge field is L {sub P} {proportional_to} G {sup 2}. In this application the photon mass is estimated. The SU (N) infrared regime is analysed by means of Alekseev-Arbuzov-Baikov's Lagrangian.
Wood, Billy E.; Groves, Scott E.; Larsen, Greg J.; Sanchez, Roberto J.
2006-11-14
A lightweight, small size, high sensitivity gauge for indirectly measuring displacement or absolute gap width by measuring axial strain in an orthogonal direction to the displacement/gap width. The gap gauge includes a preferably titanium base having a central tension bar with springs connecting opposite ends of the tension bar to a pair of end connector bars, and an elongated bow spring connected to the end connector bars with a middle section bowed away from the base to define a gap. The bow spring is capable of producing an axial strain in the base proportional to a displacement of the middle section in a direction orthogonal to the base. And a strain sensor, such as a Fabry-Perot interferometer strain sensor, is connected to measure the axial strain in the base, so that the displacement of the middle section may be indirectly determined from the measurement of the axial strain in the base.
NASA Technical Reports Server (NTRS)
Sumrall, Daniel R.; Nichols, Vincent P.
1992-01-01
Gauge aligns itself and retains indication for later reading. Measuring tool indicates height of protrusion of pin from flat surface. Tool surrounds pin and holds itself square with flat surface, ensuring proper alignment and accuracy of measurement. Used in hard-to-see and hard-to-reach places. Holds indication of height until read. Metal scale slides in and out through slot in top plate. Scale value at slot gives height of pin under piston. Dimensions in inches.
NASA Astrophysics Data System (ADS)
Gan, W. S.
2008-12-01
This paper is to be dedicated to Prof C N Yang's 85th birthday celebration because the idea here was inspired by Prof Yang's public lecture in Singapore in 2006. There are many similarities between electromagnetic waves and acoustic waves. Maxwell's equations for em waves is the oldest gauge theory. We discover symmetries in the pair of wave equations in the acoustic stress field and the velocity field. We also derive a new equation in terms of the stress field for sound propagation in solids. This is different from the Christoffel's equation which is in term of the velocity field. We feel that stress field can better characterize the elastic properties of the sound waves. We also derive the acoustic gauge field condition and gauge invariance and symmetries for the acoustic fields. We also apply symmetries to study negative refraction. Note from Publisher: This article contains the abstract only.
Temperature-Compensating Inactive Strain Gauge
NASA Technical Reports Server (NTRS)
Moore, Thomas C., Sr.
1993-01-01
Thermal contribution to output of active gauge canceled. High-temperature strain gauges include both active gauge wires sensing strains and inactive gauge wires providing compensation for thermal contributions to gauge readings. Inactive-gauge approach to temperature compensation applicable to commercially available resistance-type strain gauges operating at temperatures up to 700 degrees F and to developmental strain gauges operating at temperatures up to 2,000 degrees F.
Gauge mediation with D-term SUSY breaking
Watari, Taizan; Nakayama, Y.; Taki, Masato; Watari, Taizan; Yanagida, T.T.
2007-05-07
We construct a gauge-mediation model with a D-term supersymmetry (SUSY) breaking. R-symmetry breaking necessary for generating the SUSY standard-model gaugino masses is given by gaugino condensation of a strongly coupled gauge theory in the hidden sector. The energy scale of the strong dynamics of the hidden sector gauge theory should be around the messenger mass scale M, or otherwise perturbative calculations would be reliable and would lead to negative soft mass squared for squarks and sleptons. Thus, all the mass scales are controlled by a virtually single parameter, \\sqrt{D}/M. This model covers a very wide range of gravitino mass, m_{3/2} \\simeq 1 eV--100 TeV. Possible embeddings of the model in string theory are also discussed.
Exact BPS domain walls at finite gauge coupling
NASA Astrophysics Data System (ADS)
Blaschke, Filip
2017-01-01
Bogomol'nyi-Prasad-Sommerfield solitons in models with spontaneously broken gauge symmetry have been intensively studied at the infinite gauge coupling limit, where the governing equation-the so-called master equation-is exactly solvable. Except for a handful of special solutions, the standing impression is that analytic results at finite coupling are generally unavailable. The aim of this paper is to demonstrate, using domain walls in Abelian-Higgs models as the simplest example, that exact solitons at finite gauge coupling can be readily obtained if the number of Higgs fields (N) is large enough. In particular, we present a family of exact solutions, describing N domain walls at arbitrary positions in models with at least N≥2N+1. We have also found that adding together any pair of solutions can produce a new exact solution if the combined tension is below a certain limit.
Coulomb gauge ghost propagator and the Coulomb form factor
NASA Astrophysics Data System (ADS)
Quandt, M.; Burgio, G.; Chimchinda, S.; Reinhardt, H.
The ghost propagator and the Coulomb potential are evaluated in Coulomb gauge on the lattice, using an improved gauge fixing scheme which includes the residual symmetry. This setting has been shown to be essential in order to explain the scaling violations in the instantaneous gluon propagator. We find that both the ghost propagator and the Coulomb potential are insensitive to the Gribov problem or the details of the residual gauge fixing, even if the Coulomb potential is evaluated from the A0 -propagator instead of the Coulomb kernel. In particular, no signs of scaling violations could be found in either quantity, at least to well below the numerical accuracy where these violations were visible for the gluon propagator. The Coulomb potential from the A0 -propagator is shown to be in qualitative agreement with the (formally equivalent) expression evaluated from the Coulomb kernel.
Symmetry-preserving difference schemes for some heat transfer equations
NASA Astrophysics Data System (ADS)
Bakirova, M. I.; Dorodnitsyn, V. A.; Kozlov, R. V.
1997-12-01
Lie group analysis of differential equations is a generally recognized method, which provides invariant solutions, integrability, conservation laws etc. In this paper we present three characteristic examples of the construction of invariant difference equations and meshes, where the original continuous symmetries are preserved in discrete models. Conservation of symmetries in difference modelling helps to retain qualitative properties of the differential equations in their difference counterparts.
Infrared modification of gravity from conformal symmetry
NASA Astrophysics Data System (ADS)
Gegenberg, Jack; Rahmati, Shohreh; Seahra, Sanjeev S.
2016-03-01
We reconsider a gauge theory of gravity in which the gauge group is the conformal group SO(4,2), and the action is of the Yang-Mills form, quadratic in the curvature. The resulting gravitational theory exhibits local conformal symmetry and reduces to Weyl-squared gravity under certain conditions. When the theory is linearized about flat spacetime, we find that matter which couples to the generators of special conformal transformations reproduces Newton's inverse square law. Conversely, matter which couples to generators of translations induces a constant and possibly repulsive force far from the source, which may be relevant for explaining the late-time acceleration of the Universe. The coupling constant of the theory is dimensionless, which means that it is potentially renormalizable.
NASA Astrophysics Data System (ADS)
Jiang, Shenghan; Ran, Ying
2017-03-01
We present systematic constructions of tensor-network wave functions for bosonic symmetry-protected topological (SPT) phases respecting both onsite and spatial symmetries. From the classification point of view, our results show that in spatial dimensions d =1 ,2 ,3 , the cohomological bosonic SPT phases protected by a general symmetry group SG involving onsite and spatial symmetries are classified by the cohomology group Hd +1[SG,U(1 ) ] , in which both the time-reversal symmetry and mirror-reflection symmetries should be treated as antiunitary operations. In addition, for every SPT phase protected by a discrete symmetry group and some SPT phases protected by continuous symmetry groups, generic tensor-network wave functions can be constructed which would be useful for the purpose of variational numerical simulations. As a by-product, our results demonstrate a generic connection between rather conventional symmetry-enriched topological phases and SPT phases via an anyon condensation mechanism.
Observational constraints on gauge field production in axion inflation
Meerburg, P.D.; Pajer, E. E-mail: enrico.pajer@gmail.com
2013-02-01
Models of axion inflation are particularly interesting since they provide a natural justification for the flatness of the potential over a super-Planckian distance, namely the approximate shift-symmetry of the inflaton. In addition, most of the observational consequences are directly related to this symmetry and hence are correlated. Large tensor modes can be accompanied by the observable effects of a the shift-symmetric coupling φF F-tilde to a gauge field. During inflation this coupling leads to a copious production of gauge quanta and consequently a very distinct modification of the primordial curvature perturbations. In this work we compare these predictions with observations. We find that the leading constraint on the model comes from the CMB power spectrum when considering both WMAP 7-year and ACT data. The bispectrum generated by the non-Gaussian inverse-decay of the gauge field leads to a comparable but slightly weaker constraint. There is also a constraint from μ-distortion using TRIS plus COBE/FIRAS data, but it is much weaker. Finally we comment on a generalization of the model to massive gauge fields. When the mass is generated by some light Higgs field, observably large local non-Gaussianity can be produced.
27 CFR 19.289 - Production gauge.
Code of Federal Regulations, 2011 CFR
2011-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2011-04-01 2011-04-01 false Production gauge. 19.289... OF THE TREASURY LIQUORS DISTILLED SPIRITS PLANTS Gauging Rules for Gauging § 19.289 Production gauge. (a) General requirements for production gauges. A proprietor must gauge all spirits by...
Special relativity in a discrete quantum universe
NASA Astrophysics Data System (ADS)
Bisio, Alessandro; D'Ariano, Giacomo Mauro; Perinotti, Paolo
2016-10-01
The hypothesis of a discrete fabric of the universe, the "Planck scale," is always on stage since it solves mathematical and conceptual problems in the infinitely small. However, it clashes with special relativity, which is designed for the continuum. Here, we show how the clash can be overcome within a discrete quantum theory where the evolution of fields is described by a quantum cellular automaton. The reconciliation is achieved by defining the change of observer as a change of representation of the dynamics, without any reference to space-time. We use the relativity principle, i.e., the invariance of dynamics under change of inertial observer, to identify a change of inertial frame with a symmetry of the dynamics. We consider the full group of such symmetries, and recover the usual Lorentz group in the relativistic regime of low energies, while at the Planck scale the covariance is nonlinearly distorted.
Symmetry protected topological superfluid (3)He-B.
Mizushima, Takeshi; Tsutsumi, Yasumasa; Sato, Masatoshi; Machida, Kazushige
2015-03-25
Owing to the richness of symmetry and well-established knowledge of bulk superfluidity, the superfluid (3)He has offered a prototypical system to study intertwining of topology and symmetry. This article reviews recent progress in understanding the topological superfluidity of (3)He in a multifaceted manner, including symmetry considerations, the Jackiw-Rebbi's index theorem, and the quasiclassical theory. Special focus is placed on the symmetry protected topological superfuidity of the (3)He-B confined in a slab geometry. The (3)He-B under a magnetic field is separated to two different sub-phases: the symmetry protected topological phase and non-topological phase. The former phase is characterized by the existence of symmetry protected Majorana fermions. The topological phase transition between them is triggered by the spontaneous breaking of a hidden discrete symmetry. The critical field is quantitatively determined from the microscopic calculation that takes account of magnetic dipole interaction of the (3)He nucleus. It is also demonstrated that odd-frequency even-parity Cooper pair amplitudes are emergent in low-lying quasiparticles. The key ingredients, symmetry protected Majorana fermions and odd-frequency pairing, bring an important consequence that the coupling of the surface states to an applied field is prohibited by the hidden discrete symmetry, while the topological phase transition with the spontaneous symmetry breaking is accompanied by anomalous enhancement and anisotropic quantum criticality of surface spin susceptibility. We also illustrate common topological features between topological crystalline superconductors and symmetry protected topological superfluids, taking UPt3 and Rashba superconductors as examples.
Gauge theory of fermions on R X S{sup 3} spacetime
Dariescu, M.A.; Dariescu, C.; Gottlieb, I.
1995-06-01
A Lorentz-invariant gauge theory for massive fermions on R X S{sup 3} spacetime is built up. Using the symmetry of S{sup 3}, the authors obtain Dirac-type equations and derive the expression of the fermionic propagator. Finally, starting from the SU(N) gauge-invariant Lagrangian, they obtain the set of Dirac-Yang-Mills equations on R X S{sup 3} spacetime, pointing out major differences from the Minkowskian case.
Ward identities and gauge flow for M-theory in N =3 superspace
NASA Astrophysics Data System (ADS)
Upadhyay, Sudhaker
2015-09-01
We derive the Becchi-Rouet-Stora-Tyutin (BRST) symmetry, Slavnov-Taylor identities, and Nielsen identities for the Aharony-Bergman-Jafferis-Maldacena theories in N =3 harmonic superspace. Further, the gauge dependence of one-particle irreducible amplitudes in this superconformal Chern-Simons theory is shown to be generated by a canonical flow with respect to the extended Slavnov-Taylor identity, induced by the extended BRST transformations (including the BRST transformations of the gauge parameters).
Gedanken Worlds without Higgs: QCD-Induced Electroweak Symmetry Breaking
Quigg, Chris; Shrock, Robert; /YITP, Stony Brook
2009-01-01
To illuminate how electroweak symmetry breaking shapes the physical world, we investigate toy models in which no Higgs fields or other constructs are introduced to induce spontaneous symmetry breaking. Two models incorporate the standard SU(3){sub c} {circle_times} SU(2){sub L} {circle_times} U(1){sub Y} gauge symmetry and fermion content similar to that of the standard model. The first class--like the standard electroweak theory--contains no bare mass terms, so the spontaneous breaking of chiral symmetry within quantum chromodynamics is the only source of electroweak symmetry breaking. The second class adds bare fermion masses sufficiently small that QCD remains the dominant source of electroweak symmetry breaking and the model can serve as a well-behaved low-energy effective field theory to energies somewhat above the hadronic scale. A third class of models is based on the left-right-symmetric SU(3){sub c} {circle_times} SU(2){sub L} {circle_times} SU(2){sub R} {circle_times} U(1)B?L gauge group. In a fourth class of models, built on SU(4){sub PS} {circle_times} SU(2){sub L} {circle_times} SU(2){sub R} gauge symmetry, lepton number is treated as a fourth color. Many interesting characteristics of the models stem from the fact that the effective strength of the weak interactions is much closer to that of the residual strong interactions than in the real world. The Higgs-free models not only provide informative contrasts to the real world, but also lead us to consider intriguing issues in the application of field theory to the real world.
Electroweak symmetry breaking by extra dimensions
Hsin-Chia Cheng; Bogdan A. Dobrescu and Christopher T. Hill
2000-05-25
Electroweak symmetry breaking may be naturally induced by the observed quark and gauge fields in extra dimensions without a fundamental Higgs field. The authors show that a composite Higgs doublet can arise as a bound state of (t,b){sub L} and a linear combination of the Kaluza-Klein states of t{sub R}, due to QCD in extra dimensions. The top quark mass depends on the number of active t{sub R} Kaluza-Klein modes, and is consistent with the experimental value.
Confinement and flavor symmetry breaking via monopolecondensation
Murayama, Hitoshi
2000-09-19
We discuss dynamics of N=2 supersymmetric SU(n_c) gaugetheories with n_f quark hypermultiplets. Upon N=1 perturbation ofintroducing a finite mass for the adjoint chiral multiplet, we show thatthe flavor U(n_f) symmetry is dynamically broken to U(r) times U(n_f-r),where r\\leq [n_f/2]is an integer. This flavor symmetry breaking occursdue to the condensates of magnetic degrees of freedom which acquireflavor quantum numbers due to the quark zero modes. We briefly comment onthe USp(2n_c) gauge theories. This talk is based on works with GiuseppeCarlino and Ken Konishi, hep-th/0001036 and hep-th/0005076.
Synthetic-gauge-field-induced Dirac semimetal state in an acoustic resonator system
NASA Astrophysics Data System (ADS)
Yang, Zhaoju; Gao, Fei; Shi, Xihang; Zhang, Baile
2016-12-01
Recently, a proposal of synthetic gauge field in reduced two-dimensional (2D) system from three-dimensional (3D) acoustic structure shows an analogue of the gapped Haldane model with fixed k z , and achieves the gapless Weyl semimetal phase in 3D momentum space. Here, extending this approach of synthetic gauge flux, we propose a reduced square lattice of acoustic resonators, which exhibits Dirac nodes with broken effective time-reversal symmetry. Protected by an additional hidden symmetry, these Dirac nodes with quantized values of topological charge are characterized by nonzero winding number and the finite structure exhibits flat edge modes that cannot be destroyed by perturbations.
[Investigations in dynamics of gauge theories in theoretical particle physics
Not Available
1993-02-01
The major theme of the theoretical physics research conducted under DOE support over the past several years has been within the rubric of the standard model, and concerned the interplay between symmetries and dynamics. The research was thus carried out mostly in the context of gauge field theories, and usually in the presence of chiral fermions. Dynamical symmetry breaking was examined both from the point of view of perturbation theory, as well as from non-perturbative techniques associated with certain characteristic features of specific theories. Among the topics of research were: the implications of abelian and non-abelian anomalies on the spectrum and possible dynamical symmetry breaking in any theory, topological and conformal properties of quantum fields in two and higher dimensions, the breaking of global chiral symmetries by vector-like gauge theories such as QCD, the phenomenological implications of a strongly interacting Higgs sector in the standard model, and the application of soliton ideas to the physics to be explored at the SSC.
The symmetry behind extended flavour democracy and large leptonic mixing
NASA Astrophysics Data System (ADS)
Branco, G. C.; Silva-Marcos, J. I.
2002-01-01
We show that there is a minimal discrete symmetry which leads to the extended flavour democracy scenario constraining the Dirac neutrino, the charged lepton and the Majorana neutrino mass term (MR) to be all proportional to the democratic matrix, with all elements equal. In particular, this discreet symmetry forbids other large contributions to MR, such as a term proportional to the unit matrix, which would normally be allowed by a S3L×S3R permutation symmetry. This feature is crucial in order to obtain large leptonic mixing, without violating 't Hooft's naturalness principle.
Discrete breathers for a discrete nonlinear Schrödinger ring coupled to a central site.
Jason, Peter; Johansson, Magnus
2016-01-01
We examine the existence and properties of certain discrete breathers for a discrete nonlinear Schrödinger model where all but one site are placed in a ring and coupled to the additional central site. The discrete breathers we focus on are stationary solutions mainly localized on one or a few of the ring sites and possibly also the central site. By numerical methods, we trace out and study the continuous families the discrete breathers belong to. Our main result is the discovery of a split bifurcation at a critical value of the coupling between neighboring ring sites. Below this critical value, families form closed loops in a certain parameter space, implying that discrete breathers with and without central-site occupation belong to the same family. Above the split bifurcation the families split up into several separate ones, which bifurcate with solutions with constant ring amplitudes. For symmetry reasons, the families have different properties below the split bifurcation for even and odd numbers of sites. It is also determined under which conditions the discrete breathers are linearly stable. The dynamics of some simpler initial conditions that approximate the discrete breathers are also studied and the parameter regimes where the dynamics remain localized close to the initially excited ring site are related to the linear stability of the exact discrete breathers.
General gauge mediation at the weak scale
NASA Astrophysics Data System (ADS)
Knapen, Simon; Redigolo, Diego; Shih, David
2016-03-01
We completely characterize General Gauge Mediation (GGM) at the weak scale by solving all IR constraints over the full parameter space. This is made possible through a combination of numerical and analytical methods, based on a set of algebraic relations among the IR soft masses derived from the GGM boundary conditions in the UV. We show how tensions between just a few constraints determine the boundaries of the parameter space: electroweak symmetry breaking (EWSB), the Higgs mass, slepton tachyons, and left-handed stop/sbottom tachyons. While these constraints allow the left-handed squarks to be arbitrarily light, they place strong lower bounds on all of the right-handed squarks. Meanwhile, light EW superpartners are generic throughout much of the parameter space. This is especially the case at lower messenger scales, where a positive threshold correction to m h coming from light Higgsinos and winos is essential in order to satisfy the Higgs mass constraint.
Origin of Mass Hierarchies in Gauge Theories
NASA Astrophysics Data System (ADS)
Cvetic, Mirjam
We study the origin of mass hierarchies for different systems of fundamental interactions; in particular, we analyze whether the W(,L)-W(,R) mass splitting, and the fermion mass hierarchy can be of radiative origin. Within the left-right symmetric gauge structure G (TBOND) SU(2)(,L) x SU(2)(,R) x U(1)(,B-L), where fermions remain massless, the W(,L)-W(,R) mass splitting can be of radiative origin with (eta) = M(,W(,R))/m(,W(,L))) < 2 to 4. This result evades the Georgi-Pais constraint, which claims that quantum corrections can not change the symmetry of the vacuum solution at the tree level. It is found that for a realistic model, where fermions acquire mass, quantum corrections do not, however, restrict (eta) anymore. When the constraints of N = 1 supergravity are imposed on the gauge structure G with the minimal set of Higgs fields, one arrives at the following results: (i) the gravitino mass, is the only relevant scale of the model, it sets the scale for the mass of W(,R), (ii) the mass of W(,L) is necessarily derived radiatively, and (iii) (eta) = (m(,W(,R))/m(,W(,L))) < 0 (16(pi)('2)/g('2))(' 1/4) = 0(10). When the parity-odd singlet is added, a maxi-hierarchy with n >> 1 is a permissible solution. The origin of interfamily mass hierarchy (m(,(tau)) >> m(,(mu)) >> m(,e)) is studied in an instructive model where the three families and the corresponding Higgs fields appear symmetrically in the original Lagrangian. The desired interfamily hierarchy can have radiative origin. This approach again evades the Georgi-Pais constraint. The model suffers from the problem of light pseudo-Goldstone particles. In an attempt to study a complete fermion mass hierarchy problem we study the fermionic mass matrix within a realistic preonic model with four (e, (mu),(tau), (tau)') -fermionic families. The fermion mass hierarchy is realized as a hierarchy in sizes between (e,(mu))- and ((tau),(tau)') -families and as a hierarchy between the condensates formed out of preonic
Gauge invariance and reciprocity in quantum mechanics
Leung, P. T.; Young, K.
2010-03-15
Reciprocity in wave propagation usually refers to the symmetry of the Green's function under the interchange of the source and the observer coordinates, but this condition is not gauge invariant in quantum mechanics, a problem that is particularly significant in the presence of a vector potential. Several possible alternative criteria are given and analyzed with reference to different examples with nonzero magnetic fields and/or vector potentials, including the case of a multiply connected spatial domain. It is shown that the appropriate reciprocity criterion allows for specific phase factors separable into functions of the source and observer coordinates and that this condition is robust with respect to the addition of any scalar potential. In the Aharonov-Bohm effect, reciprocity beyond monoenergetic experiments holds only because of subsidiary conditions satisfied in actual experiments: the test charge is in units of e and the flux is produced by a condensate of particles with charge 2e.
McPherson, M.J.; Bellman, R.A.
1982-09-27
A precision manometer gauge which locates a zero height and a measured height of liquid using an open tube in communication with a reservoir adapted to receive the pressure to be measured. The open tube has a reference section carried on a positioning plate which is moved vertically with machine tool precision. Double scales are provided to read the height of the positioning plate accurately, the reference section being inclined for accurate meniscus adjustment, and means being provided to accurately locate a zero or reference position.
McPherson, Malcolm J.; Bellman, Robert A.
1984-01-01
A precision manometer gauge which locates a zero height and a measured height of liquid using an open tube in communication with a reservoir adapted to receive the pressure to be measured. The open tube has a reference section carried on a positioning plate which is moved vertically with machine tool precision. Double scales are provided to read the height of the positioning plate accurately, the reference section being inclined for accurate meniscus adjustment, and means being provided to accurately locate a zero or reference position.
Ault, Stanley K.
1993-01-01
A gauge for detecting the impulse generated in sample materials by X-rays or other impulse producing mechanisms utilizes a pair of flat annular springs to support a plunger relative to a housing which may itself be supported by a pair of flat annular springs in a second housing. The plunger has a mounting plate mounted on one end and at the other, a position or velocity transducer is mounted. The annular springs consist of an outer ring and an inner ring with at least three arcuate members connecting the outer ring with the inner ring.
Polchinski, Joseph [Kavli Institute for Theoretical Physics
2016-07-12
Gauge theories, which describe the particle interactions, are well understood, while quantum gravity leads to many puzzles. Remarkably, in recent years we have learned that these are actually dual, the same system written in different variables. On the one hand, this provides our most precise description of quantum gravity, resolves some long-standing paradoxes, and points to new principles. On the other, it gives a new perspective on strong interactions, with surprising connections to other areas of physics. I describe these ideas, and discuss current and future directions.
Ault, S.K.
1993-12-21
A gauge for detecting the impulse generated in sample materials by X-rays or other impulse producing mechanisms utilizes a pair of flat annular springs to support a plunger relative to a housing which may itself be supported by a pair of flat annular springs in a second housing. The plunger has a mounting plate mounted on one end and at the other, a position or velocity transducer is mounted. The annular springs consist of an outer ring and an inner ring with at least three arcuate members connecting the outer ring with the inner ring. 4 figures.
On systems having Poincaré and Galileo symmetry
Holland, Peter
2014-12-15
Using the wave equation in d≥1 space dimensions it is illustrated how dynamical equations may be simultaneously Poincaré and Galileo covariant with respect to different sets of independent variables. This provides a method to obtain dynamics-dependent representations of the kinematical symmetries. When the field is a displacement function both symmetries have a physical interpretation. For d=1 the Lorentz structure is utilized to reveal hitherto unnoticed features of the non-relativistic Chaplygin gas including a relativistic structure with a limiting case that exhibits the Carroll group, and field-dependent symmetries and associated Noether charges. The Lorentz transformations of the potentials naturally associated with the Chaplygin system are given. These results prompt the search for further symmetries and it is shown that the Chaplygin equations support a nonlinear superposition principle. A known spacetime mixing symmetry is shown to decompose into label-time and superposition symmetries. It is shown that a quantum mechanical system in a stationary state behaves as a Chaplygin gas. The extension to d>1 is used to illustrate how the physical significance of the dual symmetries is contingent on the context by showing that Maxwell’s equations exhibit an exact Galileo covariant formulation where Lorentz and gauge transformations are represented by field-dependent symmetries. A natural conceptual and formal framework is provided by the Lagrangian and Eulerian pictures of continuum mechanics.
On systems having Poincaré and Galileo symmetry
NASA Astrophysics Data System (ADS)
Holland, Peter
2014-12-01
Using the wave equation in d ≥ 1 space dimensions it is illustrated how dynamical equations may be simultaneously Poincaré and Galileo covariant with respect to different sets of independent variables. This provides a method to obtain dynamics-dependent representations of the kinematical symmetries. When the field is a displacement function both symmetries have a physical interpretation. For d = 1 the Lorentz structure is utilized to reveal hitherto unnoticed features of the non-relativistic Chaplygin gas including a relativistic structure with a limiting case that exhibits the Carroll group, and field-dependent symmetries and associated Noether charges. The Lorentz transformations of the potentials naturally associated with the Chaplygin system are given. These results prompt the search for further symmetries and it is shown that the Chaplygin equations support a nonlinear superposition principle. A known spacetime mixing symmetry is shown to decompose into label-time and superposition symmetries. It is shown that a quantum mechanical system in a stationary state behaves as a Chaplygin gas. The extension to d > 1 is used to illustrate how the physical significance of the dual symmetries is contingent on the context by showing that Maxwell's equations exhibit an exact Galileo covariant formulation where Lorentz and gauge transformations are represented by field-dependent symmetries. A natural conceptual and formal framework is provided by the Lagrangian and Eulerian pictures of continuum mechanics.
Golden Probe of Electroweak Symmetry Breaking
NASA Astrophysics Data System (ADS)
Chen, Yi; Lykken, Joe; Spiropulu, Maria; Stolarski, Daniel; Vega-Morales, Roberto
2016-12-01
The ratio of the Higgs couplings to W W and Z Z pairs, λW Z, is a fundamental parameter in electroweak symmetry breaking as well as a measure of the (approximate) custodial symmetry possessed by the gauge boson mass matrix. We show that Higgs decays to four leptons are sensitive, via tree level or one-loop interference effects, to both the magnitude and, in particular, overall sign of λW Z. Determining this sign requires interference effects, as it is nearly impossible to measure with rate information. Furthermore, simply determining the sign effectively establishes the custodial representation of the Higgs boson. We find that h →4 ℓ (4 ℓ≡2 e 2 μ , 4 e , 4 μ ) decays have excellent prospects of directly establishing the overall sign at a high luminosity 13 TeV LHC. We also examine the ultimate LHC sensitivity in h →4 ℓ to the magnitude of λW Z. Our results are independent of other measurements of the Higgs boson couplings and, in particular, largely free of assumptions about the top quark Yukawa couplings which also enter at one loop. This makes h →4 ℓ a unique and independent probe of electroweak symmetry breaking and custodial symmetry.
Toward a gauge theory for evolution equations on vector-valued spaces
Cardanobile, Stefano; Mugnolo, Delio
2009-10-15
We investigate symmetry properties of vector-valued diffusion and Schroedinger equations. For a separable Hilbert space H we characterize the subspaces of L{sup 2}(R{sup 3};H) that are local (i.e., defined pointwise) and discuss the issue of their invariance under the time evolution of the differential equation. In this context, the possibility of a connection between our results and the theory of gauge symmetries in mathematical physics is explored.
On the flexibility and symmetry of overconstrained mechanisms
Stachel, Hellmuth
2014-01-01
In kinematics, a framework is called overconstrained if its continuous flexibility is caused by particular dimensions; in the generic case, a framework of this type is rigid. Famous examples of overconstrained structures are the Bricard octahedra, the Bennett isogram, the Grünbaum framework, Bottema's 16-bar mechanism, Chasles’ body–bar framework, Burmester's focal mechanism or flexible quad meshes. The aim of this paper is to present some examples in detail and to focus on their symmetry properties. It turns out that only for a few is a global symmetry a necessary condition for flexibility. Sometimes, there is a hidden symmetry, and in some cases, for example, at the flexible type-3 octahedra or at discrete Voss surfaces, there is only a local symmetry. However, there remain overconstrained frameworks where the underlying algebraic conditions for flexibility have no relation to symmetry at all. PMID:24379430
Gauge Blocks - A Zombie Technology.
Doiron, Ted
2008-01-01
Gauge blocks have been the primary method for disseminating length traceability for over 100 years. Their longevity was based on two things: the relatively low cost of delivering very high accuracy to users, and the technical limitation that the range of high precision gauging systems was very small. While the first reason is still true, the second factor is being displaced by changes in measurement technology since the 1980s. New long range sensors do not require master gauges that are nearly the same length as the part being inspected, and thus one of the primary attributes of gauge blocks, wringing stacks to match the part, is no longer needed. Relaxing the requirement that gauges wring presents an opportunity to develop new types of end standards that would increase the accuracy and usefulness of gauging systems.
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.
Spin-orbit coupling, spin currents and emergent gauge fields in solids
NASA Astrophysics Data System (ADS)
Sa, Debanand
2012-07-01
The role of spin-orbit interaction has been exploited to construct an emergent gauge theory in solids. It has been shown that the charge and spin currents in such a solid form a SU(2)×U(1) gauge theory. The lack of gauge symmetry in the SU(2) sector and as a consequence, the non-conservation of spin is spelled out. The phenomenon of spin motive force and spin Hall effect is discussed. The importance of such force in the mesoscopic transport as well as Aharonov-Casher effect is outlined. It is shown that the spin currents in such a theory become the source of electric field.
Spin-orbit coupling, spin currents and emergent gauge fields in solids
Sa, Debanand
2012-07-23
The role of spin-orbit interaction has been exploited to construct an emergent gauge theory in solids. It has been shown that the charge and spin currents in such a solid form a SU(2) Multiplication-Sign U(1) gauge theory. The lack of gauge symmetry in the SU(2) sector and as a consequence, the non-conservation of spin is spelled out. The phenomenon of spin motive force and spin Hall effect is discussed. The importance of such force in the mesoscopic transport as well as Aharonov-Casher effect is outlined. It is shown that the spin currents in such a theory become the source of electric field.
Gauge invariances of higher derivative Maxwell-Chern-Simons field theory: A new Hamiltonian approach
NASA Astrophysics Data System (ADS)
Mukherjee, Pradip; Paul, Biswajit
2012-02-01
A new method of abstracting the independent gauge invariances of higher derivative systems, recently introduced in [R. Banerjee, P. Mukherjee, and B. Paul, J. High Energy Phys.JHEPFG1029-8479 08 (2011) 085.10.1007/JHEP08(2011)085], has been applied to higher derivative field theories. This has been discussed taking the extended Maxwell-Chern-Simons model as an example. A new Hamiltonian analysis of the model is provided. This Hamiltonian analysis has been used to construct the independent gauge generator. An exact mapping between the Hamiltonian gauge transformations and the U(1) symmetries of the action has been established.
Higgs decays in gauge extensions of the standard model
NASA Astrophysics Data System (ADS)
Bunk, Don; Hubisz, Jay; Jain, Bithika
2014-02-01
We explore the phenomenology of virtual spin-1 contributions to the h→γγ and h→Zγ decay rates in gauge extensions of the standard model. We consider generic Lorentz and gauge-invariant vector self-interactions, which can have nontrivial structure after diagonalizing the quadratic part of the action. Such features are phenomenologically relevant in models where the electroweak gauge bosons mix with additional spin-1 fields, such as occurs in little Higgs models, extra dimensional models, strongly coupled variants of electroweak symmetry breaking, and other gauge extensions of the standard model. In models where nonrenormalizable operators mix field strengths of gauge groups, the one-loop Higgs decay amplitudes can be logarithmically divergent, and we provide power counting for the size of the relevant counterterm. We provide an example calculation in a four-site moose model that contains degrees of freedom that model the effects of vector and axial-vector resonances arising from TeV scale strong dynamics.
NASA Astrophysics Data System (ADS)
Nieto, Carlos M.; Rodríguez, Yeinzon
2016-06-01
Gauge-flation model at zeroth-order in cosmological perturbation theory offers an interesting scenario for realizing inflation within a particle physics context, allowing us to investigate interesting possible connections between inflation and the subsequent evolution of the Universe. Difficulties, however, arise at the perturbative level, thus motivating a modification of the original model. In order to agree with the latest Planck observations, we modify the model such that the new dynamics can produce a relation between the spectral index ns and the tensor-to-scalar ratio r allowed by the data. By including an identical mass term for each of the fields of the system, we find interesting dynamics leading to slow-roll inflation of the right length. The presence of the mass term has the potential to modify the ns versus r relation so as to agree with the data. As a first step, we study the model at zeroth-order in cosmological perturbation theory, finding the conditions required for slow-roll inflation and the number of e-foldings of inflation. Numerical solutions are used to explore the impact of the mass term. We conclude that the massive version of gauge-flation offers a viable inflationary model.
The Friedberg-Lee symmetry and minimal seesaw model
NASA Astrophysics Data System (ADS)
He, Xiao-Gang; Liao, Wei
2009-11-01
The Friedberg-Lee (FL) symmetry is generated by a transformation of a fermionic field q to q + ξz. This symmetry puts very restrictive constraints on allowed terms in a Lagrangian. Applying this symmetry to N fermionic fields, we find that the number of independent fields is reduced to N - 1 if the fields have gauge interaction or the transformation is a local one. Using this property, we find that a seesaw model originally with three generations of left- and right-handed neutrinos, with the left-handed neutrinos unaffected but the right-handed neutrinos transformed under the local FL translation, is reduced to an effective theory of minimal seesaw which has only two right-handed neutrinos. The symmetry predicts that one of the light neutrino masses must be zero.
Bias in the Weibull Strength Estimation of a SiC Fiber for the Small Gauge Length Case
NASA Astrophysics Data System (ADS)
Morimoto, Tetsuya; Nakagawa, Satoshi; Ogihara, Shinji
It is known that the single-modal Weibull model describes well the size effect of brittle fiber tensile strength. However, some ceramic fibers have been reported that single-modal Weibull model provided biased estimation on the gauge length dependence. A hypothesis on the bias is that the density of critical defects is very small, thus, fracture probability of small gauge length samples distributes in discrete manner, which makes the Weibull parameters dependent on the gauge length. Tyranno ZMI Si-Zr-C-O fiber has been selected as an example fiber. The tensile tests have been done on several gauge lengths. The derived Weibull parameters have shown a dependence on the gauge length. Fracture surfaces were observed with SEM. Then we classified the fracture surfaces into the characteristic fracture patterns. Percentage of each fracture pattern was found dependent on the gauge length, too. This may be an important factor of the Weibull parameter dependence on the gauge length.
Chiral Gauge Dynamics and Dynamical Supersymmetry Breaking
Poppitz, Erich; Unsal, Mithat; /SLAC /Stanford U.
2009-05-07
We study the dynamics of a chiral SU(2) gauge theory with a Weyl fermion in the I = 3/2 representation and of its supersymmetric generalization. In the former, we find a new and exotic mechanism of confinement, induced by topological excitations that we refer to as magnetic quintets. The supersymmetric version was examined earlier in the context of dynamical supersymmetry breaking by Intriligator, Seiberg, and Shenker, who showed that if this gauge theory confines at the origin of moduli space, one may break supersymmetry by adding a tree level superpotential. We examine the dynamics by deforming the theory on S{sup 1} x R{sup 3}, and show that the infrared behavior of this theory is an interacting CFT at small S{sup 1}. We argue that this continues to hold at large S{sup 1}, and if so, that supersymmetry must remain unbroken. Our methods also provide the microscopic origin of various superpotentials in SQCD on S{sup 1} x R{sup 3}--which were previously obtained by using symmetry and holomorphy--and resolve a long standing interpretational puzzle concerning a flux operator discovered by Affleck, Harvey, and Witten. It is generated by a topological excitation, a 'magnetic bion', whose stability is due to fermion pair exchange between its constituents. We also briefly comment on composite monopole operators as leading effects in two dimensional antiferromagnets.
Toward realistic gauge-Higgs grand unification
NASA Astrophysics Data System (ADS)
Furui, Atsushi; Hosotani, Yutaka; Yamatsu, Naoki
2016-09-01
The SO(11) gauge-Higgs grand unification in the Randall-Sundrum warped space is presented. The 4D Higgs field is identified as the zero mode of the fifth-dimensional component of the gauge potentials, or as the fluctuation mode of the Aharonov-Bohm phase θ along the fifth dimension. Fermions are introduced in the bulk in the spinor and vector representations of SO(11). SO(11) is broken to SO(4)×SO(6) by the orbifold boundary conditions, which is broken to SU2×U1×SU3 by a brane scalar. Evaluating the effective potential V(θ), we show that the electroweak symmetry is dynamically broken to U1. The quark-lepton masses are generated by the Hosotani mechanism and brane interactions, with which the observed mass spectrum is reproduced. Proton decay is forbidden thanks to the new fermion number conservation. It is pointed out that there appear light exotic fermions. The Higgs boson mass is determined with the quark-lepton masses given; however, it turns out to be smaller than the observed value.
Symmetries in Lagrangian Dynamics
ERIC Educational Resources Information Center
Ferrario, Carlo; Passerini, Arianna
2007-01-01
In the framework of Noether's theorem, a distinction between Lagrangian and dynamical symmetries is made, in order to clarify some aspects neglected by textbooks. An intuitive setting of the concept of invariance of differential equations is presented. The analysis is completed by deriving the symmetry properties in the motion of a charged…
ERIC Educational Resources Information Center
Marchis, Iuliana
2009-01-01
Symmetry is one of the fundamental concepts in Geometry. It is a Mathematical concept, which can be very well connected with Art and Ethnography. The aim of the article is to show how to link the geometrical concept symmetry with interculturality. For this mosaics from different countries are used.
Tractors and twistors from conformal Cartan geometry: a gauge theoretic approach II. Twistors
NASA Astrophysics Data System (ADS)
Attard, J.; François, J.
2017-04-01
Tractor and Twistor bundles provide natural conformally covariant calculi on 4D-Riemannian manifolds. They have different origins but are closely related, and usually constructed bottom–up through prolongation of defining differential equations. We propose alternative top–down gauge theoretic constructions, starting from the conformal Cartan bundle P and its vectorial E and spinorial {E associated bundles. Our key ingredient is the dressing field method of gauge symmetry reduction, which allows tractors and twistors and their associated connections to exhibit as gauge fields of a non-standard kind as far as Weyl rescaling transformation is concerned. By non-standard we mean that they implement the gauge principle of physics, but are of a different geometric nature than the well-known differential geometric objects usually underlying gauge theories. We provide the corresponding BRST treatment. In a companion paper we dealt with tractors, in the present one we address the case of twistors.
Finite field-dependent symmetry in the Thirring model
NASA Astrophysics Data System (ADS)
Upadhyay, Sudhaker; Ganai, Prince A.
2016-06-01
In this paper, we consider a D-dimensional massive Thirring model with (2
Topological aspects of systems with broken time-reversal symmetry
NASA Astrophysics Data System (ADS)
Raghu, Srinivas
This thesis deals with two topics involving topological "vortex-like" defects arising due to the breaking of time-reversal symmetry. A recurring theme shall be the interplay between the bulk properties and the physics at the boundaries of such systems. In the first part of the thesis, we construct direct analogs of quantum Hall effect edge modes in photonic systems with broken time-reversal symmetry. We will show how "photonic crystals" built out of time-reversal breaking Faraday effect media can exhibit "chiral" edge modes in which light propagates unidirectionally along boundaries across which the Faraday axis reverses. The crucial feature underlying this idea is that the photon bands of interest have non-zero Chern numbers (topological integers, which in the case at hand, represent the winding number of the Berry gauge connection of the bands). Using both numerical diagonalization and simple analytical models, we show how to construct photon bands with non-zero Chern invariants, and we use them to realize the precise classical counterpart of the electronic edge modes of the quantum Hall effect. To study these modes numerically, we have designed and implemented novel real-space treatments of the source-free Maxwell normal mode problem on a discrete network. In the second part of the thesis, we focus on extreme type II superconductors in externally applied magnetic fields. Motivated by experiments of Ong and collaborators on the Nernst effect in the cuprate superconductors, we consider a model of a superconductor which permits fluctuations only in the phase of the order parameter. In the presence of the magnetic field, a net vorticity is induced in the system, and we consider the various static and thermoelectric signatures of these superconducting vortices. Using numerical simulations, analytical calculations, and arguments from duality, we study thermoelectric transport and boundary diamagnetic currents. We conclude that such simple models of superconductors
Natural discretization in noncommutative field theory
NASA Astrophysics Data System (ADS)
Acatrinei, Ciprian Sorin
2015-12-01
A discretization scheme for field theory is developed, in which the space time coordinates are assumed to be operators forming a noncommutative algebra. Generic waves without rotational symmetry are studied in (2+1) - dimensional scalar field theory with Heisenberg-type noncommutativity. In the representation chosen, the radial coordinate is naturally rendered discrete. Nonlocality along this coordinate, induced by noncommutativity, accounts for the angular dependence of the fields. A complete solution and the interpretation of its nonlocal features are given. The exact form of standing and propagating waves on such a discrete space is found in terms of finite series. A precise correspondence is established between the degree of nonlocality and the angular momentum of a field configuration. At small distance no classical singularities appear, even at the location of the sources. At large radius one recovers the usual commutative/continuum behaviour.
Natural discretization in noncommutative field theory
Acatrinei, Ciprian Sorin
2015-12-07
A discretization scheme for field theory is developed, in which the space time coordinates are assumed to be operators forming a noncommutative algebra. Generic waves without rotational symmetry are studied in (2+1) - dimensional scalar field theory with Heisenberg-type noncommutativity. In the representation chosen, the radial coordinate is naturally rendered discrete. Nonlocality along this coordinate, induced by noncommutativity, accounts for the angular dependence of the fields. A complete solution and the interpretation of its nonlocal features are given. The exact form of standing and propagating waves on such a discrete space is found in terms of finite series. A precise correspondence is established between the degree of nonlocality and the angular momentum of a field configuration. At small distance no classical singularities appear, even at the location of the sources. At large radius one recovers the usual commutative/continuum behaviour.
Compatible Spatial Discretizations for Partial Differential Equations
Arnold, Douglas, N, ed.
2004-11-25
From May 11--15, 2004, the Institute for Mathematics and its Applications held a hot topics workshop on Compatible Spatial Discretizations for Partial Differential Equations. The numerical solution of partial differential equations (PDE) is a fundamental task in science and engineering. The goal of the workshop was to bring together a spectrum of scientists at the forefront of the research in the numerical solution of PDEs to discuss compatible spatial discretizations. We define compatible spatial discretizations as those that inherit or mimic fundamental properties of the PDE such as topology, conservation, symmetries, and positivity structures and maximum principles. A wide variety of discretization methods applied across a wide range of scientific and engineering applications have been designed to or found to inherit or mimic intrinsic spatial structure and reproduce fundamental properties of the solution of the continuous PDE model at the finite dimensional level. A profusion of such methods and concepts relevant to understanding them have been developed and explored: mixed finite element methods, mimetic finite differences, support operator methods, control volume methods, discrete differential forms, Whitney forms, conservative differencing, discrete Hodge operators, discrete Helmholtz decomposition, finite integration techniques, staggered grid and dual grid methods, etc. This workshop seeks to foster communication among the diverse groups of researchers designing, applying, and studying such methods as well as researchers involved in practical solution of large scale problems that may benefit from advancements in such discretizations; to help elucidate the relations between the different methods and concepts; and to generally advance our understanding in the area of compatible spatial discretization methods for PDE. Particular points of emphasis included: + Identification of intrinsic properties of PDE models that are critical for the fidelity of numerical
Colloquium: Artificial gauge potentials for neutral atoms
Dalibard, Jean; Gerbier, Fabrice; Juzeliunas, Gediminas; Oehberg, Patrik
2011-10-01
When a neutral atom moves in a properly designed laser field, its center-of-mass motion may mimic the dynamics of a charged particle in a magnetic field, with the emergence of a Lorentz-like force. In this Colloquium the physical principles at the basis of this artificial (synthetic) magnetism are presented. The corresponding Aharonov-Bohm phase is related to the Berry's phase that emerges when the atom adiabatically follows one of the dressed states of the atom-laser interaction. Some manifestations of artificial magnetism for a cold quantum gas, in particular, in terms of vortex nucleation are discussed. The analysis is then generalized to the simulation of non-Abelian gauge potentials and some striking consequences are presented, such as the emergence of an effective spin-orbit coupling. Both the cases of bulk gases and discrete systems, where atoms are trapped in an optical lattice, are addressed.
Noncommutative spaces, the quantum of time, and Lorentz symmetry
Romero, Juan M.; Vergara, J. D.; Santiago, J. A.
2007-03-15
We introduce three space-times that are discrete in time and compatible with the Lorentz symmetry. We show that these spaces are not commutative, with commutation relations similar to the relations of the Snyder and Yang spaces. Furthermore, using a reparametrized relativistic particle we obtain a realization of the Snyder type spaces and we construct an action for them.
NASA Astrophysics Data System (ADS)
Alonso, R.; Fernandez Martinez, E.; Gavela, M. B.; Grinstein, B.; Merlo, L.; Quilez, P.
2016-12-01
The gauging of the lepton flavour group is considered in the Standard Model context and in its extension with three right-handed neutrinos. The anomaly cancellation conditions lead to a Seesaw mechanism as underlying dynamics for all leptons; requiring in addition a phenomenologically viable setup leads to Majorana masses for the neutral sector: the type I Seesaw Lagrangian in the Standard Model case and the inverse Seesaw in the extended model. Within the minimal extension of the scalar sector, the Yukawa couplings are promoted to scalar fields in the bifundamental of the flavour group. The resulting low-energy Yukawa couplings are proportional to inverse powers of the vacuum expectation values of those scalars; the protection against flavour changing neutral currents differs from that of Minimal Flavour Violation. In all cases, the μ- τ flavour sector exhibits rich and promising phenomenological signals.
Global defects in theories with Lorentz symmetry violation
NASA Astrophysics Data System (ADS)
Lubo, Musongela
2005-02-01
We study global topological defects in the Jacobson-Corley model which breaks Lorentz symmetry and involves up to fourth order derivatives. There is a window in the parameter space in which no solution exists. Otherwise, different profiles are allowed for the same values of the parameters. For a scale of Lorentz violation much higher than the scale of gauge symmetry breaking, the energy densities are higher, of the same order or smaller than in the usual case for domain walls, cosmic strings, and hedgehogs, respectively. Possible cosmological implications are suggested.
Global defects in theories with Lorentz symmetry violation
Lubo, Musongela
2005-02-15
We study global topological defects in the Jacobson-Corley model which breaks Lorentz symmetry and involves up to fourth order derivatives. There is a window in the parameter space in which no solution exists. Otherwise, different profiles are allowed for the same values of the parameters. For a scale of Lorentz violation much higher than the scale of gauge symmetry breaking, the energy densities are higher, of the same order or smaller than in the usual case for domain walls, cosmic strings, and hedgehogs, respectively. Possible cosmological implications are suggested.
Unifying left-right symmetry and 331 electroweak theories
NASA Astrophysics Data System (ADS)
Reig, Mario; Valle, José W. F.; Vaquera-Araujo, C. A.
2017-03-01
We propose a realistic theory based on the SU (3)c ⊗ SU (3)L ⊗ SU (3)R ⊗ U(1)X gauge group which requires the number of families to match the number of colors. In the simplest realization neutrino masses arise from the canonical seesaw mechanism and their smallness correlates with the observed V-A nature of the weak force. Depending on the symmetry breaking path to the Standard Model one recovers either a left-right symmetric theory or one based on the SU (3)c ⊗ SU (3)L ⊗ U (1) symmetry as the ;next; step towards new physics.
Multigrid Methods for the Computation of Propagators in Gauge Fields
NASA Astrophysics Data System (ADS)
Kalkreuter, Thomas
Multigrid methods were invented for the solution of discretized partial differential equations in order to overcome the slowness of traditional algorithms by updates on various length scales. In the present work generalizations of multigrid methods for propagators in gauge fields are investigated. Gauge fields are incorporated in algorithms in a covariant way. The kernel C of the restriction operator which averages from one grid to the next coarser grid is defined by projection on the ground-state of a local Hamiltonian. The idea behind this definition is that the appropriate notion of smoothness depends on the dynamics. The ground-state projection choice of C can be used in arbitrary dimension and for arbitrary gauge group. We discuss proper averaging operations for bosons and for staggered fermions. The kernels C can also be used in multigrid Monte Carlo simulations, and for the definition of block spins and blocked gauge fields in Monte Carlo renormalization group studies. Actual numerical computations are performed in four-dimensional SU(2) gauge fields. We prove that our proposals for block spins are “good”, using renormalization group arguments. A central result is that the multigrid method works in arbitrarily disordered gauge fields, in principle. It is proved that computations of propagators in gauge fields without critical slowing down are possible when one uses an ideal interpolation kernel. Unfortunately, the idealized algorithm is not practical, but it was important to answer questions of principle. Practical methods are able to outperform the conjugate gradient algorithm in case of bosons. The case of staggered fermions is harder. Multigrid methods give considerable speed-ups compared to conventional relaxation algorithms, but on lattices up to 184 conjugate gradient is superior.
String Theory and Gauge Theories
Maldacena, Juan
2009-02-20
We will see how gauge theories, in the limit that the number of colors is large, give string theories. We will discuss some examples of particular gauge theories where the corresponding string theory is known precisely, starting with the case of the maximally supersymmetric theory in four dimensions which corresponds to ten dimensional string theory. We will discuss recent developments in this area.
Cold cathode vacuum gauging system
Denny, Edward C.
2004-03-09
A vacuum gauging system of the cold cathode type is provided for measuring the pressure of a plurality of separate vacuum systems, such as in a gas centrifuge cascade. Each casing is fitted with a gauge tube assembly which communicates with the vacuum system in the centrifuge casing. Each gauge tube contains an anode which may be in the form of a slender rod or wire hoop and a cathode which may be formed by the wall of the gauge tube. The tube is provided with an insulated high voltage connector to the anode which has a terminal for external connection outside the vacuum casing. The tube extends from the casing so that a portable magnet assembly may be inserted about the tube to provide a magnetic field in the area between the anode and cathode necessary for pressure measurements in a cold cathode-type vacuum gauge arrangement. The portable magnetic assembly is provided with a connector which engages the external high voltage terminal for providing power to the anode within in the gauge tube. Measurement is made in the same manner as the prior cold cathode gauges in that the current through the anode to the cathode is measured as an indication of the pressure. By providing the portable magnetic assembly, a considerable savings in cost, installation, and maintenance of vacuum gauges for pressure measurement in a gas centrifuge cascade is realizable.
Nonadiabatic transitions and gauge structure
Nakamura, K. ); Rice, S.A. )
1994-04-01
We examine the role of fictitious gauge structure in nonadiabatic transitions for transport in open paths. Local features of the gauge potential modify the nature of the intersection of the adiabatic energy surfaces and thereby affect crucially the Landau-Zener formula for a single-passage transition rate.
NASA Astrophysics Data System (ADS)
Dolan, Louise; Sun, Yang
2015-06-01
We compute the partition function of four-dimensional abelian gauge theory on a general four-torus T 4 with flat metric using Dirac quantization. In addition to an symmetry, it possesses symmetry that is electromagnetic S-duality. We show explicitly how this S-duality of the 4 d abelian gauge theory has its origin in symmetries of the 6 d (2 , 0) tensor theory, by computing the partition function of a single fivebrane compactified on T 2 times T 4, which has symmetry. If we identify the couplings of the abelian gauge theory with the complex modulus of the T 2 torus , then in the small T 2 limit, the partition function of the fivebrane tensor field can be factorized, and contains the partition function of the 4 d gauge theory. In this way the symmetry of the 6d tensor partition function is identified with the S-duality symmetry of the 4d gauge partition function. Each partition function is the product of zero mode and oscillator contributions, where the acts suitably. For the 4d gauge theory, which has a Lagrangian, this product redistributes when using path integral quantization.
A symmetry principle for topological quantum order
Nussinov, Zohar Ortiz, Gerardo
2009-05-15
We present a unifying framework to study physical systems which exhibit topological quantum order (TQO). The major guiding principle behind our approach is that of symmetries and entanglement. These symmetries may be actual symmetries of the Hamiltonian characterizing the system, or emergent symmetries. To this end, we introduce the concept of low-dimensional Gauge-like symmetries (GLSs), and the physical conservation laws (including topological terms, fractionalization, and the absence of quasi-particle excitations) which emerge from them. We prove then sufficient conditions for TQO at both zero and finite temperatures. The physical engine for TQO are topological defects associated with the restoration of GLSs. These defects propagate freely through the system and enforce TQO. Our results are strongest for gapped systems with continuous GLSs. At zero temperature, selection rules associated with the GLSs enable us to systematically construct general states with TQO; these selection rules do not rely on the existence of a finite gap between the ground states to all other excited states. Indices associated with these symmetries correspond to different topological sectors. All currently known examples of TQO display GLSs. Other systems exhibiting such symmetries include Hamiltonians depicting orbital-dependent spin-exchange and Jahn-Teller effects in transition metal orbital compounds, short-range frustrated Klein spin models, and p+ip superconducting arrays. The symmetry based framework discussed herein allows us to go beyond standard topological field theories and systematically engineer new physical models with finite temperature TQO (both Abelian and non-Abelian). Furthermore, we analyze the insufficiency of entanglement entropy (we introduce SU(N) Klein models on small world networks to make the argument even sharper), spectral structures, maximal string correlators, and fractionalization in establishing TQO. We show that Kitaev's Toric code model and Wen
Dirac sigma models from gauging
NASA Astrophysics Data System (ADS)
Salnikov, Vladimir; Strobl, Thomas
2013-11-01
The G/G WZW model results from the WZW-model by a standard procedure of gauging. G/G WZW models are members of Dirac sigma models, which also contain twisted Poisson sigma models as other examples. We show how the general class of Dirac sigma models can be obtained from a gauging procedure adapted to Lie algebroids in the form of an equivariantly closed extension. The rigid gauge groups are generically infinite dimensional and a standard gauging procedure would give a likewise infinite number of 1-form gauge fields; the proposed construction yields the requested finite number of them. Although physics terminology is used, the presentation is kept accessible also for a mathematical audience.
Generalized Legendre transformations and symmetries of the WDVV equations
NASA Astrophysics Data System (ADS)
Strachan, Ian A. B.; Stedman, Richard
2017-03-01
The Witten–Dijkgraaf–Verlinde–Verlinde (or WDVV) equations, as one would expect from an integrable system, has many symmetries, both continuous and discrete. One class—the so-called Legendre transformations—were introduced by Dubrovin. They are a discrete set of symmetries between the stronger concept of a Frobenius manifold, and are generated by certain flat vector fields. In this paper this construction is generalized to the case where the vector field (called here the Legendre field) is non-flat but satisfies a certain set of defining equations. One application of this more general theory is to generate the induced symmetry between almost-dual Frobenius manifolds whose underlying Frobenius manifolds are related by a Legendre transformation. This also provides a map between rational and trigonometric solutions of the WDVV equations.
Visinescu, M.
2012-10-15
Hidden symmetries in a covariant Hamiltonian framework are investigated. The special role of the Stackel-Killing and Killing-Yano tensors is pointed out. The covariant phase-space is extended to include external gauge fields and scalar potentials. We investigate the possibility for a higher-order symmetry to survive when the electromagnetic interactions are taken into account. Aconcrete realization of this possibility is given by the Killing-Maxwell system. The classical conserved quantities do not generally transfer to the quantized systems producing quantum gravitational anomalies. As a rule the conformal extension of the Killing vectors and tensors does not produce symmetry operators for the Klein-Gordon operator.
Twofold symmetries of the pure gravity action
NASA Astrophysics Data System (ADS)
Cheung, Clifford; Remmen, Grant N.
2017-01-01
We recast the action of pure gravity into a form that is invariant under a twofold Lorentz symmetry. To derive this representation, we construct a general parameterization of all theories equivalent to the Einstein-Hilbert action up to a local field redefinition and gauge fixing. We then exploit this freedom to eliminate all interactions except those exhibiting two sets of independently contracted Lorentz indices. The resulting action is local, remarkably simple, and naturally expressed in a field basis analogous to the exponential parameterization of the nonlinear sigma model. The space of twofold Lorentz invariant field redefinitions then generates an infinite class of equivalent representations. By construction, all off-shell Feynman diagrams are twofold Lorentz invariant while all on-shell tree amplitudes are automatically twofold gauge invariant. We extend our results to curved spacetime and calculate the analogue of the Einstein equations. While these twofold invariances are hidden in the canonical approach of graviton perturbation theory, they are naturally expected given the double copy relations for scattering amplitudes in gauge theory and gravity.
Symmetry-enriched string nets: Exactly solvable models for SET phases
NASA Astrophysics Data System (ADS)
Heinrich, Chris; Burnell, Fiona; Fidkowski, Lukasz; Levin, Michael
2016-12-01
We construct exactly solvable models for a wide class of symmetry-enriched topological (SET) phases. Our construction applies to two-dimensional (2D) bosonic SET phases with finite unitary on-site symmetry group G and we conjecture that our models realize every phase in this class that can be described by a commuting projector Hamiltonian. Our models are designed so that they have a special property: If we couple them to a dynamical lattice gauge field with gauge group G , the resulting gauge theories are equivalent to string-net models. This property is what allows us to analyze our models in generality. As an example, we present a model for a phase with the same anyon excitations as the toric code and with a Z2 symmetry which exchanges the e and m type anyons. We further illustrate our construction with a number of additional examples.
A universal symmetry detection algorithm.
Maurer, Peter M
2015-01-01
Research on symmetry detection focuses on identifying and detecting new types of symmetry. The paper presents an algorithm that is capable of detecting any type of permutation-based symmetry, including many types for which there are no existing algorithms. General symmetry detection is library-based, but symmetries that can be parameterized, (i.e. total, partial, rotational, and dihedral symmetry), can be detected without using libraries. In many cases it is faster than existing techniques. Furthermore, it is simpler than most existing techniques, and can easily be incorporated into existing software. The algorithm can also be used with virtually any type of matrix-based symmetry, including conjugate symmetry.
Gauge theory in deformed mathcal{N} = (1, 1) superspace
NASA Astrophysics Data System (ADS)
Buchbinder, I. L.; Ivanov, E. A.; Lechtenfeld, O.; Samsonov, I. B.; Zupnik, B. M.
2008-09-01
We review the non-anticommutative Q-deformations of mathcal{N} = (1, 1) supersymmetric theories in four-dimensional Euclidean harmonic superspace. These deformations preserve chirality and harmonic Grassmann analyticity. The associated field theories arise as a low-energy limit of string theory in specific backgrounds and generalize the Moyal-deformed supersymmetric field theories. A characteristic feature of the Q-deformed theories is the half-breaking of supersymmetry in the chiral sector of the Euclidean superspace. Our main focus is on the chiral singlet Q-deformation, which is distinguished by preserving the SO(4) ˜ Spin(4) “Lorentz” symmetry and the SU(2) R-symmetry. We present the superfield and component structures of the deformed mathcal{N} = (1, 0) supersymmetric gauge theory as well as of hypermultiplets coupled to a gauge superfield: invariant actions, deformed transformation rules, and so on. We discuss quantum aspects of these models and prove their renormalizability in the Abelian case. For the charged hypermultiplet in an Abelian gauge superfield background we construct the deformed holomorphic effective action.
NASA Astrophysics Data System (ADS)
Maleknejad, A.; Sheikh-Jabbari, M. M.; Soda, J.
2013-07-01
The isotropy and homogeneity of the cosmic microwave background (CMB) favors “scalar driven” early Universe inflationary models. However, gauge fields and other non-scalar fields are far more common at all energy scales, in particular at high energies seemingly relevant to inflation models. Hence, in this review we consider the role and consequences, theoretical and observational, that gauge fields can have during the inflationary era. Gauge fields may be turned on in the background during inflation, or may become relevant at the level of cosmic perturbations. There have been two main classes of models with gauge fields in the background, models which show violation of the cosmic no-hair theorem and those which lead to isotropic FLRW cosmology, respecting the cosmic no-hair theorem. Models in which gauge fields are only turned on at the cosmic perturbation level, may source primordial magnetic fields. We also review specific observational features of these models on the CMB and/or the primordial cosmic magnetic fields. Our discussions will be mainly focused on the inflation period, with only a brief discussion on the post inflationary (p)reheating era. Large field models: The initial value of the inflaton field is large, generically super-Planckian, and it rolls slowly down toward the potential minimum at smaller φ values. For instance, chaotic inflation is one of the representative models of this class. The typical potential of large-field models has a monomial form as V(φ)=V0φn. A simple analysis using the dynamical equations reveals that for number of e-folds Ne larger than 60, we require super-Planckian initial field values,5φ0>3M. For these models typically ɛ˜η˜Ne-1. Small field models: Inflaton field is initially small and slowly evolves toward the potential minimum at larger φ values. The small field models are characterized by the following potential V(φ)=V0(1-(), which corresponds to a Taylor expansion about the origin, but more realistic
Quantum simulations of lattice gauge theories using ultracold atoms in optical lattices.
Zohar, Erez; Cirac, J Ignacio; Reznik, Benni
2016-01-01
Can high-energy physics be simulated by low-energy, non-relativistic, many-body systems such as ultracold atoms? Such ultracold atomic systems lack the type of symmetries and dynamical properties of high energy physics models: in particular, they manifest neither local gauge invariance nor Lorentz invariance, which are crucial properties of the quantum field theories which are the building blocks of the standard model of elementary particles. However, it turns out, surprisingly, that there are ways to configure an atomic system to manifest both local gauge invariance and Lorentz invariance. In particular, local gauge invariance can arise either as an effective low-energy symmetry, or as an exact symmetry, following from the conservation laws in atomic interactions. Hence, one could hope that such quantum simulators may lead to a new type of (table-top) experiments which will be used to study various QCD (quantum chromodynamics) phenomena, such as the confinement of dynamical quarks, phase transitions and other effects, which are inaccessible using the currently known computational methods. In this report, we review the Hamiltonian formulation of lattice gauge theories, and then describe our recent progress in constructing the quantum simulation of Abelian and non-Abelian lattice gauge theories in 1 + 1 and 2 + 1 dimensions using ultracold atoms in optical lattices.
Origami Optimization: Role of Symmetry in Accelerating Design
NASA Astrophysics Data System (ADS)
Buskohl, Philip; Fuchi, Kazuko; Bazzan, Giorgio; Durstock, Michael; Reich, Gregory; Joo, James; Vaia, Richard
Origami structures morph between 2D and 3D conformations along predetermined fold lines that efficiently program the form, function and mobility of the structure. Design optimization tools have recently been developed to predict optimal fold patterns with mechanics-based metrics, such as the maximal energy storage, auxetic response and actuation. Origami actuator design problems possess inherent symmetries associated with the grid, mechanical boundary conditions and the objective function, which are often exploited to reduce the design space and computational cost of optimization. However, enforcing symmetry eliminates the prediction of potentially better performing asymmetric designs, which are more likely to exist given the discrete nature of fold line optimization. To better understand this effect, actuator design problems with different combinations of rotation and reflection symmetries were optimized while varying the number of folds allowed in the final design. In each case, the optimal origami patterns transitioned between symmetric and asymmetric solutions depended on the number of folds available for the design, with fewer symmetries present with more fold lines allowed. This study investigates the interplay of symmetry and discrete vs continuous optimization in origami actuators and provides insight into how the symmetries of the reference grid regulate the performance landscape. This work was supported by the Air Force Office of Scientific Research.
Principles of Discrete Time Mechanics
NASA Astrophysics Data System (ADS)
Jaroszkiewicz, George
2014-04-01
1. Introduction; 2. The physics of discreteness; 3. The road to calculus; 4. Temporal discretization; 5. Discrete time dynamics architecture; 6. Some models; 7. Classical cellular automata; 8. The action sum; 9. Worked examples; 10. Lee's approach to discrete time mechanics; 11. Elliptic billiards; 12. The construction of system functions; 13. The classical discrete time oscillator; 14. Type 2 temporal discretization; 15. Intermission; 16. Discrete time quantum mechanics; 17. The quantized discrete time oscillator; 18. Path integrals; 19. Quantum encoding; 20. Discrete time classical field equations; 21. The discrete time Schrodinger equation; 22. The discrete time Klein-Gordon equation; 23. The discrete time Dirac equation; 24. Discrete time Maxwell's equations; 25. The discrete time Skyrme model; 26. Discrete time quantum field theory; 27. Interacting discrete time scalar fields; 28. Space, time and gravitation; 29. Causality and observation; 30. Concluding remarks; Appendix A. Coherent states; Appendix B. The time-dependent oscillator; Appendix C. Quaternions; Appendix D. Quantum registers; References; Index.
Dynamical symmetries for fermions
Guidry, M.
1989-01-01
An introduction is given to the Fermion Dynamical Symmetry Model (FDSM). The analytical symmetry limits of the model are then applied to the calculation of physical quantities such as ground-state masses and B(E{sub 2}) values in heavy nuclei. These comparisons with data provide strong support for a new principle of collective motion, the Dynamical Pauli Effect, and suggest that dynamical symmetries which properly account for the pauli principle are much more persistent in nuclear structure than the corresponding boson symmetries. Finally, we present an assessment of criticisms which have been voiced concerning the FDSM, and a discussion of new phenomena and exotic spectroscopy'' which may be suggested by the model. 14 refs., 8 figs., 4 tabs.
Sekhar Chivukula
2016-07-12
The symmetries of a quantum field theory can be realized in a variety of ways. Symmetries can be realized explicitly, approximately, through spontaneous symmetry breaking or, via an anomaly, quantum effects can dynamically eliminate a symmetry of the theory that was presentÂ at the classical level. Â Quantum Chromodynamics (QCD),Â the modern theoryÂ of the strong interactions, exemplify each ofÂ these possibilities.Â The interplayÂ of these effects determine theÂ spectrum of particles that we observeÂ and, ultimately, account forÂ 99% of the mass of ordinary matter.Â
NASA Astrophysics Data System (ADS)
Golubitsky, Martin
2012-04-01
Many gaits of four-legged animals are described by symmetry. For example, when a horse paces it moves both left legs in unison and then both right legs and so on. The motion is described by two symmetries: Interchange front and back legs, and swap left and right legs with a half-period phase shift. Biologists postulate the existence of a central pattern generator (CPG) in the neuronal system that sends periodic signals to the legs. CPGs can be thought of as electrical circuits that produce periodic signals and can be modeled by systems with symmetry. In this lecture we discuss animal gaits; use gait symmetries to construct a simplest CPG architecture that naturally produces quadrupedal gait rhythms; and make several testable predictions about gaits.
Nongeometric Calabi-Yau compactifications and fractional mirror symmetry
NASA Astrophysics Data System (ADS)
Israël, Dan
2015-03-01
We construct a wide class of nongeometric compactifications of type II superstring theories preserving N =1 space-time supersymmetry in four dimensions, starting from Calabi-Yau compactifications at Gepner points. Particular examples of this construction provide quantum equivalences between Calabi-Yau compactifications and non-Calabi-Yau ones, generalizing mirror symmetry. The associated Landau-Ginzburg models involve both chiral and twisted chiral multiplets and hence cannot be lifted to ordinary Calabi-Yau gauged linear sigma models.
Bose symmetry and chiral decomposition of 2D fermionic determinants
NASA Astrophysics Data System (ADS)
Abreu, E. M. C.; Banerjee, R.; Wotzasek, C.
1998-01-01
We show in a precise way, either in the fermionic or its bosonized version, that Bose symmetry provides a systematic way to carry out the chiral decomposition of the two-dimensional fermionic determinant. Interpreted properly, we show that there is no obstruction of this decomposition to gauge invariance, as is usually claimed. Finally, a new way of interpreting the Polyakov-Wiegman identity is proposed.
SU(2/1) gauge-Higgs unification
NASA Astrophysics Data System (ADS)
Loginov, E. K.
2016-06-01
We discuss a question whether the observed Weinberg angle and Higgs mass are calculable in the formalism based on a construction in which the electroweak gauge group SU(2) × U(1)Y is embedded in the graded Lie group SU(2/1). Here, we follow original works of Ne’eman and Fairlie believing that bosonic fields take their values in the Lie superalgebra and fermionic fields take their values in its representation space. At the same time, our approach differs significantly. The main one is that while for them the gauge symmetry group is SU(2/1), here we consider only symmetries generated by its even subgroup, i.e. symmetries of the standard electroweak model. The reason is that such formalism fixes the quartic Higgs coupling and at the same time removes the sign and statistics problems. The main result is that the presented model predicts values of the Weinberg angle and the Higgs mass correctly up to the two-loop level. Moreover, the model sets the unification scale coinciding with the electroweak scale and automatically describes the fermions correctly with the correct quark and lepton charges.
NASA Astrophysics Data System (ADS)
Hamhalter, Jan; Turilova, Ekaterina
2017-02-01
Quantum symmetries of spectral lattices are studied. Basic properties of spectral order on A W ∗-algebras are summarized. Connection between projection and spectral automorphisms is clarified by showing that, under mild conditions, any spectral automorphism is a composition of function calculus and Jordan ∗-automorphism. Complete description of quantum spectral symmetries on Type I and Type II A W ∗-factors are completely described.
NASA Astrophysics Data System (ADS)
Baldo, M.; Burgio, G. F.
2016-11-01
The nuclear symmetry energy characterizes the variation of the binding energy as the neutron to proton ratio of a nuclear system is varied. This is one of the most important features of nuclear physics in general, since it is just related to the two component nature of the nuclear systems. As such it is one of the most relevant physical parameters that affect the physics of many phenomena and nuclear processes. This review paper presents a survey of the role and relevance of the nuclear symmetry energy in different fields of research and of the accuracy of its determination from the phenomenology and from the microscopic many-body theory. In recent years, a great interest was devoted not only to the Nuclear Matter symmetry energy at saturation density but also to its whole density dependence, which is an essential ingredient for our understanding of many phenomena. We analyze the nuclear symmetry energy in different realms of nuclear physics and astrophysics. In particular we consider the nuclear symmetry energy in relation to nuclear structure, astrophysics of Neutron Stars and supernovae, and heavy ion collision experiments, trying to elucidate the connections of these different fields on the basis of the symmetry energy peculiarities. The interplay between experimental and observational data and theoretical developments is stressed. The expected future developments and improvements are schematically addressed, together with most demanded experimental and theoretical advances for the next few years.
A Robust, Microwave Rain Gauge
NASA Astrophysics Data System (ADS)
Mansheim, T. J.; Niemeier, J. J.; Kruger, A.
2008-12-01
Researchers at The University of Iowa have developed an all-electronic rain gauge that uses microwave sensors operating at either 10 GHz or 23 GHz, and measures the Doppler shift caused by falling raindrops. It is straightforward to interface these sensors with conventional data loggers, or integrate them into a wireless sensor network. A disadvantage of these microwave rain gauges is that they consume significant power when they are operating. However, this may be partially negated by using data loggers' or sensors networks' sleep-wake-sleep mechanism. Advantages of the microwave rain gauges are that one can make them very robust, they cannot clog, they don't have mechanical parts that wear out, and they don't have to be perfectly level. Prototype microwave rain gauges were collocated with tipping-bucket rain gauges, and data were collected for two seasons. At higher rain rates, microwave rain gauge measurements compare well with tipping-bucket measurements. At lower rain rates, the microwave rain gauges provide more detailed information than tipping buckets, which quantize measurement typically in 1 tip per 0.01 inch, or 1 tip per mm of rainfall.
The algebra of physical observables in non-linearly realized gauge theories
NASA Astrophysics Data System (ADS)
Quadri, Andrea
2010-11-01
We classify the physical observables in spontaneously broken non-linearly realized gauge theories in the recently proposed loopwise expansion governed by the Weak Power-Counting (WPC) and the Local Functional Equation. The latter controls the non-trivial quantum deformation of the classical non-linearly realized gauge symmetry, to all orders in the loop expansion. The Batalin-Vilkovisky (BV) formalism is used. We show that the dependence of the vertex functional on the Goldstone fields is obtained via a canonical transformation w.r.t. the BV bracket associated with the BRST symmetry of the model. We also compare the WPC with strict power-counting renormalizability in linearly realized gauge theories. In the case of the electroweak group we find that the tree-level Weinberg relation still holds if power-counting renormalizability is weakened to the WPC condition.
Constraint analysis for variational discrete systems
Dittrich, Bianca; Höhn, Philipp A.
2013-09-15
A canonical formalism and constraint analysis for discrete systems subject to a variational action principle are devised. The formalism is equivalent to the covariant formulation, encompasses global and local discrete time evolution moves and naturally incorporates both constant and evolving phase spaces, the latter of which is necessary for a time varying discretization. The different roles of constraints in the discrete and the conditions under which they are first or second class and/or symmetry generators are clarified. The (non-) preservation of constraints and the symplectic structure is discussed; on evolving phase spaces the number of constraints at a fixed time step depends on the initial and final time step of evolution. Moreover, the definition of observables and a reduced phase space is provided; again, on evolving phase spaces the notion of an observable as a propagating degree of freedom requires specification of an initial and final step and crucially depends on this choice, in contrast to the continuum. However, upon restriction to translation invariant systems, one regains the usual time step independence of canonical concepts. This analysis applies, e.g., to discrete mechanics, lattice field theory, quantum gravity models, and numerical analysis.
Observation of a discrete time crystal
NASA Astrophysics Data System (ADS)
Zhang, J.; Hess, P. W.; Kyprianidis, A.; Becker, P.; Lee, A.; Smith, J.; Pagano, G.; Potirniche, I.-D.; Potter, A. C.; Vishwanath, A.; Yao, N. Y.; Monroe, C.
2017-03-01
Spontaneous symmetry breaking is a fundamental concept in many areas of physics, including cosmology, particle physics and condensed matter. An example is the breaking of spatial translational symmetry, which underlies the formation of crystals and the phase transition from liquid to solid. Using the analogy of crystals in space, the breaking of translational symmetry in time and the emergence of a ‘time crystal’ was recently proposed, but was later shown to be forbidden in thermal equilibrium. However, non-equilibrium Floquet systems, which are subject to a periodic drive, can exhibit persistent time correlations at an emergent subharmonic frequency. This new phase of matter has been dubbed a ‘discrete time crystal’. Here we present the experimental observation of a discrete time crystal, in an interacting spin chain of trapped atomic ions. We apply a periodic Hamiltonian to the system under many-body localization conditions, and observe a subharmonic temporal response that is robust to external perturbations. The observation of such a time crystal opens the door to the study of systems with long-range spatio-temporal correlations and novel phases of matter that emerge under intrinsically non-equilibrium conditions.
Observation of a discrete time crystal.
Zhang, J; Hess, P W; Kyprianidis, A; Becker, P; Lee, A; Smith, J; Pagano, G; Potirniche, I-D; Potter, A C; Vishwanath, A; Yao, N Y; Monroe, C
2017-03-08
Spontaneous symmetry breaking is a fundamental concept in many areas of physics, including cosmology, particle physics and condensed matter. An example is the breaking of spatial translational symmetry, which underlies the formation of crystals and the phase transition from liquid to solid. Using the analogy of crystals in space, the breaking of translational symmetry in time and the emergence of a 'time crystal' was recently proposed, but was later shown to be forbidden in thermal equilibrium. However, non-equilibrium Floquet systems, which are subject to a periodic drive, can exhibit persistent time correlations at an emergent subharmonic frequency. This new phase of matter has been dubbed a 'discrete time crystal'. Here we present the experimental observation of a discrete time crystal, in an interacting spin chain of trapped atomic ions. We apply a periodic Hamiltonian to the system under many-body localization conditions, and observe a subharmonic temporal response that is robust to external perturbations. The observation of such a time crystal opens the door to the study of systems with long-range spatio-temporal correlations and novel phases of matter that emerge under intrinsically non-equilibrium conditions.
NASA Astrophysics Data System (ADS)
Ma, Yong-Liang; Harada, Masayasu; Lee, Hyun Kyu; Oh, Yongseok; Park, Byung-Yoon; Rho, Mannque
2014-08-01
We find that, when the dilaton is implemented as a (pseudo-)Nambu-Goldstone boson using a conformal compensator or "conformon" in a hidden gauge symmetric Lagrangian written to O(p4) from which baryons arise as solitons, namely, skyrmions, the vector manifestation and chiral symmetry restoration at high density predicted in hidden local symmetry theory—which is consistent with Brown-Rho scaling—are lost or sent to infinite density. It is shown that they can be restored if in medium the behavior of the ω field is taken to deviate from that of the ρ meson in such a way that the flavor U(2) symmetry is strongly broken at increasing density. The hitherto unexposed crucial role of the ω meson in the structure of elementary baryon and multibaryon systems is uncovered in this work. In the state of half-skyrmions to which the skyrmions transform at a density n1/2≳n0 (where n0 is the normal nuclear matter density), characterized by the vanishing (space averaged) quark condensate but nonzero pion decay constant, the nucleon mass remains more or less constant at a value ≳60% of the vacuum value, indicating a large component of the nucleon mass that is not associated with the spontaneous breaking of chiral symmetry. We discuss its connection to the chiral-invariant mass m0 that figures in the parity-doublet baryon model.
Gauge coupling unification and nonequilibrium thermal dark matter.
Mambrini, Yann; Olive, Keith A; Quevillon, Jérémie; Zaldívar, Bryan
2013-06-14
We study a new mechanism for the production of dark matter in the Universe which does not rely on thermal equilibrium. Dark matter is populated from the thermal bath subsequent to inflationary reheating via a massive mediator whose mass is above the reheating scale T(RH). To this end, we consider models with an extra U(1) gauge symmetry broken at some intermediate scale (M(int) ≃ 10(10)-10(12) GeV). We show that not only does the model allow for gauge coupling unification (at a higher scale associated with grand unification) but it can provide a dark matter candidate which is a standard model singlet but charged under the extra U(1). The intermediate scale gauge boson(s) which are predicted in several E6/SO(10) constructions can be a natural mediator between dark matter and the thermal bath. We show that the dark matter abundance, while never having achieved thermal equilibrium, is fixed shortly after the reheating epoch by the relation T(RH)(3)/M(int)(4). As a consequence, we show that the unification of gauge couplings which determines M(int) also fixes the reheating temperature, which can be as high as T(RH) ≃ 10(11) GeV.
Behavior in strong fields of Euclidean gauge theories. II
NASA Astrophysics Data System (ADS)
Haba, Z.
1984-04-01
Functional determinants resulting from functional integration in quantum gauge theories are studied. We derive an expansion around the constant field strength for the (renormalized) spinor determinant detMF in QED. We show that, if the field strength F is large and its derivatives are bounded, then detMF≡exp(-W)~exp(cF2lnF2), where c>0. Hence, the effective action W in (four-dimensional) QED is unbounded from below. Moreover, we prove that exp(-W) is not integrable. A similar result is established in the Yukawa model [detMY~exp(φ4lnφ4)]. We estimate the scalar determinant detMA2 for a non-Abelian gauge field. We show that (like in the Abelian case studied earlier) detMA2=exp[c|F|2ln|F|2+r2(F,DF,DDF)], where c>0 and r2 is bounded by a quadratic form of the gauge-invariant variables |F|, |DF|, and |DDF|. We investigate the effect of gluon self-interaction on the stability of models with broken gauge symmetry G-->H (we discuss in detail the Georgi-Glashow model). We sum up (in an approximation) the contribution of massive gluons to the O(2)-invariant effective action. It is shown that this effective action is bounded from below for slowly varying fields, if the couplings are asymptotically free at the one-loop level.
Lattice gauge theory simulations in the quantum information era
NASA Astrophysics Data System (ADS)
Dalmonte, M.; Montangero, S.
2016-07-01
The many-body problem is ubiquitous in the theoretical description of physical phenomena, ranging from the behaviour of elementary particles to the physics of electrons in solids. Most of our understanding of many-body systems comes from analysing the symmetric properties of Hamiltonian and states: the most striking examples are gauge theories such as quantum electrodynamics, where a local symmetry strongly constrains the microscopic dynamics. The physics of such gauge theories is relevant for the understanding of a diverse set of systems, including frustrated quantum magnets and the collective dynamics of elementary particles within the standard model. In the last few years, several approaches have been put forward to tackle the complex dynamics of gauge theories using quantum information concepts. In particular, quantum simulation platforms have been put forward for the realisation of synthetic gauge theories, and novel classical simulation algorithms based on quantum information concepts have been formulated. In this review, we present an introduction to these approaches, illustrating the basics concepts and highlighting the connections between apparently very different fields, and report the recent developments in this new thriving field of research.
NASA Astrophysics Data System (ADS)
Haas, Fernando
2016-11-01
A didactic and systematic derivation of Noether point symmetries and conserved currents is put forward in special relativistic field theories, without a priori assumptions about the transformation laws. Given the Lagrangian density, the invariance condition develops as a set of partial differential equations determining the symmetry transformation. The solution is provided in the case of real scalar, complex scalar, free electromagnetic, and charged electromagnetic fields. Besides the usual conservation laws, a less popular symmetry is analyzed: the symmetry associated with the linear superposition of solutions, whenever applicable. The role of gauge invariance is emphasized. The case of the charged scalar particle under external electromagnetic fields is considered, and the accompanying Noether point symmetries determined. Noether point symmetries for a dynamical system in extended gravity cosmology are also deduced.
Lorentz violating p-form gauge theories in superspace
NASA Astrophysics Data System (ADS)
Upadhyay, Sudhaker; Shah, Mushtaq B.; Ganai, Prince A.
2017-03-01
Very special relativity (VSR) keeps the main features of special relativity but breaks rotational invariance due to an intrinsic preferred direction. We study the VSR-modified extended BRST and anti-BRST symmetry of the Batalin-Vilkovisky (BV) actions corresponding to the p=1,2,3-form gauge theories. Within the VSR framework, we discuss the extended BRST invariant and extended BRST and anti-BRST invariant superspace formulations for these BV actions. Here we observe that the VSR-modified extended BRST invariant BV actions corresponding to the p=1,2,3-form gauge theories can be written in a manifestly covariant manner in a superspace with one Grassmann coordinate. Moreover, two Grassmann coordinates are required to describe the VSR-modified extended BRST and extended anti-BRST invariant BV actions in a superspace. These results are consistent with the Lorentz-invariant (special relativity) formulation.
Reflections on the renormalization procedure for gauge theories
NASA Astrophysics Data System (ADS)
't Hooft, Gerard
2016-11-01
Various pieces of insight were needed to formulate the rules for working with gauge theories of the electro-magnetic, weak and strong forces. First, it was needed to understand how to formulate the Feynman rules. We had to learn that there are many different ways to derive them, and it was needed to know how different formulations of the gauge constraint lead to the same final results: the calculated values of the scattering amplitudes. The rules for dealing with the infinities that had to be subtracted were a big challenge, culminating in the discovery of the Becchi-Rouet-Stora-Tyutin symmetry. Fond recollections of the numerous discussions the author had with Raymond Stora on this topic are memorised here. We end with some reflections on the mathematical status of quantum field theories, and the transcription of a letter by R. Stora to the author.
Yang-Mills gauge theory and Higgs particle
NASA Astrophysics Data System (ADS)
Wu, Tai Tsun; Wu, Sau Lan
2015-12-01
Motivated by the experimental data on the Higgs particle from the ATLAS Collaboration and the CMS Collaboration at CERN, the standard model, which is a Yang-Mills non-Abelian gauge theory with the group U(1) × SU(2) × SU(3), is augmented by scalar quarks and scalar leptons without changing the gauge group and without any additional Higgs particle. Thus there is fermion-boson symmetry between these new particles and the known quarks and leptons. In a simplest scenario, the cancellation of the quadratic divergences in this augmented standard model leads to a determination of the masses of all these scalar quarks and scalar leptons. All these masses are found to be less than 100 GeV/c2, and the right-handed scalar neutrinos are especially light. Alterative procedures are given with less reliance on the experimental data, leading to the same conclusions.
Yang-Mills Gauge Theory and Higgs Particle
NASA Astrophysics Data System (ADS)
Wu, Tai Tsun; Wu, Sau Lan
Motivated by the experimental data on the Higgs particle from the ATLAS Collaboration and the CMS Collaboration at CERN, the standard model, which is a Yang-Mills non-Abelian gauge theory with the group U(1) × SU (2) × SU (3), is augmented by scalar quarks and scalar leptons without changing the gauge group and without any additional Higgs particle. Thus there is fermion-boson symmetry between these new particles and the known quarks and leptons. In a simplest scenario, the cancellation of the quadratic divergences in this augmented standard model leads to a determination of the masses of all these scalar quarks and scalar leptons. All these masses are found to be less than 100 GeV/c2, and the right-handed scalar neutrinos are especially light. Alterative procedures are given with less reliance on the experimental data, leading to the same conclusions.
Gain-Sparsity and Symmetry-Forced Rigidity in the Plane.
Jordán, Tibor; Kaszanitzky, Viktória E; Tanigawa, Shin-Ichi
We consider planar bar-and-joint frameworks with discrete point group symmetry in which the joint positions are as generic as possible subject to the symmetry constraint. We provide combinatorial characterizations for symmetry-forced rigidity of such structures with rotation symmetry or dihedral symmetry of order 2k with odd k, unifying and extending previous work on this subject. We also explore the matroidal background of our results and show that the matroids induced by the row independence of the orbit matrices of the symmetric frameworks are isomorphic to gain sparsity matroids defined on the quotient graph of the framework, whose edges are labeled by elements of the corresponding symmetry group. The proofs are based on new Henneberg type inductive constructions of the gain graphs that correspond to the bases of the matroids in question, which can also be seen as symmetry preserving graph operations in the original graph.
Canonical quantization of general relativity in discrete space-times.
Gambini, Rodolfo; Pullin, Jorge
2003-01-17
It has long been recognized that lattice gauge theory formulations, when applied to general relativity, conflict with the invariance of the theory under diffeomorphisms. We analyze discrete lattice general relativity and develop a canonical formalism that allows one to treat constrained theories in Lorentzian signature space-times. The presence of the lattice introduces a "dynamical gauge" fixing that makes the quantization of the theories conceptually clear, albeit computationally involved. The problem of a consistent algebra of constraints is automatically solved in our approach. The approach works successfully in other field theories as well, including topological theories. A simple cosmological application exhibits quantum elimination of the singularity at the big bang.
Gauge action improvement and smearing
NASA Astrophysics Data System (ADS)
Dürr, Stephan
2005-11-01
The effect of repeatedly smearing SU(3) gauge configurations is investigated. Six gauge actions (Wilson, Symanzik, Iwasaki, DBW2, Beinlich-Karsch-Laermann, Langfeld; combined with a direct SU(3)-overrelaxation step) and three smearings (APE, HYP, EXP) are compared. The impact on large Wilson loops is monitored, confirming the signal-to-noise prediction by Lepage. The fat-link definition of the "naive" topological charge proves most useful on improved action ensembles.
Aspects of finite field-dependent symmetry in SU(2) Cho-Faddeev-Niemi decomposition
NASA Astrophysics Data System (ADS)
Upadhyay, Sudhaker
2013-11-01
In this Letter we consider SU(2) Yang-Mills theory analyzed in Cho-Faddeev-Niemi variables which remains invariant under local gauge transformations. The BRST symmetries of this theory are generalized by making the infinitesimal parameter finite and field-dependent. Further, we show that under appropriate choices of finite and field-dependent parameter, the gauge-fixing and ghost terms corresponding to Landau as well as maximal Abelian gauge for such Cho-Faddeev-Niemi decomposed theory appear naturally within functional integral through Jacobian calculation.
Conformal symmetry and light flavor baryon spectra
NASA Astrophysics Data System (ADS)
Kirchbach, M.; Compean, C. B.
2010-08-01
The degeneracy among parity pairs systematically observed in the N and Δ spectra is interpreted to hint on a possible conformal symmetry realization in the light flavor baryon sector in line with AdS5/CFT4. The case is made by showing that all the observed N and Δ resonances with masses below 2500 MeV distribute fairly well each over the first levels of a unitary representation of the conformal group, a representation that covers the spectrum of a quark-diquark system, placed directly on a conformally compactified Minkowski spacetime, R1⊗S3, as approached from the AdS5 cone. The free geodesic motion on the S3 manifold is described by means of the scalar conformal equation there, which is of the Klein-Gordon-type. The equation is then gauged by the curved Coulomb potential that has the form of a cotangent function. Conformal symmetry is not exact, this because the gauge potential slightly modifies the conformal centrifugal barrier of the free geodesic motion. Thanks to this, the degeneracy between P11-S11 pairs from same level is relaxed, while the remaining states belonging to same level remain practically degenerate. The model describes the correct mass ordering in the P11-S11 pairs through the spectra as a combined effect of the above conformal symmetry breaking, on the one side, and a parity change of the diquark from a scalar at low masses, to a pseudoscalar at higher masses, on the other. The quality of the wave functions is illustrated by calculations of realistic mean square charge radii and electric charge form factors on the examples of the proton, and the protonic P11(1440), and S11(1535) resonances. The scheme also allows for a prediction of the dressing function of an effective instantaneous gluon propagator from the Fourier transform of the gauge potential. We find a dressing function that is finite in the infrared and tends to zero at infinity.
A gauge model for right handed neutrinos as dark matter
NASA Astrophysics Data System (ADS)
Hernández-Pinto, R. J.; Pérez-Lorenzana, A.
2008-07-01
We suggest a simple extension of the electroweak group, SU(2)L×U(1)Y×U(1)B-L, where the breaking of U(1)B-L symmetry provides masses for right handed neutrinos, N, at an acceptable range for them to be Dark Matter (DM). We study the contributions to Mo/ller and Bhabha scattering due to B-L neutral boson to constrain its gauge coupling. We analize N decay rates to determine the number of families that should be considered as DM candidates. The decoupling temperature between active and sterile neutrinos is also calculated.
Symmetry of priapulids (Priapulida). 2. Symmetry of larvae.
Adrianov, A V; Malakhov, V V
2001-02-01
Larvae of priapulids are characterized by radial symmetry evident from both external and internal characters of the introvert and lorica. The bilaterality appears as a result of a combination of several radial symmetries: pentaradial symmetry of the teeth, octaradial symmetry of the primary scalids, 25-radial symmetry of scalids, biradial symmetry of the neck, and biradial and decaradial symmetry of the trunk. Internal radiality is exhibited by musculature and the circumpharyngeal nerve ring. Internal bilaterality is evident from the position of the ventral nerve cord and excretory elements. Externally, the bilaterality is determined by the position of the anal tubulus and two shortened midventral rows of scalids bordering the ventral nerve cord. The lorical elements define the biradial symmetry that is missing in adult priapulids. The radial symmetry of larvae is a secondary appearance considered an evolutionary adaptation to a lifestyle within the three-dimensional environment of the benthic sediment.
Symmetry in context: salience of mirror symmetry in natural patterns.
Cohen, Elias H; Zaidi, Qasim
2013-05-31
Symmetry is a biologically relevant, mathematically involving, and aesthetically compelling visual phenomenon. Mirror symmetry detection is considered particularly rapid and efficient, based on experiments with random noise. Symmetry detection in natural settings, however, is often accomplished against structured backgrounds. To measure salience of symmetry in diverse contexts, we assembled mirror symmetric patterns from 101 natural textures. Temporal thresholds for detecting the symmetry axis ranged from 28 to 568 ms indicating a wide range of salience (1/Threshold). We built a model for estimating symmetry-energy by connecting pairs of mirror-symmetric filters that simulated cortical receptive fields. The model easily identified the axis of symmetry for all patterns. However, symmetry-energy quantified at this axis correlated weakly with salience. To examine context effects on symmetry detection, we used the same model to estimate approximate symmetry resulting from the underlying texture throughout the image. Magnitudes of approximate symmetry at flanking and orthogonal axes showed strong negative correlations with salience, revealing context interference with symmetry detection. A regression model that included the context-based measures explained the salience results, and revealed why perceptual symmetry can differ from mathematical characterizations. Using natural patterns thus produces new insights into symmetry perception and its possible neural circuits.
Symmetry in context: Salience of mirror symmetry in natural patterns
Cohen, Elias H.; Zaidi, Qasim
2013-01-01
Symmetry is a biologically relevant, mathematically involving, and aesthetically compelling visual phenomenon. Mirror symmetry detection is considered particularly rapid and efficient, based on experiments with random noise. Symmetry detection in natural settings, however, is often accomplished against structured backgrounds. To measure salience of symmetry in diverse contexts, we assembled mirror symmetric patterns from 101 natural textures. Temporal thresholds for detecting the symmetry axis ranged from 28 to 568 ms indicating a wide range of salience (1/Threshold). We built a model for estimating symmetry-energy by connecting pairs of mirror-symmetric filters that simulated cortical receptive fields. The model easily identified the axis of symmetry for all patterns. However, symmetry-energy quantified at this axis correlated weakly with salience. To examine context effects on symmetry detection, we used the same model to estimate approximate symmetry resulting from the underlying texture throughout the image. Magnitudes of approximate symmetry at flanking and orthogonal axes showed strong negative correlations with salience, revealing context interference with symmetry detection. A regression model that included the context-based measures explained the salience results, and revealed why perceptual symmetry can differ from mathematical characterizations. Using natural patterns thus produces new insights into symmetry perception and its possible neural circuits. PMID:23729773
NASA Astrophysics Data System (ADS)
Reshetnyak, A. A.; Moshin, P. Yu.
2017-03-01
A review of the finite field-dependent Becchi-Rouet-Stora-Tyutin (BRST) and BRST-antiBRST transformations is presented. Exact rules for calculating the Jacobian of the corresponding change of variables in the partition function are given. Infrared peculiarities under Rξ-gauges in the Yang-Mills theory and the Standard Model are examined in a gauge-invariant way with an appropriate horizon functional and unaffected N = 1, 2 BRST symmetries.
Local Activity Principle:. the Cause of Complexity and Symmetry Breaking
NASA Astrophysics Data System (ADS)
Mainzer, Klaus
2013-01-01
The principle of local activity is precisely the missing concept to explain the emergence of complex patterns in a homogeneous medium. Leon O. Chua discovered and defined this principle in the theory of nonlinear electronic circuits in a mathematically rigorous way. The local principle can be generalized and proven at least for the class of nonlinear reaction-diffusion systems in physics, chemistry, biology and brain research. Recently, it was realized by memristors for nanoelectronic device applications in technical brains. In general, the emergence of complex patterns and structures is explained by symmetry breaking in homogeneous media. The principle of local activity is the cause of symmetry breaking in homogeneous media. We argue that the principle of local activity is really fundamental in science and can even be identified in quantum cosmology as symmetry breaking of local gauge symmetries generating the complexity of matter and forces in our universe. Finally, we consider applications in economic, financial, and social systems with the emergence of equilibrium states, symmetry breaking at critical points of phase transitions and risky acting at the edge of chaos. In any case, the driving causes of symmetry breaking and the emergence of complexity are locally active elements, cells, units, or agents.
Pairing symmetry and vortex zero mode for superconducting Dirac fermions
Lu, C.-K.; Herbut, Igor F.
2010-10-01
We study vortex zero-energy bound states in presence of pairing between low-energy Dirac fermions on the surface of a topological insulator. The pairing symmetries considered include the s-wave, p-wave, and, in particular, the mixed-parity symmetry, which arises in absence of the inversion symmetry on the surface. The zero mode is analyzed within the generalized Jackiw-Rossi-Dirac Hamiltonian that contains a momentum-dependent mass term, and includes the effects of the electromagnetic gauge field and the Zeeman coupling as well. At a finite chemical potential, as long as the spectrum without the vortex is fully gapped, the presence of a single Fermi surface with a definite helicity always leads to one Majorana zero mode, in which both electron's spin projections participate. In particular, the critical effects of the Zeeman coupling on the zero mode are discussed.
Enhanced baryon number violation due to gauged non-topological solitons.
NASA Astrophysics Data System (ADS)
Lee, C. H.; Yoon, S. U.
1993-12-01
In the context of the Callan-Rubakov effect, it is, in principle, possible for a gauged non-topological soliton (NTS) inside which a grand unified symmetry is realized to catalyse baryon decay. In this paper, assuming a gauged NTS which the localized FLS (Friedberg, Lee, and Sirlin)'s model admits to form during a grand unified phase transition, the authors calculate the cross-section for quark-to-lepton transition due to the gauged NTS, and learn that there is a range of parameters for which their cross-section gets away from a naive geometric one, and which is consistent with that for the existence of stable gauged NTSs.
Right-handed neutrino dark matter under the B - L gauge interaction
NASA Astrophysics Data System (ADS)
Kaneta, Kunio; Kang, Zhaofeng; Lee, Hye-Sung
2017-02-01
We study the right-handed neutrino (RHN) dark matter candidate in the minimal U(1) B-L gauge extension of the standard model. The U(1) B-L gauge symmetry offers three RHNs which can address the origin of the neutrino mass, the relic dark matter, and the matter-antimatter asymmetry of the universe. The lightest among the three is taken as the dark matter candidate, which is under the B - L gauge interaction. We investigate various scenarios for this dark matter candidate with the correct relic density by means of the freeze-out or freeze-in mechanism. A viable RHN dark matter mass lies in a wide range including keV to TeV scale. We emphasize the sub-electroweak scale light B - L gauge boson case, and identify the parameter region motivated from the dark matter physics, which can be tested with the planned experiments including the CERN SHiP experiment.
Code of Federal Regulations, 2010 CFR
2010-10-01
... 49 Transportation 4 2010-10-01 2010-10-01 false Air gauges. 230.73 Section 230.73 Transportation... Signal Equipment § 230.73 Air gauges. (a) Location. Air gauges shall be so located that they may be conveniently read by the engineer from his or her usual position in the cab. No air gauge may be more than...
Code of Federal Regulations, 2011 CFR
2011-10-01
... 49 Transportation 4 2011-10-01 2011-10-01 false Air gauges. 230.73 Section 230.73 Transportation... Signal Equipment § 230.73 Air gauges. (a) Location. Air gauges shall be so located that they may be conveniently read by the engineer from his or her usual position in the cab. No air gauge may be more than...
49 CFR 229.107 - Pressure gauge.
Code of Federal Regulations, 2013 CFR
2013-10-01
... 49 Transportation 4 2013-10-01 2013-10-01 false Pressure gauge. 229.107 Section 229.107....107 Pressure gauge. (a) Each steam generator shall have an illuminated steam gauge that correctly indicates the pressure. The steam pressure gauge shall be graduated to not less than one and one-half...
49 CFR 229.107 - Pressure gauge.
Code of Federal Regulations, 2014 CFR
2014-10-01
... 49 Transportation 4 2014-10-01 2014-10-01 false Pressure gauge. 229.107 Section 229.107....107 Pressure gauge. (a) Each steam generator shall have an illuminated steam gauge that correctly indicates the pressure. The steam pressure gauge shall be graduated to not less than one and one-half...