Infrared Maximally Abelian Gauge
Mendes, Tereza; Cucchieri, Attilio; Mihara, Antonio
2007-02-27
The confinement scenario in Maximally Abelian gauge (MAG) is based on the concepts of Abelian dominance and of dual superconductivity. Recently, several groups pointed out the possible existence in MAG of ghost and gluon condensates with mass dimension 2, which in turn should influence the infrared behavior of ghost and gluon propagators. We present preliminary results for the first lattice numerical study of the ghost propagator and of ghost condensation for pure SU(2) theory in the MAG.
Magnetic monopoles and Abelian gauge fixing in SU(4) gauge group
NASA Astrophysics Data System (ADS)
Rafibakhsh, Shahnoosh; Eshraghi, Mojtaba; Kahnemuii, Mohammad Javad
2016-01-01
Abelian gauge fixing procedure is used to create the SU (4) magnetic monopoles in the vicinity of the points where the gluon field becomes singular. The matrix of the scalar field is considered as almost diagonal in the SU (2) and SU (3) subspaces. The gauge transformation which diagonalizes the hedgehog filed, transforms the gluon field into two regular and singular parts. The abelian magnetic monopoles which appear in the latter part obey the quantization condition.
Momentum subtraction scheme renormalization group functions in the maximal Abelian gauge
NASA Astrophysics Data System (ADS)
Bell, J. M.; Gracey, J. A.
2013-10-01
The one-loop 3-point vertex functions of QCD in the maximal Abelian gauge are evaluated at the fully symmetric point at one loop. As a consequence the theory is renormalized in the various momentum subtraction schemes, which are defined by the trivalent vertices, as well as in the MS¯ scheme. From these the two-loop renormalization group functions in the momentum schemes are derived using the one-loop conversion functions. In parallel we repeat the analysis for the Curci-Ferrari gauge, which corresponds to the maximal Abelian gauge in a specific limit. The relation between the Λ parameters in different schemes is also provided.
Non-Abelian Gauge Groups for Real and Complex Amended Maxwell's Equations
NASA Astrophysics Data System (ADS)
Rauscher, E. A.
2002-04-01
We have developed an eight dimensional complex Minkowski space M4, compiled of four real dimensions and four imaginary dimensions, which is constant with Lorentz invariance and analytic continuation in the complex plane(1). Complexification, of Maxwell's equations requires a non-Abelian gauge group, which amends the usual theory which utilizes the usual unimodular Weyl U1 group. We have examined the modification of gauge conditions using higher symmetry groups such as SU2, SUn and other groups such as the SL(2,c) double cover group of the rotational group SO(3,1). The mappability of the twistor algebra and the spinor calculus is analyzed in the context of the electromagnetic theory. Thus we are led to new and interesting physics involving extended metrical space constraints, the usual transverse and also longitudinal, non Hertzian electric and magnetic field solutions to Maxwell's equations, possibly leading to new communications systems and antennae theory, non-zero solutions to Ñ·B, and a possible finite but small rest mass of the photon. Comparison of our theoretical approach is made to the work of T.W. Barrett and H.F. Hermuth?s work on amended Maxwell's theories. (1) C. Ramon and E. A. Rauscher, Found. of Phys. 10, 661 (1980)
NASA Astrophysics Data System (ADS)
Gerbier, Fabrice; Goldman, Nathan; Lewenstein, Maciej; Sengstock, Klaus
2013-07-01
-orbit coupling (Rashba and Dresselhaus couplings), familiar from AMO and condensed matter physics. They lead to yet another variety of fascinating phenomena such as the quantum spin Hall effect, three-dimensional topological insulators, topological superconductors and superfluids of various kinds. One also expects here the appearance of excitations in a form of topological edge states that can support robust transport, or entangled Majorana fermions in the case of topological superconductors or superfluids. Again, while many kinds of topological insulators have been realized in condensed matter systems, a controlled way of creating them in AMO systems and studying quantum phase transitions between various kinds of them is obviously very appealing and challenging. The various systems listed so far correspond to static gauge fields, which are externally imposed by the experimentalists. Even more fascinating is the possibility of generating synthetically dynamical gauge fields, i.e. gauge fields that evolve in time according to an interacting gauge theory, e.g., a full lattice gauge theory (LGT). These dynamical gauge fields can also couple to matter fields, allowing the quantum simulation of such complex systems (notoriously hard to simulate using 'traditional' computers), which are particularly relevant for modern high-energy physics. So far, most of the theoretical proposals concern the simulation of Abelian gauge theories, however, several groups have recently proposed extensions to the non-Abelian scenarios. The scope of the present focused issue of Journal of Physics B is to cover all of these developments, with particular emphasis on the non-Abelian gauge fields. The 14 papers in this issue include contributions from the leading theory groups working in this field; we believe that this collection will provide the reference set for quantum simulations of gauge fields. Although the special issue contains exclusively theoretical proposals and studies, it should be stressed that
S-duality in SU(3) Yang-Mills theory with non-abelian unbroken gauge group
NASA Astrophysics Data System (ADS)
Schroers, B. J.; Bais, F. A.
1998-12-01
It is observed that the magnetic charges of classical monopole solutions in Yang-Mills-Higgs theory with non-abelian unbroken gauge group H are in one-to-one correspondence with coherent states of a dual or magnetic group H˜. In the spirit of the Goddard-Nuyts-Olive conjecture this observation is interpreted as evidence for a hidden magnetic symmetry of Yang-Mills theory. SU(3) Yang-Mills-Higgs theory with unbroken gauge group U(2) is studied in detail. The action of the magnetic group on semi-classical states is given explicitly. Investigations of dyonic excitations show that electric and magnetic symmetry are never manifest at the same time: Non-abelian magnetic charge obstructs the realisation of electric symmetry and vice-versa. On the basis of this fact the charge sectors in the theory are classified and their fusion rules are discussed. Non-abelian electric-magnetic duality is formulated as a map between charge sectors. Coherent states obey particularly simple fusion rules, and in the set of coherent states S-duality can be formulated as an SL(2, Z) mapping between sectors which leaves the fusion rules invariant.
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.
NASA Astrophysics Data System (ADS)
Gao, Ya-Jun
2006-01-01
The so-called extended hyperbolic complex (EHC) function method is used to study further the stationary axisymmetric Einstein-Maxwell theory with p Abelian gauge fields (EM-p theory, for short). Two EHC structural Riemann-Hilbert (RH) transformations are constructed and are then shown to give an infinite-dimensional symmetry group of the EM-p theory. This symmetry group is verified to have the structure of semidirect product of Kac-Moody group SU(hat p+1,1) and Virasoro group. Moreover, the infinitesimal forms of these two RH transformations are calculated and found to give exactly the same infinitesimal transformations as in previous author's paper by a different scheme. This demonstrates that the results obtained in the present paper provide some exponentiations of all the infinitesimal symmetry transformations obtained before.
Gauge invariance for a whole Abelian model
Chauca, J.; Doria, R.; Soares, W.
2012-09-24
Light invariance is a fundamental principle for physics be done. It generates Maxwell equations, relativity, Lorentz group. However there is still space for a fourth picture be developed which is to include fields with same Lorentz nature. It brings a new room for field theory. It says that light invariance does not work just to connect space and time but it also associates different fields with same nature. Thus for the ((1/2),(1/2)) representation there is a fields family {l_brace}A{sub {mu}I}{r_brace} to be studied. This means that given such fields association one should derive its corresponding gauge theory. This is the effort at this work. Show that there is a whole gauge theory to cover these fields relationships. Considering the abelian case, prove its gauge invariance. It yields the kinetic, massive, trilinear and quadrilinear gauge invariant terms.
NASA Astrophysics Data System (ADS)
Gerbier, Fabrice; Goldman, Nathan; Lewenstein, Maciej; Sengstock, Klaus
2013-07-01
Building a universal quantum computer is a central goal of emerging quantum technologies, which has the potential to revolutionize science and technology. Unfortunately, this future does not seem to be very close at hand. However, quantum computers built for a special purpose, i.e. quantum simulators , are currently developed in many leading laboratories. Many schemes for quantum simulation have been proposed and realized using, e.g., ultracold atoms in optical lattices, ultracold trapped ions, atoms in arrays of cavities, atoms/ions in arrays of traps, quantum dots, photonic networks, or superconducting circuits. The progress in experimental implementations is more than spectacular. Particularly interesting are those systems that simulate quantum matter evolving in the presence of gauge fields. In the quantum simulation framework, the generated (synthetic) gauge fields may be Abelian, in which case they are the direct analogues of the vector potentials commonly associated with magnetic fields. In condensed matter physics, strong magnetic fields lead to a plethora of fascinating phenomena, among which the most paradigmatic is perhaps the quantum Hall effect. The standard Hall effect consists in the appearance of a transverse current, when a longitudinal voltage difference is applied to a conducting sample. For quasi-two-dimensional semiconductors at low temperatures placed in very strong magnetic fields, the transverse conductivity, the ratio between the transverse current and the applied voltage, exhibits perfect and robust quantization, independent for instance of the material or of its geometry. Such an integer quantum Hall effect, is now understood as a deep consequence of underlying topological order. Although such a system is an insulator in the bulk, it supports topologically robust edge excitations which carry the Hall current. The robustness of these chiral excitations against backscattering explains the universality of the quantum Hall effect. Another
Abelian 3-form gauge theory: Superfield approach
NASA Astrophysics Data System (ADS)
Malik, R. P.
2012-09-01
We discuss a D-dimensional Abelian 3-form gauge theory within the framework of Bonora-Tonin's superfield formalism and derive the off-shell nilpotent and absolutely anticommuting Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for this theory. To pay our homage to Victor I. Ogievetsky (1928-1996), who was one of the inventors of Abelian 2-form (antisymmetric tensor) gauge field, we go a step further and discuss the above D-dimensional Abelian 3-form gauge theory within the framework of BRST formalism and establish that the existence of the (anti-)BRST invariant Curci-Ferrari (CF) type of restrictions is the hallmark of any arbitrary p-form gauge theory (discussed within the framework of BRST formalism).
Non-Abelian discrete gauge symmetries in F-theory
NASA Astrophysics Data System (ADS)
Grimm, Thomas W.; Pugh, Tom G.; Regalado, Diego
2016-02-01
The presence of non-Abelian discrete gauge symmetries in four-dimensional F-theory compactifications is investigated. Such symmetries are shown to arise from seven-brane configurations in genuine F-theory settings without a weak string coupling description. Gauge fields on mutually non-local seven-branes are argued to gauge both R-R and NS-NS two-form bulk axions. The gauging is completed into a generalisation of the Heisenberg group with either additional seven-brane gauge fields or R-R bulk gauge fields. The former case relies on having seven-brane fluxes, while the latter case requires torsion cohomology and is analysed in detail through the M-theory dual. Remarkably, the M-theory reduction yields an Abelian theory that becomes non-Abelian when translated into the correct duality frame to perform the F-theory limit. The reduction shows that the gauge coupling function depends on the gauged scalars and transforms non-trivially as required for the groups encountered. This field dependence agrees with the expectations for the kinetic mixing of seven-branes and is unchanged if the gaugings are absent.
Non-Abelian gauge field theory in scale relativity
NASA Astrophysics Data System (ADS)
Nottale, Laurent; Célérier, Marie-Noëlle; Lehner, Thierry
2006-03-01
Gauge field theory is developed in the framework of scale relativity. In this theory, space-time is described as a nondifferentiable continuum, which implies it is fractal, i.e., explicitly dependent on internal scale variables. Owing to the principle of relativity that has been extended to scales, these scale variables can themselves become functions of the space-time coordinates. Therefore, a coupling is expected between displacements in the fractal space-time and the transformations of these scale variables. In previous works, an Abelian gauge theory (electromagnetism) has been derived as a consequence of this coupling for global dilations and/or contractions. We consider here more general transformations of the scale variables by taking into account separate dilations for each of them, which yield non-Abelian gauge theories. We identify these transformations with the usual gauge transformations. The gauge fields naturally appear as a new geometric contribution to the total variation of the action involving these scale variables, while the gauge charges emerge as the generators of the scale transformation group. A generalized action is identified with the scale-relativistic invariant. The gauge charges are the conservative quantities, conjugates of the scale variables through the action, which find their origin in the symmetries of the "scale-space." We thus found in a geometric way and recover the expression for the covariant derivative of gauge theory. Adding the requirement that under the scale transformations the fermion multiplets and the boson fields transform such that the derived Lagrangian remains invariant, we obtain gauge theories as a consequence of scale symmetries issued from a geometric space-time description.
Introducing Abelian Groups Using Bullseyes and Jenga
ERIC Educational Resources Information Center
Smith, Michael D.
2016-01-01
The purpose of this article is to share a new approach for introducing students to the definition and standard examples of Abelian groups. The definition of an Abelian group is revised to include six axioms. A bullseye provides a way to visualize elementary examples and non-examples of Abelian groups. An activity based on the game of Jenga is used…
Maximal Abelian gauge and a generalized BRST transformation
NASA Astrophysics Data System (ADS)
Deguchi, Shinichi; Pandey, Vipul Kumar; Mandal, Bhabani Prasad
2016-05-01
We apply a generalized Becchi-Rouet-Stora-Tyutin (BRST) formulation to establish a connection between the gauge-fixed SU (2) Yang-Mills (YM) theories formulated in the Lorenz gauge and in the Maximal Abelian (MA) gauge. It is shown that the generating functional corresponding to the Faddeev-Popov (FP) effective action in the MA gauge can be obtained from that in the Lorenz gauge by carrying out an appropriate finite and field-dependent BRST (FFBRST) transformation. In this procedure, the FP effective action in the MA gauge is found from that in the Lorenz gauge by incorporating the contribution of non-trivial Jacobian due to the FFBRST transformation of the path integral measure. The present FFBRST formulation might be useful to see how Abelian dominance in the MA gauge is realized in the Lorenz gauge.
Ward-Takahashi identities for Abelian chiral gauge theories
NASA Astrophysics Data System (ADS)
de Lima, Ana Paula Cardoso Rodrigues; Dias, Sebastião Alves
2016-04-01
By considering a general Abelian chiral gauge theory, we investigate the behavior of anomalous Ward-Takahashi (WT) identities concerning their prediction for the usual relationship between the vertex and two-point fermion functions. Using gauge anomaly vanishing results, we show that the usual (in the nonanomalous case) WT identity connecting the vertex and two-point fermion 1PI functions is modified for Abelian chiral gauge theories. The modification, however, implies a relation between fermion and charge renormalization constants that can be important in a future study of renormalization of such theories.
Maximal Abelian and Curci-Ferrari gauges in momentum subtraction at three loops
NASA Astrophysics Data System (ADS)
Bell, J. M.; Gracey, J. A.
2015-12-01
The vertex structure of QCD fixed in the maximal Abelian gauge (MAG) and Curci-Ferrari gauge is analyzed at two loops at the fully symmetric point for the 3-point functions corresponding to the three momentum subtraction (MOM) renormalization schemes. Consequently, the three-loop renormalization group functions are determined for each of these three schemes in each gauge using properties of the renormalization group equation.
Enhancing Gauge Symmetries of Non-Abelian Supersymmetric Chern-Simons Model
NASA Astrophysics Data System (ADS)
Gharavi, Kh. Bahalke; Monemzadeh, M.; Nejad, S. Abarghouei
2016-07-01
In this article, we study gauge symmetries of the Non-Abelian Supersymmetric Chern-Simons model (SCS) of SU(2) group at (2+1)-dimensions in the framework of the formalism of constrained systems. Since, broken gauge symmetries in this physical system lead to the presence of nonphysical degrees of freedom, the Non-Abelian SCS model is strictly constrained to second-class constraints. Hence, by introducing some auxiliary fields and using finite order BFT method, we obtain a gauge symmetric model by converting second-class constraint to first-class ones. Ultimately, the partition function of the model is obtained in the extended phase space.
Sun, Fadi; Yu, Xiao-Lu; Ye, Jinwu; Fan, Heng; Liu, Wu-Ming
2013-01-01
The method of synthetic gauge potentials opens up a new avenue for our understanding and discovering novel quantum states of matter. We investigate the topological quantum phase transition of Fermi gases trapped in a honeycomb lattice in the presence of a synthetic non-Abelian gauge potential. We develop a systematic fermionic effective field theory to describe a topological quantum phase transition tuned by the non-Abelian gauge potential and explore its various important experimental consequences. Numerical calculations on lattice scales are performed to compare with the results achieved by the fermionic effective field theory. Several possible experimental detection methods of topological quantum phase transition are proposed. In contrast to condensed matter experiments where only gauge invariant quantities can be measured, both gauge invariant and non-gauge invariant quantities can be measured by experimentally generating various non-Abelian gauges corresponding to the same set of Wilson loops. PMID:23846153
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.
Quantization of higher abelian gauge theory in generalized differential cohomology
NASA Astrophysics Data System (ADS)
Szabo, R.
We review and elaborate on some aspects of the quantization of certain classes of higher abelian gauge theories using techniques of generalized differential cohomology. Particular emphasis is placed on the examples of generalized Maxwell theory and Cheeger-Simons cohomology, and of Ramond-Ramond fields in Type II superstring theory and differential K-theory.
Study of the zero modes of the Faddeev–Popov operator in the maximal Abelian gauge
Capri, M.A.L. Guimaraes, M.S. Lemes, V.E.R. Sorella, S.P. Tedesco, D.G.
2014-05-15
A study of the zero modes of the Faddeev–Popov operator in the maximal Abelian gauge is presented in the case of the gauge group SU(2) and for different Euclidean space–time dimensions. Explicit examples of classes of normalizable zero modes and corresponding gauge field configurations are constructed by taking into account two boundary conditions, namely: (i) the finite Euclidean Yang–Mills action, (ii) the finite Hilbert norm. -- Highlights: •We study the zero modes of the Faddeev–Popov operator in the maximal Abelian gauge. •For d=2 we obtain solutions with finite action but not finite Hilbert norm. •For d=3,4 we obtain solutions with finite action and finite Hilbert norm. •These results can be compared with those previously obtained in the Landau gauge.
NASA Astrophysics Data System (ADS)
Schröck, Mario; Vogt, Hannes
2016-01-01
On lattice gauge field configurations with 2 +1 dynamical quark flavors, we investigate the momentum space quark and gluon propagators in the combined maximally Abelian plus U (1 )3×U (1 )8 Landau gauge. We extract the gluon fields from the lattice link variables and study the diagonal and off-diagonal gluon propagators. We find that the infrared region of the transverse diagonal gluon propagator is strongly enhanced compared to the off-diagonal propagator. The Dirac operator from the Asqtad action is inverted on the diagonal and off-diagonal gluon backgrounds separately. In agreement with the hypothesis of infrared Abelian dominance, we find that the off-diagonal gluon background hardly gives rise to any nontrivial quark dynamics while the quark propagator from the diagonal gluon background closely resembles its Landau gauge counterpart.
AGT relations for abelian quiver gauge theories on ALE spaces
NASA Astrophysics Data System (ADS)
Pedrini, Mattia; Sala, Francesco; Szabo, Richard J.
2016-05-01
We construct level one dominant representations of the affine Kac-Moody algebra gl̂k on the equivariant cohomology groups of moduli spaces of rank one framed sheaves on the orbifold compactification of the minimal resolution Xk of the Ak-1 toric singularity C2 /Zk. We show that the direct sum of the fundamental classes of these moduli spaces is a Whittaker vector for gl̂k, which proves the AGT correspondence for pure N = 2 U(1) gauge theory on Xk. We consider Carlsson-Okounkov type Ext-bundles over products of the moduli spaces and use their Euler classes to define vertex operators. Under the decomposition gl̂k ≃ h ⊕sl̂k, these vertex operators decompose as products of bosonic exponentials associated to the Heisenberg algebra h and primary fields of sl̂k. We use these operators to prove the AGT correspondence for N = 2 superconformal abelian quiver gauge theories on Xk.
Non-Abelian gauge invariance and the infrared approximation
Cho, H.h.; Fried, H.M.; Grandou, T.
1988-02-15
Two constructions are given of infrared approximations, defined by a nonlocal configuration-space restrictions, which preserve the local, non-Abelian gauge invariance of SU(N) two-dimensional QCD (QCD/sub 2/). These continuum infrared methods are used to estimate the quenched order parameter
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.
Cold Atoms in Non-Abelian Gauge Potentials: From the Hofstadter Moth to Lattice Gauge Theory
Osterloh, K.; Baig, M.; Santos, L.; Zoller, P.; Lewenstein, M.
2005-07-01
We demonstrate how to create artificial external non-Abelian gauge potentials acting on cold atoms in optical lattices. The method employs atoms with k internal states, and laser assisted state sensitive tunneling, described by unitary kxk matrices. The single-particle dynamics in the case of intense U(2) vector potentials lead to a generalized Hofstadter butterfly spectrum which shows a complex mothlike structure. We discuss the possibility to realize non-Abelian interferometry (Aharonov-Bohm effect) and to study many-body dynamics of ultracold matter in external lattice gauge fields.
Non-Abelian gauge redundancy and entropic ambiguities
NASA Astrophysics Data System (ADS)
Balachandran, A. P.; de Queiroz, A. R.; Vaidya, S.
2015-04-01
The von Neumann entropy of a generic quantum state is not unique unless the state can be uniquely decomposed as a sum of extremal or pure states. Therefore one reaches the remarkable possibility that there may be many entropies for a given state. We show that this happens if the GNS representation (of the algebra of observables in some quantum state) is reducible, and some representations in the decomposition occur with non-trivial degeneracy. This ambiguity in entropy, which can occur at zero temperature, can often be traced to a gauge symmetry emergent from the non-trivial topological character of the configuration space of the underlying system. We also establish the analogue of an H-theorem for this entropy by showing that its evolution is Markovian, determined by a stochastic matrix. After demonstrating this entropy ambiguity for the simple example of the algebra of 2 × 2 matrices, we argue that the degeneracies in the GNS representation can be interpreted as an emergent broken gauge symmetry, and play an important role in the analysis of emergent entropy due to non-Abelian anomalies. We work out the simplest situation with such non-Abelian symmetry, that of an ethylene molecule.
Gauge invariance of color confinement due to the dual Meissner effect caused by Abelian monopoles
Suzuki, Tsuneo; Hasegawa, Masayasu; Ishiguro, Katsuya; Koma, Yoshiaki; Sekido, Toru
2009-09-01
The mechanism of non-Abelian color confinement is studied in SU(2) lattice gauge theory in terms of the Abelian fields and monopoles extracted from non-Abelian link variables without adopting gauge fixing. First, the static quark-antiquark potential and force are computed with the Abelian and monopole Polyakov loop correlators, and the resulting string tensions are found to be identical to the non-Abelian string tension. These potentials also show the scaling behavior with respect to the change of lattice spacing. Second, the profile of the color-electric field between a quark and an antiquark is investigated with the Abelian and monopole Wilson loops. The color-electric field is squeezed into a flux tube due to monopole supercurrent with the same Abelian color direction. The parameters corresponding to the penetration and coherence lengths show the scaling behavior, and the ratio of these lengths, i.e., the Ginzburg-Landau parameter, indicates that the vacuum type is near the border of the type 1 and type 2 (dual) superconductors. These results are summarized in which the Abelian fundamental charge defined in an arbitrary color direction is confined inside a hadronic state by the dual Meissner effect. As the color-neutral state in any Abelian color direction corresponds to the physical color-singlet state, this effect explains non-Abelian color confinement and supports the existence of a gauge-invariant mechanism of color confinement due to the dual Meissner effect caused by Abelian monopoles.
On abelian group actions and Galois quantizations
NASA Astrophysics Data System (ADS)
Huru, H. L.; Lychagin, V. V.
2013-08-01
Quantizations of actions of finite abelian groups G are explicitly described by elements in the tensor square of the group algebra of G. Over algebraically closed fields of characteristic 0 these are in one to one correspondence with the second cohomology group of the dual of G. With certain adjustments this result is applied to group actions over any field of characteristic 0. In particular we consider the quantizations of Galois extensions, which are quantized by "deforming" the multiplication. For the splitting fields of products of quadratic polynomials this produces quantized Galois extensions that all are Clifford type algebras.
Non-Abelian Aharonov-Bohm effect with the time-dependent gauge fields
NASA Astrophysics Data System (ADS)
Hosseini Mansoori, Seyed Ali; Mirza, Behrouz
2016-04-01
We investigate the non-Abelian Aharonov-Bohm (AB) effect for time-dependent gauge fields. We prove that the non-Abelian AB phase shift related to time-dependent gauge fields, in which the electric and magnetic fields are written in the adjoint representation of SU (N) generators, vanishes up to the first order expansion of the phase factor. Therefore, the flux quantization in a superconductor ring does not appear in the time-dependent Abelian or non-Abelian AB effect.
Simulation of non-Abelian gauge theories with optical lattices.
Tagliacozzo, L; Celi, A; Orland, P; Mitchell, M W; Lewenstein, M
2013-01-01
Many phenomena occurring in strongly correlated quantum systems still await conclusive explanations. The absence of isolated free quarks in nature is an example. It is attributed to quark confinement, whose origin is not yet understood. The phase diagram for nuclear matter at general temperatures and densities, studied in heavy-ion collisions, is not settled. Finally, we have no definitive theory of high-temperature superconductivity. Though we have theories that could underlie such physics, we lack the tools to determine the experimental consequences of these theories. Quantum simulators may provide such tools. Here we show how to engineer quantum simulators of non-Abelian lattice gauge theories. The systems we consider have several applications: they can be used to mimic quark confinement or to study dimer and valence-bond states (which may be relevant for high-temperature superconductors). PMID:24162080
Simulation of non-Abelian gauge theories with optical lattices
NASA Astrophysics Data System (ADS)
Tagliacozzo, L.; Celi, A.; Orland, P.; Mitchell, M. W.; Lewenstein, M.
2013-10-01
Many phenomena occurring in strongly correlated quantum systems still await conclusive explanations. The absence of isolated free quarks in nature is an example. It is attributed to quark confinement, whose origin is not yet understood. The phase diagram for nuclear matter at general temperatures and densities, studied in heavy-ion collisions, is not settled. Finally, we have no definitive theory of high-temperature superconductivity. Though we have theories that could underlie such physics, we lack the tools to determine the experimental consequences of these theories. Quantum simulators may provide such tools. Here we show how to engineer quantum simulators of non-Abelian lattice gauge theories. The systems we consider have several applications: they can be used to mimic quark confinement or to study dimer and valence-bond states (which may be relevant for high-temperature superconductors).
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.
Non-Abelian SU(2) Lattice Gauge Theories in Superconducting Circuits.
Mezzacapo, A; Rico, E; Sabín, C; Egusquiza, I L; Lamata, L; Solano, E
2015-12-11
We propose a digital quantum simulator of non-Abelian pure-gauge models with a superconducting circuit setup. Within the framework of quantum link models, we build a minimal instance of a pure SU(2) gauge theory, using triangular plaquettes involving geometric frustration. This realization is the least demanding, in terms of quantum simulation resources, of a non-Abelian gauge dynamics. We present two superconducting architectures that can host the quantum simulation, estimating the requirements needed to run possible experiments. The proposal establishes a path to the experimental simulation of non-Abelian physics with solid-state quantum platforms. PMID:26705616
Non-abelian gauge extensions for B-decay anomalies
NASA Astrophysics Data System (ADS)
Boucenna, Sofiane M.; Celis, Alejandro; Fuentes-Martín, Javier; Vicente, Avelino; Virto, Javier
2016-09-01
We study the generic features of minimal gauge extensions of the Standard Model in view of recent hints of lepton-flavor non-universality in semi-leptonic b → sℓ+ℓ- and b → cℓν decays. We classify the possible models according to the symmetry-breaking pattern and the source of flavor non-universality. We find that in viable models the SU (2) L factor is embedded non-trivially in the extended gauge group, and that gauge couplings should be universal, hinting to the presence of new degrees of freedom sourcing non-universality. Finally, we provide an explicit model that can explain the B-decay anomalies in a coherent way and confront it with the relevant phenomenological constraints.
Constraint Structure and Quantization of a Non-Abelian Gauge Theory by Means of Dirac Brackets
NASA Astrophysics Data System (ADS)
Bracken, Paul
An SO(3) non-Abelian gauge theory is introduced. The Hamiltonian density is determined and the constraint structure of the model is derived. The first-class constraints are obtained and gauge-fixing constraints are introduced into the model. Finally, using the constraints, the Dirac brackets can be determined and a canonical quantization is found using Dirac's procedure.
Electric-magnetic dualities in non-abelian and non-commutative gauge theories
NASA Astrophysics Data System (ADS)
Ho, Jun-Kai; Ma, Chen-Te
2016-08-01
Electric-magnetic dualities are equivalence between strong and weak coupling constants. A standard example is the exchange of electric and magnetic fields in an abelian gauge theory. We show three methods to perform electric-magnetic dualities in the case of the non-commutative U (1) gauge theory. The first method is to use covariant field strengths to be the electric and magnetic fields. We find an invariant form of an equation of motion after performing the electric-magnetic duality. The second method is to use the Seiberg-Witten map to rewrite the non-commutative U (1) gauge theory in terms of abelian field strength. The third method is to use the large Neveu Schwarz-Neveu Schwarz (NS-NS) background limit (non-commutativity parameter only has one degree of freedom) to consider the non-commutative U (1) gauge theory or D3-brane. In this limit, we introduce or dualize a new one-form gauge potential to get a D3-brane in a large Ramond-Ramond (R-R) background via field redefinition. We also use perturbation to study the equivalence between two D3-brane theories. Comparison of these methods in the non-commutative U (1) gauge theory gives different physical implications. The comparison reflects the differences between the non-abelian and non-commutative gauge theories in the electric-magnetic dualities. For a complete study, we also extend our studies to the simplest abelian and non-abelian p-form gauge theories, and a non-commutative theory with the non-abelian structure.
Controlling and probing non-abelian emergent gauge potentials in spinor Bose-Fermi mixtures
Phuc, Nguyen Thanh; Tatara, Gen; Kawaguchi, Yuki; Ueda, Masahito
2015-01-01
Gauge fields, typified by the electromagnetic field, often appear as emergent phenomena due to geometrical properties of a curved Hilbert subspace, and provide a key mechanism for understanding such exotic phenomena as the anomalous and topological Hall effects. Non-abelian gauge potentials serve as a source of non-singular magnetic monopoles. Here we show that unlike conventional solid materials, the non-abelianness of emergent gauge potentials in spinor Bose-Fermi atomic mixtures can be continuously varied by changing the relative particle-number densities of bosons and fermions. The non-abelian feature is captured by an explicit dependence of the measurable spin current density of fermions in the mixture on the variable coupling constant. Spinor mixtures also provide us with a method to coherently and spontaneously generate a pure spin current without relying on the spin Hall effect. Such a spin current is expected to have potential applications in the new generation of atomtronic devices. PMID:26330292
Abelian p-form (p = 1, 2, 3) gauge theories as the field theoretic models for the Hodge theory
NASA Astrophysics Data System (ADS)
Kumar, R.; Krishna, S.; Shukla, A.; Malik, R. P.
2014-09-01
Taking the simple examples of an Abelian 1-form gauge theory in two (1+1)-dimensions, a 2-form gauge theory in four (3+1)-dimensions and a 3-form gauge theory in six (5+1)-dimensions of space-time, we establish that such gauge theories respect, in addition to the gauge symmetry transformations that are generated by the first-class constraints of the theory, additional continuous symmetry transformations. We christen the latter symmetry transformations as the dual-gauge transformations. We generalize the above gauge and dual-gauge transformations to obtain the proper (anti-)BRST and (anti-)dual-BRST transformations for the Abelian 3-form gauge theory within the framework of BRST formalism. We concisely mention such symmetries for the 2D free Abelian 1-form and 4D free Abelian 2-form gauge theories and briefly discuss their topological aspects in our present endeavor. We conjecture that any arbitrary Abelian p-form gauge theory would respect the above cited additional symmetry in D = 2p(p = 1, 2, 3, …) dimensions of space-time. By exploiting the above inputs, we establish that the Abelian 3-form gauge theory, in six (5+1)-dimensions of space-time, is a perfect model for the Hodge theory whose discrete and continuous symmetry transformations provide the physical realizations of all aspects of the de Rham cohomological operators of differential geometry. As far as the physical utility of the above nilpotent symmetries is concerned, we demonstrate that the 2D Abelian 1-form gauge theory is a perfect model of a new class of topological theory and 4D Abelian 2-form as well as 6D Abelian 3-form gauge theories are the field theoretic models for the quasi-topological field theory.
Dyonic String-Like Solution in a Non-Abelian Gauge Theory with Two Potentials
NASA Astrophysics Data System (ADS)
Tripathi, Buddhi Vallabh; Nandan, Hemwati; Purohit, K. D.
2016-04-01
Axially symmetric dyon solutions of a non-Abelian gauge theory model with two potentials are sought. While seeking axially symmetric (flux tube like solutions) for the model, we stumbled upon an exact solution which represents an infinite string-like dyonic configuration with cylindrical symmetry.
Experimental evidence for non-Abelian gauge potentials in twisted graphene bilayers
NASA Astrophysics Data System (ADS)
Yin, Long-Jing; Qiao, Jia-Bin; Zuo, Wei-Jie; Li, Wen-Tian; He, Lin
2015-08-01
Non-Abelian gauge potentials are quite relevant in subatomic physics, but they are relatively rare in a condensed matter context. Here we report the experimental evidence for non-Abelian gauge potentials in twisted graphene bilayers by scanning tunneling microscopy and spectroscopy. At a magic twisted angle, θ ≈(1.11±0.05 ) ∘ , a pronounced sharp peak, which arises from the nondispersive flat bands at the charge neutrality point, is observed in the tunneling density of states due to the action of the non-Abelian gauge fields. Moreover, we observe confined electronic states in the twisted bilayer, as manifested by regularly spaced tunneling peaks with energy spacing δ E ≈vF/D ≈70 meV (here vF is the Fermi velocity of graphene and D is the period of the moiré patterns). This indicates that the non-Abelian gauge potentials in twisted graphene bilayers confine low-energy electrons into a triangular array of quantum dots following the modulation of the moiré patterns. Our results also directly demonstrate that the Fermi velocity in twisted bilayers can be tuned from about 106m /s to zero by simply reducing the twisted angle of about 2∘.
Origin of Abelian gauge symmetries in heterotic/F-theory duality
NASA Astrophysics Data System (ADS)
Cvetič, Mirjam; Grassi, Antonella; Klevers, Denis; Poretschkin, Maximilian; Song, Peng
2016-04-01
We study aspects of heterotic/F-theory duality for compactifications with Abelian gauge symmetries. We consider F-theory on general Calabi-Yau manifolds with a rank one Mordell-Weil group of rational sections. By rigorously performing the stable degeneration limit in a class of toric models, we derive both the Calabi-Yau geometry as well as the spectral cover describing the vector bundle in the heterotic dual theory. We carefully investigate the spectral cover employing the group law on the elliptic curve in the heterotic theory. We find in explicit examples that there are three different classes of heterotic duals that have U(1) factors in their low energy effective theories: split spectral covers describing bundles with S(U( m) × U(1)) structure group, spectral covers containing torsional sections that seem to give rise to bundles with SU( m) × Z_k structure group and bundles with purely non-Abelian structure groups having a centralizer in E8 containing a U(1) factor. In the former two cases, it is required that the elliptic fibration on the heterotic side has a non-trivial Mordell-Weil group. While the number of geometrically massless U(1)'s is determined entirely by geometry on the F-theory side, on the heterotic side the correct number of U(1)'s is found by taking into account a Stückelberg mechanism in the lower-dimensional effective theory. In geometry, this corresponds to the condition that sections in the two half K3 surfaces that arise in the stable degeneration limit of F-theory can be glued together globally.
The non-Abelian gauge theory of matrix big bangs
NASA Astrophysics Data System (ADS)
O'Loughlin, Martin; Seri, Lorenzo
2010-07-01
We study at the classical and quantum mechanical level the time-dependent Yang-Mills theory that one obtains via the generalisation of discrete light-cone quantization to singular homogeneous plane waves. The non-Abelian nature of this theory is known to be important for physics near the singularity, at least as far as the number of degrees of freedom is concerned. We will show that the quartic interaction is always subleading as one approaches the singularity and that close enough to t = 0 the evolution is driven by the diverging tachyonic mass term. The evolution towards asymptotically flat space-time also reveals some surprising features.
Particle coupled to a heat bath in non-Abelian gauge potentials
NASA Astrophysics Data System (ADS)
Guingarey, Issoufou; Avossevou, Gabriel Y. H.
2015-12-01
We derive the quantum Langevin equation (QLE) for a harmonically single trapped cold atom subjected to artificial non-Abelian gauge potentials and linearly coupled to a heat bath. The independent-oscillator (IO) and the momentum-momenta coupling models are studied. In each case, the non-Abelian effect on the QLE is pointed out for a U(2 ) gauge transformation. For the IO model, only the generalized Lorentz force is modified by the appearance of an additive term. For the momentum-momenta coupling model, the generalized Lorentz force as well as the friction force are subjected to modifications. The dependence of the system on the magnetic field is explicit even if the gauge potential is uniform in space.
Chaos, scaling and existence of a continuum limit in classical non-Abelian lattice gauge theory
Nielsen, H.B.; Rugh, H.H.; Rugh, S.E.
1996-12-31
We discuss space-time chaos and scaling properties for classical non-Abelian gauge fields discretized on a spatial lattice. We emphasize that there is a {open_quote}no go{close_quotes} for simulating the original continuum classical gauge fields over a long time span since there is a never ending dynamical cascading towards the ultraviolet. We note that the temporal chaotic properties of the original continuum gauge fields and the lattice gauge system have entirely different scaling properties thereby emphasizing that they are entirely different dynamical systems which have only very little in common. Considered as a statistical system in its own right the lattice gauge system in a situation where it has reached equilibrium comes closest to what could be termed a {open_quotes}continuum limit{close_quotes} in the limit of very small energies (weak non-linearities). We discuss the lattice system both in the limit for small energies and in the limit of high energies where we show that there is a saturation of the temporal chaos as a pure lattice artifact. Our discussion focuses not only on the temporal correlations but to a large extent also on the spatial correlations in the lattice system. We argue that various conclusions of physics have been based on monitoring the non-Abelian lattice system in regimes where the fields are correlated over few lattice units only. This is further evidenced by comparison with results for Abelian lattice gauge theory. How the real time simulations of the classical lattice gauge theory may reach contact with the real time evolution of (semi-classical aspects of) the quantum gauge theory (e.g. Q.C.D.) is left an important question to be further examined.
Stability of domain walls coupled to Abelian gauge fields
George, Damien P.; Volkas, Raymond R.
2005-11-15
Rozowsky, Volkas and Wali [J. Rozowsky, R. Volkas, and K. Wali, Phys. Lett. B 580, 249 (2004).] recently found interesting numerical solutions to the field equations for a gauged U(1)xU(1) scalar field model. Their solutions describe a reflection-symmetric domain wall with scalar fields and coupled gauge configurations that interpolate between constant magnetic fields on one side of the wall and exponentially decaying ones on the other side. This corresponds physically to an infinite sheet of supercurrent confined to the domain wall with a linearly rising gauge potential on one side and Meissner suppression on the other. While it was shown that these static solutions satisfied the field equations, their stability was left unresolved. In this paper, we analyze the normal modes of perturbations of the static solutions to demonstrate their perturbative stability.
a Note on the - Invariant Lagrangian Densities for the Free Abelian 2-FORM Gauge Theory
NASA Astrophysics Data System (ADS)
Gupta, Saurabh; Malik, R. P.
We show that the previously known off-shell nilpotent (s(a)b2 = 0) and absolutely anticommuting (sb sab + sab sb = 0) Becchi-Rouet-Stora-Tyutin (BRST) transformations (sb) and anti-BRST transformations (sab) are the symmetry transformations of the appropriate Lagrangian densities of a four (3+1)-dimensional (4D) free Abelian 2-form gauge theory which do not explicitly incorporate a very specific constrained field condition through a Lagrange multiplier 4D vector field. The above condition, which is the analogue of the Curci-Ferrari restriction of the non-Abelian 1-form gauge theory, emerges from the Euler-Lagrange equations of motion of our present theory and ensures the absolute anticommutativity of the transformations s(a)b. Thus, the coupled Lagrangian densities, proposed in our present investigation, are aesthetically more appealing and more economical.
Topological phase transitions on a triangular optical lattice with non-Abelian gauge fields
NASA Astrophysics Data System (ADS)
Iskin, M.
2016-03-01
We study the mean-field BCS-BEC evolution of a uniform Fermi gas on a single-band triangular lattice and construct its ground-state phase diagrams, showing a wealth of topological quantum phase transitions between gapped and gapless superfluids that are induced by the interplay of an out-of-plane Zeeman field and a generic non-Abelian gauge field.
Entanglement of Vortex Lattices for Ultracold Bose Gases in a Non-Abelian Gauge Potential
NASA Astrophysics Data System (ADS)
Cheng, Szu-Cheng; Jiang, T. F.; Jheng, Shih-Da; Atomic; Molecular Physics Team; Atomic; Molecular Physics Team
We develop a theory, referred to as the von Neumann lattice in a higher Landau level, for vortex lattices labelled by an integral number of flux quantums per unit cell in a higher Landau level. Using this lattice theory, we study the vortex lattice states of a pseudospin-1/2 ultracold Bose gas with contact interactions in a non-Abelian gauge potential. In addition to a uniform magnetic field, the Bose gas is also subjected to a non-Abelian gauge field, which creates an effect of the spin-orbit coupling to lift the spin degeneracy of the Landau levels. Because of interactions from the spin-orbit coupling, there are new degenerate points of the single particle spectrum due to the crossings of two Landau levels at certain coupling strengths. We show that interactions from the spin-orbit coupling force the nature and structure of the vortex lattice changing dramatically if the strength of the non-Abelian gauge field is increasing. We also find that the ground state of the vortex lattice at a degenerate point exhibits strong correlation and entanglement involving vortex lattices from different Landau levels. This entangled state builds the connection between two phases of vortex lattices during the first order phase transition of the adiabatic evolution.
Pauli-Villars Regularization of Non-Abelian Gauge Theories
NASA Astrophysics Data System (ADS)
Hiller, J. R.
2016-04-01
As an extension of earlier work on QED, we construct a BRST-invariant Lagrangian for SU(N) Yang-Mills theory with fundamental matter, regulated by the inclusion of massive Pauli-Villars (PV) gluons and PV quarks. The underlying gauge symmetry for massless PV gluons is generalized to accommodate the PV-index-changing currents that are required by the regularization. Auxiliary adjoint scalars are used, in a mechanism due to Stueckelberg, to attribute mass to the PV gluons and the PV quarks. The addition of Faddeev-Popov ghosts then establishes a residual BRST symmetry. Although there are drawbacks to the approach, in particular the computational load of a large number of PV fields and a nonlocal interaction of the ghost fields, this formulation could provide a foundation for renormalizable nonperturbative solutions of light-front QCD in an arbitrary covariant gauge.
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.
BCS-BEC crossover induced by a synthetic non-Abelian gauge field
NASA Astrophysics Data System (ADS)
Vyasanakere, Jayantha P.; Zhang, Shizhong; Shenoy, Vijay B.
2011-07-01
We investigate the ground state of interacting spin-(1)/(2) fermions in three dimensions at a finite density (ρ˜kF3) in the presence of a uniform non-Abelian gauge field. The gauge-field configuration (GFC) described by a vector λ≡(λx,λy,λz), whose magnitude λ determines the gauge coupling strength, generates a generalized Rashba spin-orbit interaction. For a weak attractive interaction in the singlet channel described by a small negative scattering length (kF|as|≲1), the ground state in the absence of the gauge field (λ=0) is a BCS (Bardeen-Cooper-Schrieffer) superfluid with large overlapping pairs. With increasing gauge-coupling strength, a non-Abelian gauge field engenders a crossover of this BCS ground state to a BEC (Bose-Einstein condensate) of bosons even with a weak attractive interaction that fails to produce a two-body bound state in free vacuum (λ=0). For large gauge couplings (λ/kF≫1), the BEC attained is a condensate of bosons whose properties are solely determined by the Rashba gauge field (and not by the scattering length so long as it is nonzero)—we call these bosons “rashbons.” In the absence of interactions (as=0-), the shape of the Fermi surface of the system undergoes a topological transition at a critical gauge coupling λT. For high-symmetry GFCs we show that the crossover from the BCS superfluid to the rashbon BEC occurs in the regime of λ near λT. In the context of cold atomic systems, these results make an interesting suggestion of obtaining BCS-BEC crossover through a route other than tuning the interaction between the fermions.
BCS-BEC crossover induced by a synthetic non-Abelian gauge field
Vyasanakere, Jayantha P.; Shenoy, Vijay B.; Zhang Shizhong
2011-07-01
We investigate the ground state of interacting spin-(1/2) fermions in three dimensions at a finite density ({rho}{approx}k{sub F}{sup 3}) in the presence of a uniform non-Abelian gauge field. The gauge-field configuration (GFC) described by a vector {lambda}{identical_to}({lambda}{sub x},{lambda}{sub y},{lambda}{sub z}), whose magnitude {lambda} determines the gauge coupling strength, generates a generalized Rashba spin-orbit interaction. For a weak attractive interaction in the singlet channel described by a small negative scattering length (k{sub F}|a{sub s}| < or approx. 1), the ground state in the absence of the gauge field ({lambda}=0) is a BCS (Bardeen-Cooper-Schrieffer) superfluid with large overlapping pairs. With increasing gauge-coupling strength, a non-Abelian gauge field engenders a crossover of this BCS ground state to a BEC (Bose-Einstein condensate) of bosons even with a weak attractive interaction that fails to produce a two-body bound state in free vacuum ({lambda}=0). For large gauge couplings ({lambda}/k{sub F}>>1), the BEC attained is a condensate of bosons whose properties are solely determined by the Rashba gauge field (and not by the scattering length so long as it is nonzero)--we call these bosons ''rashbons.'' In the absence of interactions (a{sub s}=0{sup -}), the shape of the Fermi surface of the system undergoes a topological transition at a critical gauge coupling {lambda}{sub T}. For high-symmetry GFCs we show that the crossover from the BCS superfluid to the rashbon BEC occurs in the regime of {lambda} near {lambda}{sub T}. In the context of cold atomic systems, these results make an interesting suggestion of obtaining BCS-BEC crossover through a route other than tuning the interaction between the fermions.
Dynamical breakdown of Abelian gauge chiral symmetry by strong Yukawa interactions
Benes, Petr; Brauner, Tomas; Hosek, Jiri
2007-03-01
We consider a model with anomaly-free Abelian gauge axial-vector symmetry, which is intended to mimic the standard electroweak gauge chiral SU(2){sub L}xU(1){sub Y} theory. Within this model we demonstrate: (1) Strong Yukawa interactions between massless fermion fields and a massive scalar field carrying the axial charge generate dynamically the fermion and boson proper self-energies, which are ultraviolet-finite and chirally noninvariant. (2) Solutions of the underlying Schwinger-Dyson equations found numerically exhibit a huge amplification of the fermion mass ratios as a response to mild changes of the ratios of the Yukawa couplings. (3) The 'would-be' Nambu-Goldstone boson is a composite of both the fermion and scalar fields, and it gives rise to the mass of the axial-vector gauge boson. (4) Spontaneous breakdown of the gauge symmetry further manifests by mass splitting of the complex scalar and by new symmetry-breaking vertices, generated at one loop. In particular, we work out in detail the cubic vertex of the Abelian gauge boson.
Non-Abelian black holes in D=5 maximal gauged supergravity
Cvetic, M.; Lue, H.; Pope, C. N.
2010-02-15
We investigate static non-Abelian black hole solutions of anti-de Sitter (AdS) Einstein-Yang-Mills-dilaton gravity, which is obtained as a consistent truncation of five-dimensional maximal gauged supergravity. If the dilaton is (consistently) set to zero, the remaining equations of motion, with a spherically-symmetric ansatz, may be derived from a superpotential. The associated first-order equations admit an explicit solution supported by a non-Abelian SU(2) gauge potential, which has a logarithmically growing mass term. In an extremal limit the horizon geometry becomes AdS{sub 2}xS{sup 3}. If the dilaton is also excited, the equations of motion cannot easily be solved explicitly, but we obtain the asymptotic form of the more general non-Abelian black holes in this case. An alternative consistent truncation, in which the Yang-Mills fields are set to zero, also admits a description in terms of a superpotential. This allows us to construct explicit wormhole solutions (neutral spherically-symmetric domain walls). These solutions may be generalized to dimensions other than five.
Simulation of non-Abelian lattice gauge fields with a single-component gas
NASA Astrophysics Data System (ADS)
Kosior, Arkadiusz; Sacha, Krzysztof
2014-07-01
We show that non-Abelian lattice gauge fields can be simulated with a single-component ultra-cold atomic gas in an optical-lattice potential. An optical lattice can be viewed as a Bravais lattice with a N-point basis. An atom located at different points of the basis can be considered as a particle in different internal states. The appropriate engineering of tunneling amplitudes of atoms in an optical lattice allows one to realize U(N) gauge potentials and control a mass of particles that experience such non-Abelian gauge fields. We provide and analyze a concrete example of an optical-lattice configuration that allows for simulation of a static U(2) gauge model with a constant Wilson loop and an adjustable mass of particles. In particular, we observe that the non-zero mass creates large conductive gaps in the energy spectrum, which could be important in the experimental detection of the transverse Hall conductivity.
Quantum phase transition of ultracold bosons in the presence of a non-Abelian synthetic gauge field
Grass, T.; Saha, K.; Sengupta, K.; Lewenstein, M.
2011-11-15
We study the Mott phases and the superfluid-insulator transition of two-component ultracold bosons on a square optical lattice in the presence of a non-Abelian synthetic gauge field, which renders a SU(2)-hopping matrix for the bosons. Using a resummed hopping expansion, we calculate the excitation spectra in the Mott insulating phases and demonstrate that the superfluid-insulator phase boundary displays a nonmonotonic dependence on the gauge-field strength. We also compute the momentum distribution of the bosons in the presence of the non-Abelian field and show that they develop peaks at nonzero momenta as the superfluid-insulator transition point is approached from the Mott side. Finally, we study the superfluid phases near the transition and discuss the induced spatial pattern of the superfluid density due to the presence of the non-Abelian gauge potential.
Three phases in the three-dimensional Abelian-Higgs model with nonlocal gauge interactions
Takashima, Shunsuke; Ichinose, Ikuo; Matsui, Tetsuo; Sakakibara, Kazuhiko
2006-08-15
We study the phase structure of the three-dimensional (3D) nonlocal compact U(1) lattice gauge theory coupled with a Higgs field by Monte Carlo simulations. The nonlocal interactions among gauge variables are along the temporal direction and mimic the effect of local coupling to massless particles. In contrast to the 3D local Abelian-Higgs model having only the confinement phase, the present model exhibits the confinement, Higgs, and Coulomb phases separated by three second-order transition lines emanating from a triple point. This result is relevant not only to the 3D massless QED coupled with a Higgs field but also to electron fractionalization phenomena in strongly correlated electron systems like the high-T{sub c} superconductors and the fractional quantum Hall effect.
Abelian gauge symmetries and proton decay in global F-theory GUTs
Grimm, Thomas W.; Weigand, Timo
2010-10-15
The existence of Abelian gauge symmetries in four-dimensional F-theory compactifications depends on the global geometry of the internal Calabi-Yau four-fold and has important phenomenological consequences. We study conceptual and phenomenological aspects of such U(1) symmetries along the Coulomb and the Higgs branch. As one application we examine Abelian gauge factors arising after a certain global restriction of the Tate model that goes beyond a local spectral cover analysis. In SU(5) grand unified theory (GUT) models this mechanism enforces a global U(1){sub X} symmetry that prevents dimension-4 proton decay and allows for an identification of candidate right-handed neutrinos. We invoke a detailed account of the singularities of Calabi-Yau four-folds and their mirror duals starting from an underlying E{sub 8} and E{sub 7}xU(1) enhanced Tate model. The global resolutions and deformations of these singularities can be used as the appropriate framework to analyze F-theory GUT models.
On spectral synthesis on zero-dimensional Abelian groups
Platonov, S S
2013-09-30
Let G be a zero-dimensional locally compact Abelian group all of whose elements are compact, and let C(G) be the space of all complex-valued continuous functions on G. A closed linear subspace H⊆C(G) is said to be an invariant subspace if it is invariant with respect to the translations τ{sub y}:f(x)↦f(x+y), y∈G. In the paper, it is proved that any invariant subspace H admits spectral synthesis, that is, H coincides with the closed linear span of the characters of G belonging to H. Bibliography: 25 titles.
On spectral synthesis on element-wise compact Abelian groups
NASA Astrophysics Data System (ADS)
Platonov, S. S.
2015-08-01
Let G be an arbitrary locally compact Abelian group and let C(G) be the space of all continuous complex-valued functions on G. A closed linear subspace \\mathscr H\\subseteq C(G) is referred to as an invariant subspace if it is invariant with respect to the shifts τ_y\\colon f(x)\\mapsto f(xy), y\\in G. By definition, an invariant subspace \\mathscr H\\subseteq C(G) admits strict spectral synthesis if \\mathscr H coincides with the closure in C(G) of the linear span of all characters of G belonging to \\mathscr H. We say that strict spectral synthesis holds in the space C(G) on G if every invariant subspace \\mathscr H\\subseteq C(G) admits strict spectral synthesis. An element x of a topological group G is said to be compact if x is contained in some compact subgroup of G. A group G is said to be element-wise compact if all elements of G are compact. The main result of the paper is the proof of the fact that strict spectral synthesis holds in C(G) for a locally compact Abelian group G if and only if G is element-wise compact. Bibliography: 14 titles.
NASA Astrophysics Data System (ADS)
Goldman, N.; Gerbier, F.; Lewenstein, M.
2013-07-01
We describe a scheme to engineer non-Abelian gauge potentials on a square optical lattice using laser-induced transitions. We emphasize the case of two-electron atoms, where the electronic ground state g is laser-coupled to a metastable state e within a state-dependent optical lattice. In this scheme, the alternating pattern of lattice sites hosting g and e states depicts a chequerboard structure, allowing for laser-assisted tunnelling along both spatial directions. In this configuration, the nuclear spin of the atoms can be viewed as a ‘flavour’ quantum number undergoing non-Abelian tunnelling along nearest-neighbour links. We show that this technique can be useful to simulate the equivalent of the Haldane quantum Hall model using cold atoms trapped in square optical lattices, offering an interesting route to realize Chern insulators. The emblematic Haldane model is particularly suited to investigate the physics of topological insulators, but requires, in its original form, complex hopping terms beyond nearest-neighbouring sites. In general, this drawback inhibits a direct realization with cold atoms, using standard laser-induced tunnelling techniques. We demonstrate that a simple mapping allows us to express this model in terms of matrix hopping operators that are defined on a standard square lattice. This mapping is investigated for two models that lead to anomalous quantum Hall phases. We discuss the practical implementation of such models, exploiting laser-induced tunnelling methods applied to the chequerboard optical lattice.
Gauge-invariant implementation of the Abelian-Higgs model on optical lattices
NASA Astrophysics Data System (ADS)
Bazavov, A.; Meurice, Y.; Tsai, S.-W.; Unmuth-Yockey, J.; Zhang, Jin
2015-10-01
We present a gauge-invariant effective action for the Abelian-Higgs model (scalar electrodynamics) with a chemical potential μ on a (1 +1 )-dimensional lattice. This formulation provides an expansion in the hopping parameter κ which we test with Monte Carlo simulations for a broad range of the inverse gauge coupling βp l=1 /g2 and small values of the scalar self-coupling λ . In the opposite limit of infinitely large λ , the partition function can be written as a traced product of local tensors which allows us to write exact blocking formulas. Gauss's law is automatically satisfied and the introduction of μ has consequences only if we have an external electric field, g2=0 or an explicit gauge symmetry breaking. The time-continuum limit of the blocked transfer matrix can be obtained numerically and, for g2=0 and a spin-1 truncation, the small volume energy spectrum is identical to the low energy spectrum of a two-species Bose-Hubbard model in the limit of large on-site repulsion. We extend this procedure for finite βp l and derive a spin-1 approximation of the Hamiltonian. It involves new terms corresponding to transitions among the two species in the Bose-Hubbard model. We propose an optical lattice implementation involving a ladder structure.
Dynamical symmetry breaking, gauge fields, and stability in four-Fermi, non-abelian interactions
Portney, M.N.
1983-01-01
The Nambu model of dynamical breaking of global symmetry is extended to the case of non-abelian SU(N) models. The possible patterns of symmetry breaking are investigated, and the masses of the composite spinless particles are found. Corresponding to each broken generator, this composite is the massless Goldstone boson. When the global symmetries are made local by the addition of gauge fields, the composite pseudoscalar Goldstone bosons disappear and the axial gauge fields become massive. This is analogous to the Higgs mechanism, but without the introduction of fundamental scalar fields. The composite scalar Goldstone bosons remain in the theory, and the vector gauge fields are still massless. This is in agreement with the charge conjugation argument. The stability of the possible solutions is discussed using several criteria. It is concluded that in theories with zero bare mass, if a nontrivial solution exists, the completely symmetric massive solution is realized. If the bare mass is symmetric and non-zero, asymmetric solutions may be found, with corresponding scalar Goldstone composites. These violate the persistent mass condition of Preskill and Weinberg.
NASA Astrophysics Data System (ADS)
Gupta, S.; Kumar, R.; Malik, R. P.
2010-11-01
We demonstrate the existence of the nilpotent and absolutely anticommuting Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for the four (3+1)-dimensional (4D) topologically massive Abelian U(1) gauge theory that is described by the coupled Lagrangian densities (which incorporate the celebrated ( B∧ F) term). The absolute anticommutativity of the (anti-) BRST symmetry transformations is ensured by the existence of a Curci-Ferrari type restriction that emerges from the superfield formalism as well as from the equations of motion which are derived from the above coupled Lagrangian densities. We show the invariance of the action from the point of view of the symmetry considerations as well as superfield formulation. We discuss, furthermore, the topological term within the framework of superfield formalism and provide the geometrical meaning of its invariance under the (anti-)BRST symmetry transformations.
NASA Astrophysics Data System (ADS)
Wang, Juven C.; Wen, Xiao-Gang
2015-01-01
String and particle braiding statistics are examined in a class of topological orders described by discrete gauge theories with a gauge group G and a 4-cocycle twist ω4 of G 's cohomology group H4(G ,R /Z ) in three-dimensional space and one-dimensional time (3 +1 D ) . We establish the topological spin and the spin-statistics relation for the closed strings and their multistring braiding statistics. The 3 +1 D twisted gauge theory can be characterized by a representation of a modular transformation group, SL (3 ,Z ) . We express the SL (3 ,Z ) generators Sx y z and Tx y in terms of the gauge group G and the 4-cocycle ω4. As we compactify one of the spatial directions z into a compact circle with a gauge flux b inserted, we can use the generators Sx y and Tx y of an SL (2 ,Z ) subgroup to study the dimensional reduction of the 3D topological order C3 D to a direct sum of degenerate states of 2D topological orders Cb2 D in different flux b sectors: C3 D=⊕bCb2 D . The 2D topological orders Cb2 D are described by 2D gauge theories of the group G twisted by the 3-cocycle ω3 (b ), dimensionally reduced from the 4-cocycle ω4. We show that the SL (2 ,Z ) generators, Sx y and Tx y, fully encode a particular type of three-string braiding statistics with a pattern that is the connected sum of two Hopf links. With certain 4-cocycle twists, we discover that, by threading a third string through two-string unlink into a three-string Hopf-link configuration, Abelian two-string braiding statistics is promoted to non-Abelian three-string braiding statistics.
Unitary Representations of Gauge Groups
NASA Astrophysics Data System (ADS)
Huerfano, Ruth Stella
I generalize to the case of gauge groups over non-trivial principal bundles representations that I. M. Gelfand, M. I. Graev and A. M. Versik constructed for current groups. The gauge group of the principal G-bundle P over M, (G a Lie group with an euclidean structure, M a compact, connected and oriented manifold), as the smooth sections of the associated group bundle is presented and studied in chapter I. Chapter II describes the symmetric algebra associated to a Hilbert space, its Hilbert structure, a convenient exponential and a total set that later play a key role in the construction of the representation. Chapter III is concerned with the calculus needed to make the space of Lie algebra valued 1-forms a Gaussian L^2-space. This is accomplished by studying general projective systems of finitely measurable spaces and the corresponding systems of sigma -additive measures, all of these leading to the description of a promeasure, a concept modeled after Bourbaki and classical measure theory. In the case of a locally convex vector space E, the corresponding Fourier transform, family of characters and the existence of a promeasure for every quadratic form on E^' are established, so the Gaussian L^2-space associated to a real Hilbert space is constructed. Chapter III finishes by exhibiting the explicit Hilbert space isomorphism between the Gaussian L ^2-space associated to a real Hilbert space and the complexification of its symmetric algebra. In chapter IV taking as a Hilbert space H the L^2-space of the Lie algebra valued 1-forms on P, the gauge group acts on the motion group of H defining in an straight forward fashion the representation desired.
Localizing gauge fields on a topological Abelian string and the Coulomb law
Torrealba S, Rafael S.
2010-07-15
The confinement of electromagnetic field is studied in axial symmetrical, warped, six-dimensional brane world, using a recently proposed topological Abelian string-vortex solution as background. It was found, that the massless gauge field fluctuations follow four-dimensional Maxwell equations in the Lorenz gauge. The massless zero mode is localized when the thickness of the string vortex is less than 5{beta}/4{pi}e{sup 2}v{sup 2} and there are no other localized massless modes. There is also an infinite of nonlocalized massive Fourier modes, that follow four-dimensional Proca equations with a continuous spectrum. To compute the corrections to the Coulomb potential, a radial cutoff was introduced, in order to achieve a discrete mass spectrum. As a main result, a (R{sub o}/{beta}R{sup 2}) correction was found for the four-dimensional effective Coulomb law; the result is in correspondence with the observed behavior of the Coulomb potential at today's measurable distances.
Strong-weak coupling duality in non-abelian gauge theories
NASA Astrophysics Data System (ADS)
Ferrari, Frank
1997-05-01
This is a general introduction to electric-magnetic duality in non-abelian gauge theories. In chapter I, I review the general ideas which led in the late 70s to the idea of electric/magnetic duality in quantum field theory. In chapters II and III, I focus mainly on N=2 supersymmetric theories. I present the lagrangians and explain in more or less detail the non-renormalization theorems, rigid special geometry, supersymmetric instanton calculus, charge fractionization, the semiclassical theory of monopoles, duality in Maxwell theory and the famous Seiberg-Witten solution. I discuss various physical applications, as electric charge confinement, chiral symmetry breaking or non-trivial superconformal theories in four dimensions. In Section II.3 new material is presented, related to the computation of the eta invariant of certain Dirac operators coupled minimally to non-trivial monopole field configurations. I explain how these invariants can be obtained exactly by a one-loop calculation in a suitable N=2 supersymmetric gauge theory. This is an unexpected application of the holomorphy properties of N=2 supersymmetry, and constitutes a tremendous simplification of the usual computation. An expanded version of these new results will be published soon.
Gluon propagators in maximally Abelian gauge in SU(3) lattice QCD
NASA Astrophysics Data System (ADS)
Gongyo, Shinya; Suganuma, Hideo
2013-04-01
In SU(3) lattice QCD, we study diagonal and off-diagonal gluon propagators in the maximally Abelian gauge with U(1)3×U(1)8 Landau gauge fixing. These propagators are studied both in the coordinate space and in the momentum space. The Monte Carlo simulation is performed on 164 at β=6.0 and 324 at β=5.8 and 6.0 at the quenched level. In the four-dimensional Euclidean space-time, the effective mass of diagonal gluons is estimated as Mdiag≃0.3GeV and that of off-diagonal gluons as Moff≃1GeV in the region of r=0.4-1.0fm. In the momentum space, the effective mass of diagonal gluons is estimated as Mdiag≃0.3GeV and that of off-diagonal gluons as Moff≃1GeV in the region of p<1.1GeV. The off-diagonal gluon propagator is relatively suppressed in the infrared region and seems to be finite at zero momentum, while the diagonal gluon propagator is enhanced. Furthermore, we also study the functional form of these propagators in momentum space. These propagators are well fitted by Z/(p2+m2)ν with fit parameters, Z, m, and ν in the region of p<3.0GeV. From the fit results and lattice calculations, all of the spectral functions of diagonal and off-diagonal gluons would have negative regions.
Quiver gauge theory of non-Abelian vortices and noncommutative instantons in higher dimensions
Popov, Alexander D.; Szabo, Richard J.
2006-01-15
We construct explicit Bogomolnyi, Prasad, Sommerfeld (BPS) and non-BPS solutions of the Yang-Mills equations on the noncommutative space R{sub {theta}}{sup 2n}xS{sup 2} which have manifest spherical symmetry. Using SU(2)-equivariant dimensional reduction techniques, we show that the solutions imply an equivalence between instantons on R{sub {theta}}{sup 2n}xS{sup 2} and non-Abelian vortices on R{sub {theta}}{sup 2n}, which can be interpreted as a blowing-up of a chain of D0-branes on R{sub {theta}}{sup 2n} into a chain of spherical D2-branes on R{sub {theta}}{sup 2n}xS{sup 2}. The low-energy dynamics of these configurations is described by a quiver gauge theory which can be formulated in terms of new geometrical objects generalizing superconnections. This formalism enables the explicit assignment of D0-brane charges in equivariant K-theory to the instanton solutions.
Bound states of two spin-(1/2) fermions in a synthetic non-Abelian gauge field
Vyasanakere, Jayantha P.; Shenoy, Vijay B.
2011-03-01
We study the bound states of two spin-(1/2) fermions interacting via a contact attraction (characterized by a scattering length) in the singlet channel in three-dimensional space in presence of a uniform non-Abelian gauge field. The configuration of the gauge field that generates a Rashba-type spin-orbit interaction is described by three coupling parameters ({lambda}{sub x},{lambda}{sub y},{lambda}{sub z}). For a generic gauge field configuration, the critical scattering length required for the formation of a bound state is negative, i.e., shifts to the ''BCS side'' of the resonance. Interestingly, we find that there are special high-symmetry configurations (e.g., {lambda}{sub x}={lambda}{sub y}={lambda}{sub z}) for which there is a two-body bound state for anyscattering length however small and negative. Remarkably, the bound-state wave functions obtained for such configurations have nematic spin structure similar to those found in liquid {sup 3}He. Our results show that the BCS-BEC (Bose-Einstein condensation) crossover is drastically affected by the presence of a non-Abelian gauge field. We discuss possible experimental signatures of our findings both at high and low temperatures.
Abelian gauge extension of the standard model: Dark matter and radiative neutrino mass
NASA Astrophysics Data System (ADS)
Borah, Debasish; Adhikari, Rathin
2012-05-01
We study a simple extension of the standard model where the gauge group is extended by an additional U(1)X gauge symmetry. Neutrino mass arises both at tree level as well as radiatively by the anomaly-free addition of one singlet fermion NR and two triplet fermions Σ1R, Σ2R with suitable Higgs scalars. The spontaneous gauge symmetry breaking is achieved in a way that results in a residual Z2 symmetry and hence provides a stable cold dark matter candidate. We study the possible dark matter candidates in this model by incorporating the constraints from cosmology as well as direct detection experiments. We discuss both low- and high-mass (from GeV to the TeV scale) regimes of fermionic and scalar dark matter candidates in the model. We show that scalar dark matter relic density, although not significantly affected by the presence or absence of annihilation into U(1)X gauge boson pairs, is however affected by choice of U(1)X gauge charges. We discuss the neutrino mass phenomenology and its compatibility with the allowed dark matter mass ranges and we also comment on the implications of the model on Higgs signatures at colliders including those related to the fourth fermion generation.
Viennot, David
2010-10-15
We show that the holonomy of a connection defined on a principal composite bundle is related by a non-Abelian Stokes theorem to the composition of the holonomies associated with the connections of the component bundles of the composite. We apply this formalism to describe the non-Abelian geometric phase (when the geometric phase generator does not commute with the dynamical phase generator). We find then an assumption to obtain a new kind of separation between the dynamical and the geometric phases. We also apply this formalism to the gauge theory of gravity in the presence of a Dirac spinor field in order to decompose the holonomy of the Lorentz connection into holonomies of the linear connection and of the Cartan connection.
Pertermann, D.; Ranft, J.
1986-09-15
We introduce a simplicial pseudorandom version of lattice gauge theory. In this formulation it is possible to interpolate continuously between a regular simplicial lattice and a pseudorandom lattice. Using this method we study a simple three-dimensional Abelian lattice gauge theory. Calculating average plaquette expectation values, we find an extremum of the action for our regular simplicial lattice. Such a behavior was found in analytical studies in one and two dimensions.
NASA Astrophysics Data System (ADS)
Liu, YiMin; Liu, RongWan
2014-12-01
A potentially practical scheme is proposed to realize optical quantum simulation of artificial Abelian gauge field in a scalable architecture consisting of cold atomic ensembles with optical cavities. In the present model, the collective excitations of cold atomic ensembles can be converted to the bosonic modes within the low-excitation limit, where the structure of two-dimension (2D) square plaquette enables the polaritons to move like a charged particle subjected to an external magnetic field. We find that the energy spectrum of this hybrid system exhibits a shape of Hofstadter buttery. Our work provides a different perspective to the quantum simulation of condensed matter and many-body physics in the context of cavity quantum electrodynamics. The experimental feasibility are justified using the existing techniques.
NASA Astrophysics Data System (ADS)
Vyasanakere, Jayanth P.; Shenoy, Vijay B.
2013-03-01
A non-Abelian gauge field that induces a spin-orbit coupling on the motion of fermions engenders a BCS-BEC crossover even for weakly attracting fermions. The transition temperature at large spin-orbit coupling is known to be determined by the mass of the emergent boson - the rashbon. We obtain the transition temperature of the system as a function of the spin-orbit coupling by constructing and studying a Gaussian fluctuation (Nozieres-Schmitt-Rink) theory. These results will help guide the upcoming experiments on spin-orbit coupled fermions. In addition, this work suggests a route to enhance the transition temperature of a weakly attracting fermionic system by tuning the spin-orbit coupling. Work supported by CSIR, DST, DAE India
Equivalent Markov processes under gauge group
NASA Astrophysics Data System (ADS)
Caruso, M.; Jarne, C.
2015-11-01
We have studied Markov processes on denumerable state space and continuous time. We found that all these processes are connected via gauge transformations. We have used this result before as a method to resolve equations, included the case in a previous work in which the sample space is time-dependent [Phys. Rev. E 90, 022125 (2014), 10.1103/PhysRevE.90.022125]. We found a general solution through dilation of the state space, although the prior probability distribution of the states defined in this new space takes smaller values with respect to that in the initial problem. The gauge (local) group of dilations modifies the distribution on the dilated space to restore the original process. In this work, we show how the Markov process in general could be linked via gauge (local) transformations, and we present some illustrative examples for this result.
Equivalent Markov processes under gauge group.
Caruso, M; Jarne, C
2015-11-01
We have studied Markov processes on denumerable state space and continuous time. We found that all these processes are connected via gauge transformations. We have used this result before as a method to resolve equations, included the case in a previous work in which the sample space is time-dependent [Phys. Rev. E 90, 022125 (2014)]. We found a general solution through dilation of the state space, although the prior probability distribution of the states defined in this new space takes smaller values with respect to that in the initial problem. The gauge (local) group of dilations modifies the distribution on the dilated space to restore the original process. In this work, we show how the Markov process in general could be linked via gauge (local) transformations, and we present some illustrative examples for this result. PMID:26651671
Topological phase transitions with non-Abelian gauge potentials on square lattices
NASA Astrophysics Data System (ADS)
Chen, Yao-Hua; Li, Jian; Ting, C. S.
2013-11-01
We investigate the topological phase transition on interacting square lattices via the non-Abelian potential by employing the real-space cellular dynamical mean-field theory combining with the continuous-time Monte Carlo method. For a weak on-site Hubbard interaction, a topological band insulating state with a pair of gapless edge states is induced by a next-nearest-neighbor hopping. A phase transition from the metallic phase to the Mott insulating phase is observed when the interaction is increased. These two phases can be distinguished by detecting whether a bulk gap in the K-dependent spectral function exists. The whole phase diagrams as functions of the interaction, next-nearest-neighbor hopping energy, and temperature are presented. The experimental setup to observe these new interesting phase transitions is also discussed.
Haag duality for Kitaev’s quantum double model for abelian groups
NASA Astrophysics Data System (ADS)
Fiedler, Leander; Naaijkens, Pieter
2015-11-01
We prove Haag duality for cone-like regions in the ground state representation corresponding to the translational invariant ground state of Kitaev’s quantum double model for finite abelian groups. This property says that if an observable commutes with all observables localized outside the cone region, it actually is an element of the von Neumann algebra generated by the local observables inside the cone. This strengthens locality, which says that observables localized in disjoint regions commute. As an application, we consider the superselection structure of the quantum double model for abelian groups on an infinite lattice in the spirit of the Doplicher-Haag-Roberts program in algebraic quantum field theory. We find that, as is the case for the toric code model on an infinite lattice, the superselection structure is given by the category of irreducible representations of the quantum double.
Confinement Driven by Scalar Field in 4d Non Abelian Gauge Theories
Chabab, Mohamed
2007-01-12
We review some of the most recent work on confinement in 4d gauge theories with a massive scalar field (dilaton). Emphasis is put on the derivation of confining analytical solutions to the Coulomb problem versus dilaton effective couplings to gauge terms. It is shown that these effective theories can be relevant to model quark confinement and may shed some light on confinement mechanism. Moreover, the study of interquark potential, derived from Dick Model, in the heavy meson sector proves that phenomenological investigation of tmechanism is more than justified and deserves more efforts.
Regular non-Abelian vacua in N=4, SO(4) gauged supergravity
Chamseddine, Ali H.; Volkov, Mikhail S.
2004-10-15
We present a family of globally regular N=1 vacua in the D=4, N=4 gauged supergravity of Gates and Zwiebach. These solutions are labeled by the ratio {xi} of the two gauge couplings, and for {xi}=0 they reduce to the supergravity monopole previously used for constructing the gravity dual of N=1 super Yang-Mills theory. For {xi}>0 the solutions are asymptotically anti- de Sitter, but with an excess of the solid angle, and they reduce exactly to anti-de Sitter for {xi}=1. Solutions with {xi}<0 are topologically R{sup 1}xS{sup 3}, and for {xi}=-2 they become R{sup 1}xS{sup 3} geometrically. All solutions with {xi}{ne}0 can be promoted to D=11 to become vacua of M-theory.
Gauge groups from brane-anti-brane systems at angles
NASA Astrophysics Data System (ADS)
Vancea, I. V.
2001-04-01
We discuss a system formed by two pairs of brane-anti-brane that form an arbitrary angle in a plane. We identify the gauge groups from this system which presumably could be used to construct gauge theories...
C*-Algebras Associated with Endomorphisms and Polymorphisms of Compact Abelian Groups
NASA Astrophysics Data System (ADS)
Cuntz, Joachim; Vershik, Anatoly
2013-07-01
A surjective endomorphism or, more generally, a polymorphism in the sense of Schmidt and Vershik [Erg Th Dyn Sys 28(2):633-642, 2008], of a compact abelian group H induces a transformation of L 2( H). We study the C*-algebra generated by this operator together with the algebra of continuous functions C( H) which acts as multiplication operators on L 2( H). Under a natural condition on the endo- or polymorphism, this algebra is simple and can be described by generators and relations. In the case of an endomorphism it is always purely infinite, while for a polymorphism in the class we consider, it is either purely infinite or has a unique trace. We prove a formula allowing to determine the K-theory of these algebras and use it to compute the K-groups in a number of interesting examples.
On Goldman bracket for G 2 gauge group
NASA Astrophysics Data System (ADS)
Chowdhury, S. Hasibul Hassan
2016-02-01
In this paper, we obtain an infinite dimensional Lie algebra of exotic gauge invariant observables that is closed under Goldman-type bracket associated with monodromy matrices of flat connections on a compact Riemann surface for G 2 gauge group. As a byproduct, we give an alternative derivation of known Goldman bracket for classical gauge groups GL ( n, ℝ), SL( n, ℝ), U( n), SU( n), Sp(2 n, ℝ) and SO( n).
Gauge Invariance and Gauge-Factor Group in Causal Yang-Mills Theory
NASA Astrophysics Data System (ADS)
Emmenegger, N.
2001-11-01
In the present work the gauge invariance of causal Yang-Mills theory will be proven with the aid of the gauge-factor group. For that purpose it must be shown, that the operator valued distributions T_n and D_n(ret) occurring in the causal S-matrix construction can be written, after applying the gauge variation d_Q, as a divergence. Since merely local terms lead to gauge destroying expressions, one has to focus on them exclusively. In the first part of the work the local gauge-factor group will be defined in the style of the concept of gauge cohomology theory. It will be shown, that every element out of the so defined factor group under the transformation d_Q leads to a divergence of the entire operator valued distribution d_Q(T_n). In the second part all local terms arising in causal Yang-Mills theory are systematically investigated. Without further restrictions there can be proven, that every local operator valued distribution is an element of the gauge factor group or equal to zero. This concludes the demonstration of gauge invariance of causal Yang-Mills theory.
Coulomb branches for rank 2 gauge groups in 3 d N=4 gauge theories
NASA Astrophysics Data System (ADS)
Hanany, Amihay; Sperling, Marcus
2016-08-01
The Coulomb branch of 3-dimensional N=4 gauge theories is the space of bare and dressed BPS monopole operators. We utilise the conformal dimension to define a fan which, upon intersection with the weight lattice of a GNO-dual group, gives rise to a collection of semi-groups. It turns out that the unique Hilbert bases of these semi-groups are a sufficient, finite set of monopole operators which generate the entire chiral ring. Moreover, the knowledge of the properties of the minimal generators is enough to compute the Hilbert series explicitly. The techniques of this paper allow an efficient evaluation of the Hilbert series for general rank gauge groups. As an application, we provide various examples for all rank two gauge groups to demonstrate the novel interpretation.
Topological quantum liquids with quaternion non-Abelian statistics.
Xu, Cenke; Ludwig, Andreas W W
2012-01-27
Noncollinear magnetic order is typically characterized by a tetrad ground state manifold (GSM) of three perpendicular vectors or nematic directors. We study three types of tetrad orders in two spatial dimensions, whose GSMs are SO(3) = S(3)/Z(2), S(3)/Z(4), and S(3)/Q(8), respectively. Q(8) denotes the non-Abelian quaternion group with eight elements. We demonstrate that after quantum disordering these three types of tetrad orders, the systems enter fully gapped liquid phases described by Z(2), Z(4), and non-Abelian quaternion gauge field theories, respectively. The latter case realizes Kitaev's non-Abelian toric code in terms of a rather simple spin-1 SU(2) quantum magnet. This non-Abelian topological phase possesses a 22-fold ground state degeneracy on the torus arising from the 22 representations of the Drinfeld double of Q(8). PMID:22400884
Operator Algebra Quantum Homogeneous Spaces of Universal Gauge Groups
NASA Astrophysics Data System (ADS)
Mahanta, Snigdhayan; Mathai, Varghese
2011-09-01
In this paper, we quantize universal gauge groups such as SU(∞), as well as their homogeneous spaces, in the σ- C*-algebra setting. More precisely, we propose concise definitions of σ- C*-quantum groups and σ- C*-quantum homogeneous spaces and explain these concepts here. At the same time, we put these definitions in the mathematical context of countably compactly generated spaces as well as C*-compact quantum groups and homogeneous spaces. We also study the representable K-theory of these spaces and compute these groups for the quantum homogeneous spaces associated to the quantum version of the universal gauge group SU(∞).
Numerical techniques for lattice gauge theories
Creutz, M.
1981-02-06
The motivation for formulating gauge theories on a lattice is reviewed. Monte Carlo simulation techniques are then discussed for these systems. Finally, the Monte Carlo methods are combined with renormalization group analysis to give strong numerical evidence for confinement of quarks by non-Abelian gauge fields.
NASA Astrophysics Data System (ADS)
Zhu, W.; Gong, S. S.; Haldane, F. D. M.; Sheng, D. N.
2015-10-01
The non-Abelian topological order has attracted a lot of attention for its fundamental importance and exciting prospect of topological quantum computation. However, explicit demonstration or identification of the non-Abelian states and the associated statistics in a microscopic model is very challenging. Here, based on a density-matrix renormalization-group calculation, we provide a complete characterization of the universal properties of the bosonic Moore-Read state on a Haldane honeycomb lattice model at filling number ν =1 for larger systems, including both the edge spectrum and the bulk anyonic quasiparticle (QP) statistics. We first demonstrate that there are three degenerating ground states for each of which there is a definite anyonic flux threading through the cylinder. We identify the nontrivial countings for the entanglement spectrum in accordance with the corresponding conformal field theory. Through simulating a flux-inserting experiment, it is found that two of the Abelian ground states can be adiabatically connected, whereas the ground state in the Ising anyon sector evolves back to itself, which reveals the fusion rules between different QPs in real space. Furthermore, we calculate the modular matrices S and U , which contain all the information for the anyonic QPs, such as quantum dimensions, fusion rule, and topological spins.
Gauge theory of Virasoro-Kac-Moody group
NASA Astrophysics Data System (ADS)
Cho, Y. M.; Zoh, S. W.
1992-10-01
We present a prototype gauge theory of the Virasoro-Kac-Moody symmetry associated with an arbitrary grand unified group G, which could be interpreted as an effective field theory of a colored string. The theory automatically breaks the symmetry down to H⊗U(1), where H is a subgroup of G and U(1) is the Cartan subgroup of the Virasoro group. After the inevitable spontaneous symmetry breaking the particle spectrum of the theory consists of an infinite tower of massive spin-one fields, the massless gauge fields of the unbroken subgroup, and the light scalar fields which become the pseudo-Goldstone fields of the symmetry breaking
Geometry and energy of non-Abelian vortices
Manton, Nicholas S.; Rink, Norman A.
2011-04-15
We study pure Yang-Mills theory on {Sigma}xS{sup 2}, where {Sigma} is a compact Riemann surface, and invariance is assumed under rotations of S{sup 2}. It is well known that the self-duality equations in this setup reduce to vortex equations on {Sigma}. If the Yang-Mills gauge group is SU(2), the Bogomolny vortex equations of the Abelian Higgs model are obtained. For larger gauge groups, one generally finds vortex equations involving several matrix-valued Higgs fields. Here we focus on Yang-Mills theory with gauge group SU(N)/Z{sub N} and a special reduction which yields only one non-Abelian Higgs field. One of the new features of this reduction is the fact that while the instanton number of the theory in four dimensions is generally fractional with denominator N, we still obtain an integral vortex number in the reduced theory. We clarify the relation between these two topological charges at a bundle geometric level. Another striking feature is the emergence of nontrivial lower and upper bounds for the energy of the reduced theory on {Sigma}. These bounds are proportional to the area of {Sigma}. We give special solutions of the theory on {Sigma} by embedding solutions of the Abelian Higgs model into the non-Abelian theory, and we relate our work to the language of quiver bundles, which has recently proved fruitful in the study of dimensional reduction of Yang-Mills theory.
Atomic quantum simulation of U(N) and SU(N) non-Abelian lattice gauge theories.
Banerjee, D; Bögli, M; Dalmonte, M; Rico, E; Stebler, P; Wiese, U-J; Zoller, P
2013-03-22
Using ultracold alkaline-earth atoms in optical lattices, we construct a quantum simulator for U(N) and SU(N) lattice gauge theories with fermionic matter based on quantum link models. These systems share qualitative features with QCD, including chiral symmetry breaking and restoration at nonzero temperature or baryon density. Unlike classical simulations, a quantum simulator does not suffer from sign problems and can address the corresponding chiral dynamics in real time. PMID:25166816
Abelian link invariants and homology
Guadagnini, Enore; Mancarella, Francesco
2010-06-15
We consider the link invariants defined by the quantum Chern-Simons field theory with compact gauge group U(1) in a closed oriented 3-manifold M. The relation of the Abelian link invariants with the homology group of the complement of the links is discussed. We prove that, when M is a homology sphere or when a link--in a generic manifold M--is homologically trivial, the associated observables coincide with the observables of the sphere S{sup 3}. Finally, we show that the U(1) Reshetikhin-Turaev surgery invariant of the manifold M is not a function of the homology group only, nor a function of the homotopy type of M alone.
Line of critical points in 2+1 dimensions: quantum critical loop gases and non-Abelian gauge theory.
Freedman, Michael; Nayak, Chetan; Shtengel, Kirill
2005-04-15
In this Letter, we (1) construct a one-parameter family of lattice models of interacting spins; (2) obtain their exact ground states; (3) derive a statistical-mechanical analogy which relates their ground states to O(n) loop gases; (4) show that the models are critical for dgauge theory; and (7) show that its one-loop beta function vanishes for all values of the coupling constant, implying that it is also on a critical line. PMID:15904103
NASA Astrophysics Data System (ADS)
Robertson, Christopher; Worth, Graham A.
2015-10-01
The vibronic coupling Hamiltonian is a standard model used to describe the potential energy surfaces of systems in which non-adiabatic coupling is a key feature. This includes Jahn-Teller and Renner-Teller systems. The model approximates diabatic potential energy functions as polynomials expanded about a point of high symmetry. One must ensure the model Hamiltonian belongs to the totally symmetric irreducible representation of this point group. Here, a simple approach is presented to generate functions that form a basis for totally symmetric irreducible representations of non-Abelian groups and apply it to D∞h (2D) and O (3D). For the O group, the use of a well known basis-generating operator is also required. The functions generated for D∞h are then used to construct a ten state, four coordinate model of acetylene. The calculated absorption spectrum is compared to the experimental spectrum to serve as a validation of the approach.
Can (electric-magnetic) duality be gauged?
Bunster, Claudio; Henneaux, Marc
2011-02-15
There exists a formulation of the Maxwell theory in terms of two vector potentials, one electric and one magnetic. The action is then manifestly invariant under electric-magnetic duality transformations, which are rotations in the two-dimensional internal space of the two potentials, and local. We ask the question: Can duality be gauged? The only known and battle-tested method of accomplishing the gauging is the Noether procedure. In its decanted form, it amounts to turning on the coupling by deforming the Abelian gauge group of the free theory, out of whose curvatures the action is built, into a non-Abelian group which becomes the gauge group of the resulting theory. In this article, we show that the method cannot be successfully implemented for electric-magnetic duality. We thus conclude that, unless a radically new idea is introduced, electric-magnetic duality cannot be gauged. The implication of this result for supergravity is briefly discussed.
Tushev, A V
2006-10-31
In the present paper certain methods are developed that enable one to study the properties of the controller of a prime faithful ideal I of the group algebra kA of an Abelian torsion-free group A of finite rank over a field k. The main idea is that the quotient ring kA/I by the given ideal I can be embedded as an integral domain k[A] into some field F and the group A becomes a subgroup of the multiplicative group of the field F. This allows one to apply certain results of field theory, such as Kummer's theory and the properties of the multiplicative groups of fields, to the study of the integral domain k[A]. In turn, the properties of the integral domain k[A]{approx_equal}kA/I depend essentially on the properties of the ideal I. In particular, by using these methods, an independent proof of the new version of Brookes's theorem on the controllers of prime ideals of the group algebra kA of an Abelian torsion-free group A of finite rank is obtained in the case where the field k has positive characteristic.
Gauge theory of a group of diffeomorphisms. II. The conformal and de Sitter groups
NASA Astrophysics Data System (ADS)
Lord, Eric A.
1986-12-01
The extension of Hehl's Poincaré gauge theory to more general groups that include space-time diffeomorphisms is worked out for two particular examples, one corresponding to the action of the conformal group on Minkowski space, and the other to the action of the de Sitter group on de Sitter space, and the effect of these groups on physical fields.
Bound states in gauge theories as the Poincare group representations
Cherny, A. Yu.; Dorokhov, A. E.; Han, Nguyen Suan; Pervushin, V. N. Shilin, V. I.
2013-03-15
The bound-state generating functional is constructed in gauge theories. This construction is based on the Dirac Hamiltonian approach to gauge theories, the Poincare group classification of fields and their nonlocal bound states, and the Markov-Yukawa constraint of irreducibility. The generating functional contains additional anomalous creations of pseudoscalar bound states: para-positronium in QED and mesons inQCDin the two-gamma processes of the type of {gamma} + {gamma} {yields} {pi}{sub 0} +para-positronium. The functional allows us to establish physically clear and transparent relations between the perturbativeQCD to its nonperturbative low-energy model by means of normal ordering and the quark and gluon condensates. In the limit of small current quark masses, the Gell-Mann-Oakes-Renner relation is derived from the Schwinger-Dyson and Bethe-Salpeter equations. The constituent quark masses can be calculated from a self-consistent nonlinear equation.
Tensor renormalization group methods for spin and gauge models
NASA Astrophysics Data System (ADS)
Zou, Haiyuan
The analysis of the error of perturbative series by comparing it to the exact solution is an important tool to understand the non-perturbative physics of statistical models. For some toy models, a new method can be used to calculate higher order weak coupling expansion and modified perturbation theory can be constructed. However, it is nontrivial to generalize the new method to understand the critical behavior of high dimensional spin and gauge models. Actually, it is a big challenge in both high energy physics and condensed matter physics to develop accurate and efficient numerical algorithms to solve these problems. In this thesis, one systematic way named tensor renormalization group method is discussed. The applications of the method to several spin and gauge models on a lattice are investigated. theoretically, the new method allows one to write an exact representation of the partition function of models with local interactions. E.g. O(N) models, Z2 gauge models and U(1) gauge models. Practically, by using controllable approximations, results in both finite volume and the thermodynamic limit can be obtained. Another advantage of the new method is that it is insensitive to sign problems for models with complex coupling and chemical potential. Through the new approach, the Fisher's zeros of the 2D O(2) model in the complex coupling plane can be calculated and the finite size scaling of the results agrees well with the Kosterlitz-Thouless assumption. Applying the method to the O(2) model with a chemical potential, new phase diagram of the models can be obtained. The structure of the tensor language may provide a new tool to understand phase transition properties in general.
Gauging Quantum Groups: Yang-Baxter Joining Yang-Mills
NASA Astrophysics Data System (ADS)
Wu, Yong-Shi
This review is an expansion of my talk at the conference on Sixty Years of Yang-Mills Theory. I review and explain the line of thoughts that lead to a recent joint work with Hu and Geer [Hu et al., arXiv:1502.03433] on the construction, exact solutions and ubiquitous properties of a class of quantum group gauge models on a honey-comb lattice. Conceptually the construction achieves a synthesis of the ideas of Yang-Baxter equations with those of Yang-Mills theory. Physically the models describe topological anyonic states in 2D systems.
Gauging quantum groups: Yang-Baxter joining Yang-Mills
NASA Astrophysics Data System (ADS)
Wu, Yong-Shi
2016-02-01
This review is an expansion of my talk at the conference on Sixty Years of Yang-Mills Theory. I review and explain the line of thoughts that lead to a recent joint work with Hu and Geer [Hu et al., arXiv:1502.03433] on the construction, exact solutions and ubiquitous properties of a class of quantum group gauge models on a honey-comb lattice. Conceptually the construction achieves a synthesis of the ideas of Yang-Baxter equations with those of Yang-Mills theory. Physically the models describe topological anyonic states in 2D systems.
Majorana meets Coxeter: Non-Abelian Majorana fermions and non-Abelian statistics
Yasui, Shigehiro; Itakura, Kazunori; Nitta, Muneto
2011-04-01
We discuss statistics of vortices having zero-energy non-Abelian Majorana fermions inside them. Considering the system of multiple non-Abelian vortices, we derive a non-Abelian statistics that differs from the previously derived non-Abelian statistics. The non-Abelian statistics presented here is given by a tensor product of two different groups, namely the non-Abelian statistics obeyed by the Abelian Majorana fermions and the Coxeter group. The Coxeter group is a symmetric group related to the symmetry of polytopes in a high-dimensional space. As the simplest example, we consider the case in which a vortex contains three Majorana fermions that are mixed with each other under the SO(3) transformations. We concretely present the representation of the Coxeter group in our case and its geometrical expressions in the high-dimensional Hilbert space constructed from non-Abelian Majorana fermions.
Field theory aspects of non-Abelian T-duality and {N} =2 linear quivers
NASA Astrophysics Data System (ADS)
Lozano, Yolanda; Núñez, Carlos
2016-05-01
In this paper we propose a linear quiver with gauge groups of increasing rank as field theory dual to the AdS 5 background constructed by Sfetsos and Thompson through non-Abelian T-duality. The formalism to study 4d {N} = 2 SUSY CFTs developed by Gaiotto and Maldacena is essential for our proposal. We point out an interesting relation between (Hopf) Abelian and non-Abelian T-dual backgrounds that allows to see both backgrounds as different limits of a solution constructed by Maldacena and Núñez. This suggests different completions of the long quiver describing the CFT dual to the nonAbelian T-dual background that match different observables.
The arithmetic of elliptic fibrations in gauge theories on a circle
NASA Astrophysics Data System (ADS)
Grimm, Thomas W.; Kapfer, Andreas; Klevers, Denis
2016-06-01
The geometry of elliptic fibrations translates to the physics of gauge theories in F-theory. We systematically develop the dictionary between arithmetic structures on elliptic curves as well as desingularized elliptic fibrations and symmetries of gauge theories on a circle. We show that the Mordell-Weil group law matches integral large gauge transformations around the circle in Abelian gauge theories and explain the significance of Mordell-Weil torsion in this context. We also use Higgs transitions and circle large gauge transformations to introduce a group law for genus-one fibrations with multi-sections. Finally, we introduce a novel arithmetic structure on elliptic fibrations with non-Abelian gauge groups in F-theory. It is defined on the set of exceptional divisors resolving the singularities and divisor classes of sections of the fibration. This group structure can be matched with certain integral non-Abelian large gauge transformations around the circle when studying the theory on the lower-dimensional Coulomb branch. Its existence is required by consistency with Higgs transitions from the non-Abelian theory to its Abelian phases in which it becomes the Mordell-Weil group. This hints towards the existence of a new underlying geometric symmetry.
Sharma, Sandeep
2015-01-14
We extend our previous work [S. Sharma and G. K.-L. Chan, J. Chem. Phys. 136, 124121 (2012)], which described a spin-adapted (SU(2) symmetry) density matrix renormalization group algorithm, to additionally utilize general non-Abelian point group symmetries. A key strength of the present formulation is that the requisite tensor operators are not hard-coded for each symmetry group, but are instead generated on the fly using the appropriate Clebsch-Gordan coefficients. This allows our single implementation to easily enable (or disable) any non-Abelian point group symmetry (including SU(2) spin symmetry). We use our implementation to compute the ground state potential energy curve of the C{sub 2} dimer in the cc-pVQZ basis set (with a frozen-core), corresponding to a Hilbert space dimension of 10{sup 12} many-body states. While our calculated energy lies within the 0.3 mE{sub h} error bound of previous initiator full configuration interaction quantum Monte Carlo and correlation energy extrapolation by intrinsic scaling calculations, our estimated residual error is only 0.01 mE{sub h}, much more accurate than these previous estimates. Due to the additional efficiency afforded by the algorithm, the excitation energies (T{sub e}) of eight lowest lying excited states: a{sup 3}Π{sub u}, b{sup 3}Σ{sub g}{sup −}, A{sup 1}Π{sub u}, c{sup 3}Σ{sub u}{sup +}, B{sup 1}Δ{sub g}, B{sup ′1}Σ{sub g}{sup +}, d{sup 3}Π{sub g}, and C{sup 1}Π{sub g} are calculated, which agree with experimentally derived values to better than 0.06 eV. In addition, we also compute the potential energy curves of twelve states: the three lowest levels for each of the irreducible representations {sup 1}Σ{sub g}{sup +}, {sup 1}Σ{sub u}{sup +}, {sup 1}Σ{sub g}{sup −}, and {sup 1}Σ{sub u}{sup −}, to an estimated accuracy of 0.1 mE{sub h} of the exact result in this basis.
Gauge invariant composite operators of QED in the exact renormalization group formalism
NASA Astrophysics Data System (ADS)
Sonoda, H.
2014-01-01
Using the exact renormalization group (ERG) formalism, we study the gauge invariant composite operators in QED. Gauge invariant composite operators are introduced as infinitesimal changes of the gauge invariant Wilson action. We examine the dependence on the gauge fixing parameter of both the Wilson action and gauge invariant composite operators. After defining ‘gauge fixing parameter independence,’ we show that any gauge independent composite operators can be made ‘gauge fixing parameter independent’ by appropriate normalization. As an application, we give a concise but careful proof of the Adler-Bardeen non-renormalization theorem for the axial anomaly in an arbitrary covariant gauge by extending the original proof by A Zee.
Dynamical non-Abelian two-form: BRST quantization
Lahiri, A.
1997-04-01
When an antisymmetric tensor potential is coupled to the field strength of a gauge field via a BANDF coupling and a kinetic term for B is included, the gauge field develops an effective mass. The theory can be made invariant under a non-Abelian vector gauge symmetry by introducing an auxiliary vector field. The covariant quantization of this theory requires ghosts for ghosts. The resultant theory including gauge fixing and ghost terms is BRST invariant by construction, and therefore unitary. The construction of the BRST-invariant action is given for both Abelian and non-Abelian models of mass generation. {copyright} {ital 1997} {ital The American Physical Society}
Tensor Networks for Lattice Gauge Theories with Continuous Groups
NASA Astrophysics Data System (ADS)
Tagliacozzo, L.; Celi, A.; Lewenstein, M.
2014-10-01
We discuss how to formulate lattice gauge theories in the tensor-network language. In this way, we obtain both a consistent-truncation scheme of the Kogut-Susskind lattice gauge theories and a tensor-network variational ansatz for gauge-invariant states that can be used in actual numerical computations. Our construction is also applied to the simplest realization of the quantum link models or gauge magnets and provides a clear way to understand their microscopic relation with the Kogut-Susskind lattice gauge theories. We also introduce a new set of gauge-invariant operators that modify continuously Rokhsar-Kivelson wave functions and can be used to extend the phase diagrams of known models. As an example, we characterize the transition between the deconfined phase of the Z2 lattice gauge theory and the Rokhsar-Kivelson point of the U (1 ) gauge magnet in 2D in terms of entanglement entropy. The topological entropy serves as an order parameter for the transition but not the Schmidt gap.
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.
NASA Astrophysics Data System (ADS)
Matsudo, Ryutaro; Kondo, Kei-Ichi
2015-12-01
We give a gauge-independent definition of magnetic monopoles in the S U (N ) Yang-Mills theory through the Wilson loop operator. For this purpose, we give an explicit proof of the Diakonov-Petrov version of the non-Abelian Stokes theorem for the Wilson loop operator in an arbitrary representation of the S U (N ) gauge group to derive a new form for the non-Abelian Stokes theorem. The new form is used to extract the magnetic-monopole contribution to the Wilson loop operator in a gauge-invariant way, which enables us to discuss confinement of quarks in any representation from the viewpoint of the dual superconductor vacuum.
Generalization of trinification to theories with 3N SU(3) gauge groups
Carone, Christopher D.
2005-04-01
We consider a natural generalization of trinification to theories with 3N SU(3) gauge groups. These theories have a simple moose representation and a gauge boson spectrum that can be interpreted via the deconstruction of a 5D theory with unified symmetry broken on a boundary. Although the matter and Higgs sectors of the theory have no simple extra-dimensional analog, gauge unification retains features characteristic of the 5D theory. We determine possible assignments of the matter and Higgs fields to unified multiplets and present theories that are viable alternatives to minimal trinified GUTs.
Multiflavor QCD* on R_3 * S_1: Studying Transition From Abelian to Non-Abelian Confinement
Shifman, M.; Unsal, M.; /SLAC /Stanford U., Phys. Dept.
2009-03-31
The center-stabilized multiflavor QCD* theories formulated on R{sub 3} x S{sub 1} exhibit both Abelian and non-Abelian confinement as a function of the S{sub 1} radius, similar to the Seiberg-Witten theory as a function of the mass deformation parameter. For sufficiently small number of flavors and small r(S{sub 1}), we show occurrence of a mass gap in gauge fluctuations, and linear confinement. This is a regime of confinement without continuous chiral symmetry breaking ({chi}SB). Unlike one-flavor theories where there is no phase transition in r(S{sub 1}), the multiflavor theories possess a single phase transition associated with breaking of the continuous {chi}S. We conjecture that the scale of the {chi}SB is parametrically tied up with the scale of Abelian to non-Abelian confinement transition.
On Chern-Simons theory with an inhomogeneous gauge group and BF theory knot invariants
Naot, Gad
2005-12-15
We study the Chern-Simons topological quantum field theory with an inhomogeneous gauge group, a non-semi-simple group obtained from a semisimple one by taking its semidirect product with its Lie algebra. We find that the standard knot observable (i.e., trace of the holonomy along the knot) essentially vanishes, and yet, the non-semi-simplicity of the gauge group allows us to consider a class of unorthodox observables which breaks gauge invariance at one point and leads to a nontrivial theory on long knots in R{sup 3}. We have two main morals. (1) In the non-semi-simple case there is more to observe in Chern-Simons theory. There might be other interesting non-semi-simple gauge groups to study in this context beyond our example. (2) In the case of an inhomogeneous gauge group, we find that Chern-Simons theory with the unorthodox observable is actually the same as three-dimensional BF theory with the Cattaneo-Cotta-Ramusino-Martellini knot observable. This leads to a simplification of their results and enables us to generalize and solve a problem they posed regarding the relation between BF theory and the Alexander-Conway polynomial. We prove that the most general knot invariant coming from pure BF topological quantum field theory is in the algebra generated by the coefficients of the Alexander-Conway polynomial.
Dynamics of Euclideanized Einstein-Yang-Mills systems with arbitrary gauge groups
Bertolami, O.; Picken, R.F. ); Maurao, J.M. ); Volobujev, I.P. )
1991-09-30
This paper describes the dynamics of euclideanized SO(4)-symmetric Einstein-Yang-Mills (EYM) systems with arbitrary compact gauge groups K. For the case of SO(n) and SU(n) gauge groups and simple embeddings of the isotropy group in K, the authors show that in the resulting dynamical system, the Friedmann equation decouples from the Yang-Mills equations. Furthermore, the latter can be reduced to a system of two second-order differential equations. This allows the authors to find a broad class of instanton (wormhole) solutions of the EYM equations. These solutions are not afflicted by the giant-wormhole catastrophe.
Symmetries of abelian orbifolds
NASA Astrophysics Data System (ADS)
Hanany, Amihay; Seong, Rak-Kyeong
2011-01-01
Using the Polya Enumeration Theorem, we count with particular attention to {{{{mathbb{C}^3}}} left/ {Γ } right.} up to {{{{mathbb{C}^6}}} left/ {Γ } right.} , abelian orbifolds in various dimensions which are invariant under cycles of the permutation group S D . This produces a collection of multiplicative sequences, one for each cycle in the Cycle Index of the permutation group. A multiplicative sequence is controlled by its values on prime numbers and their pure powers. Therefore, we pay particular attention to orbifolds of the form {{{{mathbb{C}^D}}} left/ {Γ } right.} where the order of Γ is p α. We propose a generalization of these sequences for any D and any p.
Matrix product states and the non-Abelian rotor model
NASA Astrophysics Data System (ADS)
Milsted, Ashley
2016-04-01
We use uniform matrix product states to study the (1 +1 )D O (2 ) and O (4 ) rotor models, which are equivalent to the Kogut-Susskind formulation of matter-free non-Abelian lattice gauge theory on a "Hawaiian earring" graph for U (1 ) and S U (2 ), respectively. Applying tangent space methods to obtain ground states and determine the mass gap and the β function, we find excellent agreement with known results, locating the Berezinskii-Kosterlitz-Thouless transition for O (2 ) and successfully entering the asymptotic weak-coupling regime for O (4 ). To obtain a finite local Hilbert space, we truncate in the space of generalized Fourier modes of the gauge group, comparing the effects of different cutoff values. We find that higher modes become important in the crossover and weak-coupling regimes of the non-Abelian theory, where entanglement also suddenly increases. This could have important consequences for tensor network state studies of Yang-Mills on higher-dimensional graphs.
Universal Reconnection of Non-Abelian Cosmic Strings
Eto, Minoru; Hashimoto, Koji; Marmorini, Giacomo; Nitta, Muneto; Ohashi, Keisuke; Vinci, Walter
2007-03-02
We show that local and semilocal strings in Abelian and non-Abelian gauge theories with critical couplings always reconnect classically in collision, by using moduli space approximation. The moduli matrix formalism explicitly identifies a well-defined set of the vortex moduli parameters. Our analysis of generic geodesic motion in terms of those shows right-angle scattering in head-on collision of two vortices, which is known to give the reconnection of the strings.
Universal reconnection of non-Abelian cosmic strings.
Eto, Minoru; Hashimoto, Koji; Marmorini, Giacomo; Nitta, Muneto; Ohashi, Keisuke; Vinci, Walter
2007-03-01
We show that local and semilocal strings in Abelian and non-Abelian gauge theories with critical couplings always reconnect classically in collision, by using moduli space approximation. The moduli matrix formalism explicitly identifies a well-defined set of the vortex moduli parameters. Our analysis of generic geodesic motion in terms of those shows right-angle scattering in head-on collision of two vortices, which is known to give the reconnection of the strings. PMID:17359147
Partial gauge fixing and equivariant cohomology
NASA Astrophysics Data System (ADS)
Ferrari, Frank
2014-05-01
Given a gauge theory with gauge group G, it is sometimes useful to find an equivalent formulation in terms of a nontrivial gauge subgroup H ⊂G. This amounts to fixing the gauge partially from G down to H. We study this problem systematically, both from the algebraic and from the path integral points of view. We find that the usual BRST cohomology must be replaced by an equivariant version and that the ghost Lagrangian must always include quartic ghost terms, even at tree level. Both the Cartan and Weil models for equivariant cohomology play a role and find natural interpretations within the physics framework. Applications include the construction of D-brane models of emergent space, the 't Hooft Abelian projection scenario in quantum chromodynamics and the formulation of the low-energy effective theories of grand unified models.
Path ordered operator formalism of gauge theories in two-dimensional space-time
NASA Astrophysics Data System (ADS)
Kikkawa, K.
1980-05-01
Two-dimensional gauge theories, both abelian and non-belian, are formulated in terms of gauge invariant path ordered operators (POO). The generators of the Poincaré group are constructed with POO's. An exact equation of motion for POO's is derived and is shown to reduce to the 't Hooft eigenvalue equation in QCD in the large N limit. Nowhere appear infrared problems.
Gravity as an internal Yang-Mills gauge field theory of the Poincaré group.
NASA Astrophysics Data System (ADS)
Hennig, Jörg; Nitsch, Jürgen
1981-10-01
In the framework of affine bundles we present gravity as an “internal” gauge field theory of the Poincaré group. The resulting geometry is a Riemann-Cartan space-time carrying torsion and curvature. In order to admit a nontrivial action of the translation group we formally extend the matter Lagrangian to affine field variables. Finally, we establish the relation of our approach with the formalism of Hehl et al.
Mills, R.
1989-06-01
This article is a survey of the history and ideas of gauge theory. Described here are the gradual emergence of symmetry as a driving force in the shaping of physical theory; the elevation of Noether's theorem, relating symmetries to conservation laws, to a fundamental principle of nature; and the force of the idea (''the gauge principle'') that the symmetries of nature, like the interactions themselves, should be local in character. The fundamental role of gauge fields in mediating the interactions of physics springs from Noether's theorem and the gauge principle in a remarkably clean and elegant way, leaving, however, some tantalizing loose ends that might prove to be the clue to a future deeper level of understanding. The example of the electromagnetic field as the prototype gauge theory is discussed in some detail and serves as the basis for examining the similarities and differences that emerge in generalizing to non-Abelian gauge theories. The article concludes with a brief examination of the dream of total unification: all the forces of nature in a single unified gauge theory, with the differences among the forces due to the specific way in which the fundamental symmetries are broken in the local environment.
NASA Astrophysics Data System (ADS)
Kondo, Kei-Ichi; Kato, Seikou; Shibata, Akihiro; Shinohara, Toru
2015-05-01
confinement. The Wilson loop average is calculated according to the new reformulation written in terms of new field variables obtained from the original Yang-Mills field based on change of variables. The Maximally Abelian gauge in the original Yang-Mills theory is also reproduced by taking a specific gauge fixing in the reformulated Yang-Mills theory. This observation justifies the preceding results obtained in the maximal Abelian gauge at least for gauge-invariant quantities for SU(2) gauge group, which eliminates the criticism of gauge artifact raised for the Abelian projection. The claim has been confirmed based on the numerical simulations. However, for SU(N) (N ≥ 3), such a gauge-invariant reformulation is not unique, although the extension along the line proposed by Cho, Faddeev and Niemi is possible. In fact, we have found that there are a number of possible options of the reformulations, which are discriminated by the maximal stability group H ˜ of G, while there is a unique option of H ˜ = U(1) for G = SU(2) . The maximal stability group depends on the representation of the gauge group, to that the quark source belongs. For the fundamental quark for SU(3) , the maximal stability group is U(2) , which is different from the maximal torus group U(1) × U(1) suggested from the Abelian projection. Therefore, the chromomagnetic monopole inherent in the Wilson loop operator responsible for confinement of quarks in the fundamental representation for SU(3) is the non-Abelian magnetic monopole, which is distinct from the Abelian magnetic monopole for the SU(2) case. Therefore, we claim that the mechanism for quark confinement for SU(N) (N ≥ 3) is the non-Abelian dual superconductivity caused by condensation of non-Abelian magnetic monopoles. We give some theoretical considerations and numerical results supporting this picture. Finally, we discuss some issues to be investigated in future studies.
Electroweak theory based on S U (4 )L⊗U (1 )X gauge group
NASA Astrophysics Data System (ADS)
Long, H. N.; Hue, L. T.; Loi, D. V.
2016-07-01
This paper includes two main parts. In the first part, we present generalized gauge models based on the S U (3 )C⊗S U (4 )L⊗U (1 )X (3-4-1) gauge group with arbitrary electric charges of exotic leptons. The mixing matrix of neutral gauge bosons is analyzed, and the eigenmasses and eigenstates are obtained. The anomaly-free as well as matching conditions are discussed precisely. In the second part, we present a new development of the original 3-4-1 model [R. Foot, H. N. Long, and T. A. Tran, Phys. Rev. D 50, R34 (1994), F. Pisano and V. Pleitez, Phys. Rev. D 51, 3865 (1995).]. Different from previous works, in this paper the neutrinos, with the help of the scalar decuplet H , get the Dirac masses at the tree level. The vacuum expectation value (VEV) of the Higgs boson field in the decuplet H acquiring the VEV responsible for neutrino Dirac mass leads to mixing in separated pairs of singly charged gauge bosons, namely the Standard Model (SM) W boson and K , the new gauge boson acting in the right-handed lepton sector, as well as the singly charged bileptons X and Y . Due to the mixing, there occurs a right-handed current carried by the W boson. From the expression of the electromagnetic coupling constant, ones get the limit of the sine-squared of the Weinberg angle, sin2θW<0.25 , and a constraint on electric charges of extra leptons. In the limit of lepton number conservation, the Higgs sector contains all massless Goldstone bosons for massive gauge bosons and the SM-like Higgs boson. Some phenomenology is discussed.
Gauge anomalies in an effective field theory
Preskill, J. )
1991-09-01
A four-dimensional gauge theory with anomalous fermion content can be consistently quantized, provided that at least some gauge fields are permitted to have nonvanishing masses. Such a theory is nonrenormalizable; there is a maximal value of the ultraviolet cutoff {Lambda}, beyond which the locality of the theory breaks down. The maximal {Lambda} can be estimated in perturbation theory and has a qualitatively different character in Abelian and non-Abelian anomalous gauge theories.
Non-Abelian dynamics in the resonant decay of the Higgs after inflation
Enqvist, Kari; Nurmi, Sami; Rusak, Stanislav E-mail: sami.nurmi@helsinki.fi
2014-10-01
We study the resonant decay of the Higgs condensate into weak gauge bosons after inflation and estimate the corrections arising from the non-Abelian self-interactions of the gauge fields. We find that non-Abelian interaction terms induce an effective mass which tends to shut down the resonance. For the broad resonance relevant for the Standard Model Higgs the produced gauge particles backreact on the dynamics of the Higgs condensate before the non-Abelian terms grow large. The non-Abelian terms can however significantly affect the final stages of the resonance after the backreaction. In the narrow resonance regime, which may be important for extensions of the Standard Model, the non-Abelian terms affect already the linear stage and terminate the resonance before the Higgs condensate is affected by the backreaction of decay products.
AdS/CFT and local renormalization group with gauge fields
NASA Astrophysics Data System (ADS)
Kikuchi, Ken; Sakai, Tadakatsu
2016-03-01
We revisit a study of local renormalization group (RG) with background gauge fields incorporated using the AdS/CFT correspondence. Starting with a (d+1)-dimensional bulk gravity coupled to scalars and gauge fields, we derive a local RG equation from a flow equation by working in the Hamilton-Jacobi formulation of the bulk theory. The Gauss's law constraint associated with gauge symmetry plays an important role. RG flows of the background gauge fields are governed by vector β -functions, and some of their interesting properties are known to follow. We give a systematic rederivation of them on the basis of the flow equation. Fixing an ambiguity of local counterterms in such a manner that is natural from the viewpoint of the flow equation, we determine all the coefficients uniquely appearing in the trace of the stress tensor for d=4. A relation between a choice of schemes and a virial current is discussed. As a consistency check, these are found to satisfy the integrability conditions of local RG transformations. From these results, we are led to a proof of a holographic c-theorem by determining a full family of schemes where a trace anomaly coefficient is related with a holographic c-function.
Massive Yang-Mills theory based on the nonlinearly realized gauge group
Bettinelli, D.; Ferrari, R.; Quadri, A.
2008-02-15
We propose a subtraction scheme for a massive Yang-Mills theory realized via a nonlinear representation of the gauge group [here SU(2)]. It is based on the subtraction of the poles in D-4 of the amplitudes, in dimensional regularization, after a suitable normalization has been performed. Perturbation theory is in the number of loops, and the procedure is stable under iterative subtraction of the poles. The unphysical Goldstone bosons, the Faddeev-Popov ghosts, and the unphysical mode of the gauge field are expected to cancel out in the unitarity equation. The spontaneous symmetry breaking parameter is not a physical variable. We use the tools already tested in the nonlinear sigma model: hierarchy in the number of Goldstone boson legs and weak-power-counting property (finite number of independent divergent amplitudes at each order). It is intriguing that the model is naturally based on the symmetry SU(2){sub L} local x SU(2){sub R} global. By construction the physical amplitudes depend on the mass and on the self-coupling constant of the gauge particle and moreover on the scale parameter of the radiative corrections. The Feynman rules are in the Landau gauge.
On whole Abelian model dynamics
Chauca, J.; Doria, R.
2012-09-24
Physics challenge is to determine the objects dynamics. However, there are two ways for deciphering the part. The first one is to search for the ultimate constituents; the second one is to understand its behaviour in whole terms. Therefore, the parts can be defined either from elementary constituents or as whole functions. Historically, science has been moving through the first aspect, however, quarks confinement and complexity are interrupting this usual approach. These relevant facts are supporting for a systemic vision be introduced. Our effort here is to study on the whole meaning through gauge theory. Consider a systemic dynamics oriented through the U(1) - systemic gauge parameter which function is to collect a fields set {l_brace}A{sub {mu}I}{r_brace}. Derive the corresponding whole gauge invariant Lagrangian, equations of motion, Bianchi identities, Noether relationships, charges and Ward-Takahashi equations. Whole Lorentz force and BRST symmetry are also studied. These expressions bring new interpretations further than the usual abelian model. They are generating a systemic system governed by 2N+ 10 classical equations plus Ward-Takahashi identities. A whole dynamics based on the notions of directive and circumstance is producing a set determinism where the parts dynamics are inserted in the whole evolution. A dynamics based on state, collective and individual equations with a systemic interdependence.
Natural limits of electroweak model as contraction of its gauge group
NASA Astrophysics Data System (ADS)
Gromov, N. A.
2015-06-01
The low and higher energy limits of the electroweak model are obtained from the first principles of gauge theory. Both limits are given by the same contraction of the gauge group, but for the different consistent rescalings of the field space. Mathematical contraction parameter in both cases is interpreted as energy. Very weak neutrino-matter interactions are explained by zero tending contraction parameter, which depends on neutrino energy. The second consistent rescaling corresponds to the higher energy limit of the electroweak model. At the infinite energy all particles lose mass, electroweak interactions become long-range and are mediated by neutral currents. The limit model represents the development of the early Universe from the big bang up to the end of the first second.
Critical string from non-Abelian vortex in four dimensions
NASA Astrophysics Data System (ADS)
Shifman, M.; Yung, A.
2015-11-01
In a class of non-Abelian solitonic vortex strings supported in certain N = 2 super-Yang-Mills theories we search for the vortex which can behave as a critical fundamental string. We use the Polchinski-Strominger criterion of the ultraviolet completeness. We identify an appropriate four-dimensional bulk theory: it has the U (2) gauge group, the Fayet-Iliopoulos term and four flavor hypermultiplets. It supports semilocal vortices with the world-sheet theory for orientational (size) moduli described by the weighted CP (2 , 2) model. The latter is superconformal. Its target space is six-dimensional. The overall Virasoro central charge is critical. We show that the world-sheet theory on the vortex supported in this bulk model is the bona fide critical string.
Multiflavor QCD∗ on R3 ×S1: Studying transition from Abelian to non-Abelian confinement
NASA Astrophysics Data System (ADS)
Shifman, M.; Ünsal, M.
2009-11-01
The center-stabilized multiflavor QCD∗ theories formulated on R3 ×S1 exhibit both Abelian and non-Abelian confinement as a function of the S1 radius, similar to the Seiberg-Witten theory as a function of the mass deformation parameter. For sufficiently small number of flavors and small r (S1), we show occurrence of a mass gap in gauge fluctuations, and linear confinement. This is a regime of confinement without continuous chiral symmetry breaking (χSB). Unlike one-flavor theories where there is no phase transition in r (S1), the multiflavor theories possess a single phase transition associated with breaking of the continuous χS. We conjecture that the scale of the χSB is parametrically tied up with the scale of Abelian to non-Abelian confinement transition.
A non-perturbative argument for the non-abelian Higgs mechanism
De Palma, G.; Strocchi, F.
2013-09-15
The evasion of massless Goldstone bosons by the non-abelian Higgs mechanism is proved by a non-perturbative argument in the local BRST gauge. -- Highlights: •The perturbative explanation of the Higgs mechanism (HM) is not under mathematical control. •We offer a non-perturbative proof of the absence of Goldstone bosons from the non-abelian HM. •Our non-perturbative proof in the BRST gauge avoids a mean field ansatz and expansion.
Anomalous Abelian symmetry in the standard model
Ramond, P.
1995-12-31
The observed hierarchy of quark and lepton masses can be parametrized by nonrenormalizable operators with dimensions determined by an anomalous Abelian family symmetry, a gauge extension to the minimal supersymmetric standard model. Such an Abelian symmetry is generic to compactified superstring theories, with its anomalies compensated by the Green-Schwarz mechanism. If we assume these two symmetries to be the same, we find the electroweak mixing angle to be sin {sup 2}{theta}{sub {omega}} = 3/8 at the string scale, just by setting the ratio of the product of down quark to charged lepton masses equal to one at the string scale. This assumes no GUT structure. The generality of the result suggests a superstring origin for the standard model. We generalize our analysis to massive neutrinos, and mixings in the lepton sector.
Phenomenological analysis of heterotic strings: Non-abelian constructions and landscape studies
NASA Astrophysics Data System (ADS)
Wasnik, Vaibhav Hemant
String theory offers the unique promise of unifying all the known forces in nature. However, the internal consistency of the theory requires that spacetime have more than four dimensions. As a result, the extra dimensions must be compactified in some manner and how this compactification takes place is critical for determining the low-energy physical predictions of the theory. In this thesis we examine two distinct consequences of this fact. First, almost all of the prior research in string model-building has examined the consequences of compactifying on so-called "abelian" orbifolds. However, the most general class of compactifications, namely those on non-abelian orbifolds, remains almost completely unexplored. This thesis focuses on the low-energy phenomenological consequences of compactifying strings on non-abelian orbifolds. One of the main interests in pursuing these theories is that they can, in principle, naturally give rise to low-energy models which simultaneously have N=1 supersymmetry along with scalar particles transforming in the adjoint of the gauge group. These features, which are exceedingly difficult to achieve through abelian orbifolds, are exciting because they are the key ingredients in understanding how grand unification can emerge from string theory. Second, the need to compactify gives rise to a huge "landscape" of possible resulting low-energy phenomenologies. One of the goals of the landscape program in string theory is then to extract information about the space of string vacua in the form of statistical correlations between phenomenological features that are otherwise uncorrelated in field theory. Such correlations would thus represent features of string theory that hold independently of a vacuum-selection principle. In this thesis, we study statistical correlations between two features which are likely to be central to any potential description of nature at high-energy scales: gauge symmetries and spacetime supersymmetry. We analyze
Renormalization group and phase transitions in spin, gauge, and QCD like theories
NASA Astrophysics Data System (ADS)
Liu, Yuzhi
In this thesis, we study several different renormalization group (RG) methods, including the conventional Wilson renormalization group, Monte Carlo renormalization group (MCRG), exact renormalization group (ERG, or sometimes called functional RG), and tensor renormalization group (TRG). We use the two dimensional nearest neighbor Ising model to introduce many conventional yet important concepts. We then generalize the model to Dyson's hierarchical model (HM), which has rich phase properties depending on the strength of the interaction. The partition function zeros (Fisher zeros) of the HM model in the complex temperature plane is calculated and their connection with the complex RG flows is discussed. The two lattice matching method is used to construct both the complex RG flows and calculate the discrete beta functions. The motivation of calculating the discrete beta functions for various HM models is to test the matching method and to show how physically relevant fixed points emerge from the complex domain. We notice that the critical exponents calculated from the HM depend on the blocking parameter b. This motivated us to analyze the connection between the discrete and continuous RG transformation. We demonstrate numerical calculations of the ERG equations. We discuss the relation between Litim and Wilson-Polchinski equation and the effect of the cut-off functions in the ERG calculation. We then apply methods developed in the spin models to more complicated and more physically relevant lattice gauge theories and lattice quantum chromodynamics (QCD) like theories. Finite size scaling (FSS) technique is used to analyze the Binder cumulant of the SU(2) lattice gauge model. We calculate the critical exponent nu and omega of the model and show that it is in the same universality class as the three dimensional Ising model. Motivated by the walking technicolor theory, we study the strongly coupled gauge theories with conformal or near conformal properties. We compare
Non-Abelian strings in supersymmetric Yang-Mills
Shifman, M.
2012-09-26
I give a broad review of novel phenomena discovered in certain Yang-Mills theories: non-Abelian strings and confined monopoles. Then I explain how these phenomena allow one to study strong dynamics of gauge theories in four dimensions from two-dimensional models emerging on the string world sheet.
Investigation of gauge-fixed pure U(1) theory at strong coupling
NASA Astrophysics Data System (ADS)
Basak, S.; De, Asit K.
2002-03-01
We numerically investigate the phase diagram of pure U(1) gauge theory with gauge fixing at strong gauge coupling. The FM-FMD phase transition, which proved useful in defining Abelian lattice chiral gauge theory, persists also at strong gauge coupling. However, there the transition seems no longer to be continuous. At large gauge couplings we find evidences for confinement.
PyR@TE. Renormalization group equations for general gauge theories
NASA Astrophysics Data System (ADS)
Lyonnet, F.; Schienbein, I.; Staub, F.; Wingerter, A.
2014-03-01
Although the two-loop renormalization group equations for a general gauge field theory have been known for quite some time, deriving them for specific models has often been difficult in practice. This is mainly due to the fact that, albeit straightforward, the involved calculations are quite long, tedious and prone to error. The present work is an attempt to facilitate the practical use of the renormalization group equations in model building. To that end, we have developed two completely independent sets of programs written in Python and Mathematica, respectively. The Mathematica scripts will be part of an upcoming release of SARAH 4. The present article describes the collection of Python routines that we dubbed PyR@TE which is an acronym for “Python Renormalization group equations At Two-loop for Everyone”. In PyR@TE, once the user specifies the gauge group and the particle content of the model, the routines automatically generate the full two-loop renormalization group equations for all (dimensionless and dimensionful) parameters. The results can optionally be exported to LaTeX and Mathematica, or stored in a Python data structure for further processing by other programs. For ease of use, we have implemented an interactive mode for PyR@TE in form of an IPython Notebook. As a first application, we have generated with PyR@TE the renormalization group equations for several non-supersymmetric extensions of the Standard Model and found some discrepancies with the existing literature. Catalogue identifier: AERV_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AERV_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 924959 No. of bytes in distributed program, including test data, etc.: 495197 Distribution format: tar.gz Programming language: Python. Computer
A Gauge Theory of Massive Spin One Particles
NASA Astrophysics Data System (ADS)
Vyas, Vivek M.; Srinivasan, V.
2016-05-01
An Abelian gauge theory describing dynamics of massive spin one bosons is constructed. This is achieved by appending to the Maxwell action, a gauge invariant mass term. The theory is quantised in temporal as well as Lorentz gauge, and the corresponding Hilbert spaces are constructed. In both the gauges, it is found that, the theory respects Lorentz invariance, locality, causality and unitarity.
NASA Astrophysics Data System (ADS)
Shi, Yan-Liang; Shrock, Robert
2015-11-01
We study asymptotically free chiral gauge theories with an SU (N ) gauge group and chiral fermions transforming according to the antisymmetric rank-k tensor representation, Ak≡[k ]N , and the requisite number, nF ¯, of copies of fermions in the conjugate fundamental representation, F ¯ ≡[1] ¯ N , to render the theories anomaly-free. We denote these as AkF ¯ theories. We take N ≥2 k +1 so that nF ¯≥1 . The A2F ¯ theories form an infinite family with N ≥5 , but we show that the A3F ¯ and A4F ¯ theories are only asymptotically free for N in the respective ranges 7 ≤N ≤17 and 9 ≤N ≤11 , and that there are no asymptotically free AkF ¯ theories with k ≥5 . We investigate the types of ultraviolet to infrared evolution for these AkF ¯ theories and find that, depending on k and N , they may lead to a non-Abelian Coulomb phase, or may involve confinement with massless gauge-singlet composite fermions, bilinear fermion condensation with dynamical gauge and global symmetry breaking, or formation of multifermion condensates that preserve the gauge symmetry. We also show that there are no asymptotically free, anomaly-free SU (N ) SkF ¯ chiral gauge theories with k ≥3 , where Sk denotes the rank-k symmetric representation.
Renormalization group improved Yennie-Frautschi-Suura theory for Z/sup 0/ physics
Ward, B.F.L.
1987-06-01
Described is a recently developed renormalization group improved version of the program of Yennie, Frautschi and Suura for the exponentiation of infrared divergences in Abelian gauge theories. Particular attention is paid to the relevance of this renormalization group improved exponentiation to Z/sup 0/ physics at the SLC and LEP.
Non-Abelian family symmetries as portals to dark matter
NASA Astrophysics Data System (ADS)
de Medeiros Varzielas, I.; Fischer, O.
2016-01-01
Non-Abelian family symmetries offer a very promising explanation for the flavour structure in the Standard Model and its extensions. We explore the possibility that dark matter consists in fermions that transform under a family symmetry, such that the visible and dark sector are linked by the familons - Standard Model gauge singlet scalars, responsible for spontaneously breaking the family symmetry. We study three representative models with non-Abelian family symmetries that have been shown capable to explain the masses and mixing of the Standard Model fermions.
Escalante, Alberto Manuel-Cabrera, J.
2015-10-15
A detailed Faddeev–Jackiw quantization of an Abelian and non-Abelian exotic action for gravity in three dimensions is performed. We obtain for the theories under study the constraints, the gauge transformations, the generalized Faddeev–Jackiw brackets and we perform the counting of physical degrees of freedom. In addition, we compare our results with those found in the literature where the canonical analysis is developed, in particular, we show that both the generalized Faddeev–Jackiw brackets and Dirac’s brackets coincide to each other. Finally we discuss some remarks and prospects. - Highlights: • A detailed Faddeev–Jackiw analysis for exotic action of gravity is performed. • We show that Dirac’s brackets and Generalized [FJ] brackets are equivalent. • Without fixing the gauge exotic action is a non-commutative theory. • The fundamental gauge transformations of the theory are found. • Dirac and Faddeev–Jackiw approaches are compared.
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.
Supersymmetric composite gauge fields with compensators
NASA Astrophysics Data System (ADS)
Nishino, Hitoshi; Rajpoot, Subhash
2016-06-01
We study supersymmetric composite gauge theory, supplemented with compensator mechanism. As our first example, we give the formulation of N = 1 supersymmetric non-Abelian composite gauge theory without the kinetic term of a non-Abelian gauge field. The important ingredient is the Proca-Stueckelberg-type compensator scalar field that makes the gauge-boson field equation non-singular, i.e., the field equation can be solved for the gauge field algebraically as a perturbative expansion. As our second example, we perform the gauging of chiral-symmetry for N = 1 supersymmetry in four dimensions by a composite gauge field. These results provide supporting evidence for the consistency of the mechanism that combines the composite gauge field formulations and compensator formulations, all unified under supersymmetry.
On Geometrical Interpretation of Non-Abelian Flat Direction Constraints
NASA Astrophysics Data System (ADS)
Cleaver, G. B.; Nanopoulos, D. V.; Perkins, J. T.; Walker, J. W.
In order to produce a low-energy effective field theory from a string model, it is necessary to specify a vacuum state. In order that this vacuum be supersymmetric, it is well known that all field expectation values must be along so-called flat directions, leaving the F- and D-terms of the scalar potential to be zero. The situation becomes particularly interesting when one attempts to realize such directions while assigning vacuum expectation values to fields transforming under non-Abelian representations of the gauge group. Since the expectation value is now shared among multiple components of a field, satisfaction of flatness becomes an inherently geometrical problem in the group space. Furthermore, the possibility emerges that a single seemingly dangerous F-term might experience a self-cancellation among its components. The hope exists that the geometric language can provide an intuitive and immediate recognition of when the D and F conditions are simultaneously compatible, as well as a powerful tool for their comprehensive classification. This is the avenue explored in this paper, and applied to the cases of SU(2) and SO(2N), relevant respectively to previous attempts at reproducing the MSSM and the flipped SU(5) GUT. Geometrical interpretation of non-Abelian flat directions finds application to M-theory through the recent conjecture of equivalence between D-term strings and wrapped D-branes of Type II theory.1 Knowledge of the geometry of the flat direction "landscape" of a D-term string model could yield information about the dual brane model. It is hoped that the techniques encountered will be of benefit in extending the viability of the quasirealistic phenomenologies already developed.
Non-Abelian geometric phase and long-range atomic forces
NASA Technical Reports Server (NTRS)
Zygelman, B.
1990-01-01
It is shown how gauge fields, or geometric phases, manifest as observable effects in both bound and free diatom systems. It is shown that, in addition to altering energy splittings in bound systems, geometric phases induce transitions in levels separated by a finite-energy gap. An example is given where the non-Abelian gauge field couples nondegenerate electronic levels in a diatom. This gauge-field coupling gives rise to an observable effect. It is shown that when the diatom is 'pulled apart', the non-Abelian geometric phase manifests as a long-range atomic force.
Non-Abelian quantum holonomy of hydrogenlike atoms
Mousolou, Vahid Azimi; Canali, Carlo M.; Sjoeqvist, Erik
2011-09-15
We study the Uhlmann holonomy [Rep. Math. Phys. 24, 229 (1986)] of quantum states for hydrogenlike atoms where the intrinsic spin and orbital angular momentum are coupled by the spin-orbit interaction and are subject to a slowly varying magnetic field. We show that the holonomy for the orbital angular momentum and spin subsystems is non-Abelian while the holonomy of the whole system is Abelian. Quantum entanglement in the states of the whole system is crucially related to the non-Abelian gauge structure of the subsystems. We analyze the phase of the Wilson loop variable associated with the Uhlmann holonomy and find a relation between the phase of the whole system and corresponding marginal phases. Based on the results for the model system, we provide evidence that the phase of the Wilson loop variable and the mixed-state geometric phase [E. Sjoeqvist et al., Phys. Rev. Lett. 85, 2845 (2000).] are generally inequivalent.
Condensing Non-Abelian Quasiparticles
Hermanns, M.
2010-02-05
A most interesting feature of certain fractional quantum Hall states is that their quasiparticles obey non-Abelian fractional statistics. So far, candidate non-Abelian wave functions have been constructed from conformal blocks in cleverly chosen conformal field theories. In this work we present a hierarchy scheme by which we can construct daughter states by condensing non-Abelian quasiparticles (as opposed to quasiholes) in a parent state, and show that the daughters have a non-Abelian statistics that differs from the parent. In particular, we discuss the daughter of the bosonic, spin-polarized Moore-Read state at nu=4/3 as an explicit example.
Notoph gauge theory: Superfield formalism
NASA Astrophysics Data System (ADS)
Malik, R. P.
2011-05-01
We derive absolutely anticommuting Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for the 4D free Abelian 2-form gauge theory by exploiting the superfield approach to BRST formalism. The antisymmetric tensor gauge field of the above theory was christened as the "notoph" (i.e. the opposite of "photon") gauge field by Ogievetsky and Palubarinov way back in 1966-67. We briefly outline the problems involved in obtaining the absolute anticonimutativity of the (anti-) BRST transformations and their resolution within the framework of geometrical superfield approach to BRST formalism. One of the highlights of our results is the emergence of a Curci-Ferrari type of restriction in the context of 4D Abelian 2-form (notoph) gauge theory which renders the nilpotent (anti-) BRST symmetries of the theory to be absolutely anticommutative in nature.
Non-Abelian gerbes and enhanced Leibniz algebras
NASA Astrophysics Data System (ADS)
Strobl, Thomas
2016-07-01
We present the most general gauge-invariant action functional for coupled 1- and 2-form gauge fields with kinetic terms in generic dimensions, i.e., dropping eventual contributions that can be added in particular space-time dimensions only such as higher Chern-Simons terms. After appropriate field redefinitions it coincides with a truncation of the Samtleben-Szegin-Wimmer action. In the process one sees explicitly how the existence of a gauge-invariant functional enforces that the most general semistrict Lie 2-algebra describing the bundle of a non-Abelian gerbe gets reduced to a very particular structure, which, after the field redefinition, can be identified with the one of an enhanced Leibniz algebra. This is the first step towards a systematic construction of such functionals for higher gauge theories, with kinetic terms for a tower of gauge fields up to some highest form degree p , solved here for p =2 .
Extracting Flavor from Quiver Gauge Theories
NASA Astrophysics Data System (ADS)
Volansky, T.
2007-04-01
We consider a large class of models where an SU(5) gauge symmetry and a Froggatt-Nielsen (FN) Abelian flavor symmetry arise from a quiver gauge theory. Such quiver models are very restrictive and therefore have strong predictive power. In particular, under mild assumptions neutrino mass anarchy is predicted.
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.
NASA Astrophysics Data System (ADS)
Cvetič, G.; Kim, C. S.
We assume that the standard model (SM) breaks down around some energy Λ and is replaced there by a new (Higgsless) flavor gauge theory (FGT) with fewer input parameters in the interactions corresponding to the Yukawa sector of SM. This would imply more symmetry for the values of the Yukawa (running) parameters of SM at E Λ, possibly by a (approximate) flavor democracy (for the quark mass sector). We investigate this possibility by studying the renormalization group equations (RGE's) for the quark Yukawa couplings of SM with one and two Higgs doublets, by running them from the known physical values at low energies (E 1 GeV) to Λ (> 1 TeV) and comparing the resulting quark masses mq (E Λ) for various mt and υU/υD. Unlike previous investigations of these RGE's, we do not implement the requirement mt(Λpole) = ∞. We found that SM with two Higgs doublets (type 2) is most likely to experience a gradual transition to FGT. Our results also shed more light on the adequacy and deficiencies of the usual RGE approaches within TMSM and related models. We also found that, independent of the assumption of a transition mechanism to FGT, mt phy< ˜ 200 GeV for Λpole≪ ΛPlanck in most cases of SM with two Higgs doublets.
Wang, Juven C; Gu, Zheng-Cheng; Wen, Xiao-Gang
2015-01-23
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. We find new examples of mixed gauge-gravity actions for U(1) SPTs in (4+1)D via the gravitational Chern-Simons term. Field theory representations of SPT invariants not only serve as tools for classifying SPTs, but also guide us in designing physical probes for them. In addition, our field theory representations are independently powerful for studying group cohomology within the mathematical context. PMID:25658993
NASA Astrophysics Data System (ADS)
Wang, Juven C.; Gu, Zheng-Cheng; Wen, Xiao-Gang
2015-01-01
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. We find new examples of mixed gauge-gravity actions for U(1) SPTs in (4 +1 )D via the gravitational Chern-Simons term. Field theory representations of SPT invariants not only serve as tools for classifying SPTs, but also guide us in designing physical probes for them. In addition, our field theory representations are independently powerful for studying group cohomology within the mathematical context.
Topological invariants measured for Abelian and non-Abelian monopole fields
NASA Astrophysics Data System (ADS)
Sugawa, Seiji; Salces Carcoba, Francisco; Perry, Abigail; Yue, Yuchen; Putra, Andika; Spielman, Ian
2016-05-01
Understanding the topological nature of physical systems is an important topic in contemporary physics, ranging from condensed matter to high energy. In this talk, I will present experiments measuring the 1st and 2nd Chern number in a four-level quantum system both with degenerate and non-degenerate energies. We engineered the system's Hamiltonian by coupling hyperfine ground states of rubidium-87 Bose-Einstein condensates with rf and microwave fields. We non-adiabatically drove the system and measured the linear response to obtain the local (non-Abelian) Berry curvatures. Then, the Chern numbers were evaluated on (hyper-)spherical manifolds in parameter space. We obtain Chern numbers close to unity for both the 1st and the 2nd Chern numbers. The non-zero Chern number can be interpreted as monopole residing inside the manifold. For our system, the monopoles correspond to a Dirac monopole for non-degenerate spectra and a Yang monopole for our degenerate case. We also show how the dynamical evolution under non-Abelian gauge field emerged in degenerate quantum system is different from non-degenerate case by showing path-dependent acquisition of non-Abelian geometric phase and Wilson loops.
Nonlocal Hamiltonian gauge theories and their connection with lattice Hamiltonians
Ktorides, C.N.; Mavromatos, N.E.
1985-06-15
We introduce the concept of primitive Hamiltonian density for nonlocal Abelian gauge theories. We subsequently study the local limit both with respect to the continuum and with respect to a lattice structure introduced via hypercubic cells. The non-Abelian case is also discussed.
Linear resistivity from non-abelian black holes
NASA Astrophysics Data System (ADS)
Herzog, Christopher P.; Huang, Kuo-Wei; Vaz, Ricardo
2014-11-01
Starting with the holographic p-wave superconductor, we show how to obtain a finite DC conductivity through a non-abelian gauge transformation. The translational symmetry is preserved. We obtain phenomenological similarities with high temperature cuprate superconductors. Our results suggest that a lattice or impurities are not essential to produce a finite DC resistivity with a linear temperature dependence. An analogous field theory calculation for free fermions, presented in the appendix, indicates our results may be a special feature of strong interactions.
Gauge invariance and the physical spectrum in the two-Higgs-doublet model
NASA Astrophysics Data System (ADS)
Maas, Axel; Pedro, Leonardo
2016-03-01
Observable states are gauge invariant. In a non-Abelian gauge theory, these are necessarily composite operators. We investigate the spectrum of these operators in the two-Higgs-doublet model. For this purpose, we are working along the lines of the Fröhlich-Morchio-Strocchi mechanism to relate the physical spectrum to the spectrum of the elementary particles. We also investigate the consequences of spontaneous breaking of the global (custodial) symmetry group. Finally, we briefly comment on how to test the results using lattice methods.
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
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
Effective action for the Abelian Higgs model in FLRW
George, Damien P.; Mooij, Sander; Postma, Marieke E-mail: smooij@nikhef.nl
2012-11-01
We compute the divergent contributions to the one-loop action of the U(1) Abelian Higgs model. The calculation allows for a Friedmann-Lemaitre-Robertson-Walker space-time and a time-dependent expectation value for the scalar field. Treating the time-dependent masses as two-point interactions, we use the in-in formalism to compute the first, second and third order graphs that contribute quadratic and logarithmic divergences to the effective scalar action. Working in R{sub ξ} gauge we show that the result is gauge invariant upon using the equations of motion.
Non-Abelian clouds around Reissner-Nordström black holes: The existence line
NASA Astrophysics Data System (ADS)
Radu, Eugen; Tchrakian, D. H.; Yang, Yisong
2016-06-01
A known feature of electrically charged Reissner-Nordström-anti-de Sitter planar black holes is that they can become unstable when considered as solutions of Einstein-Yang-Mills theory. The mechanism for this is that the linearized Yang-Mills equations in the background of the Reissner-Nordström (RN) black holes possess a normalizable zero mode, resulting in non-Abelian (nA) magnetic clouds near the horizon. In this work we show that the same pattern may occur also for asymptotically flat RN black holes. Different from the anti-de Sitter case, in the Minkowskian background the prerequisites for the existence of the nA clouds are (i) a large enough gauge group, and (ii) the presence of some extra interaction terms in the matter Lagrangian. To illustrate this mechanism we present two specific examples, one in four- and the other in five-dimensional asymptotically flat spacetime. In the first case, we augment the usual S U (3 ) Yang-Mills Lagrangian with a higher-order (quartic) curvature term, while for the second one we add the Chern-Simons density to the S O (6 ) Yang-Mills system. In both cases, an Abelian gauge symmetry is spontaneously broken near a RN black hole horizon with the appearance of a condensate of nA gauge fields. In addition to these two examples, we review the corresponding picture for anti-de Sitter black holes. All these solutions are studied both analytically and numerically, existence proofs being provided for nA clouds in the background of RN black holes. The proofs use shooting techniques which are suggested by and in turn offer insights for our numerical methods. They indicate that, for a black hole of given mass, appropriate electric charge values are required to ensure the existence of solutions interpolating desired boundary behavior at the horizons and spatial infinity.
NASA Astrophysics Data System (ADS)
Ye, Peng; Gu, Zheng-Cheng
2016-05-01
Symmetry-protected topological phases (SPT) are short-range entangled gapped states protected by global symmetry. Nontrivial SPT phases cannot be adiabatically connected to the trivial disordered state (or atomic insulator) as long as certain global symmetry G is unbroken. At low energies, most of the two-dimensional SPTs with Abelian symmetry can be described by topological quantum field theory (TQFT) of the multicomponent Chern-Simons type. However, in contrast to the fractional quantum Hall effect where TQFT can give rise to interesting bulk anyons, TQFT for SPTs only supports trivial bulk excitations. The essential question in TQFT descriptions for SPTs is to understand how the global symmetry is implemented in the partition function. In this paper, we systematically study TQFT of three-dimensional SPTs with unitary Abelian symmetry (e.g., ZN1×ZN2×... ). In addition to the usual multicomponent B F topological term at level-1, we find that there are new topological terms with quantized coefficients (e.g., a1∧a2∧d a2 and a1∧a2∧a3∧a4 ) in TQFT actions, where a1,a2,... are 1-form U(1) gauge fields. These additional topological terms cannot be adiabatically turned off as long as G is unbroken. By investigating symmetry transformations for the TQFT partition function, we end up with the classification of SPTs that is consistent with the well-known group cohomology approach. We also discuss how to gauge the global symmetry and possible TQFT descriptions of Dijkgraaf-Witten gauge theory.
Solving flavor puzzles with quiver gauge theories
NASA Astrophysics Data System (ADS)
Antebi, Yaron E.; Nir, Yosef; Volansky, Tomer
2006-04-01
We consider a large class of models where the SU(5) gauge symmetry and a Froggatt-Nielsen (FN) Abelian flavor symmetry arise from a U(5)×U(5) quiver gauge theory. An intriguing feature of these models is a relation between the gauge representation and the horizontal charge, leading to a restricted set of possible FN charges. Requiring that quark masses are hierarchical, the lepton flavor structure is uniquely determined. In particular, neutrino mass anarchy is predicted.
Solving flavor puzzles with quiver gauge theories
Antebi, Yaron E.; Nir, Yosef; Volansky, Tomer
2006-04-01
We consider a large class of models where the SU(5) gauge symmetry and a Froggatt-Nielsen (FN) Abelian flavor symmetry arise from a U(5)xU(5) quiver gauge theory. An intriguing feature of these models is a relation between the gauge representation and the horizontal charge, leading to a restricted set of possible FN charges. Requiring that quark masses are hierarchical, the lepton flavor structure is uniquely determined. In particular, neutrino mass anarchy is predicted.
NASA Astrophysics Data System (ADS)
Wen, Xiao-Gang
2013-08-01
In this paper, we systematically study gauge anomalies in bosonic and fermionic weak-coupling gauge theories with gauge group G (which can be continuous or discrete) in d space-time dimensions. We show a very close relation between gauge anomalies for gauge group G and symmetry-protected trivial (SPT) orders (also known as symmetry-protected topological (SPT) orders) with symmetry group G in one-higher dimension. The SPT phases are classified by group cohomology class Hd+1(G,R/Z). Through a more careful consideration, we argue that the gauge anomalies are described by the elements in Free[Hd+1(G,R/Z)]⊕Hπ˙d+1(BG,R/Z). The well known Adler-Bell-Jackiw anomalies are classified by the free part of Hd+1(G,R/Z) (denoted as Free[Hd+1(G,R/Z)]). We refer to other kinds of gauge anomalies beyond Adler-Bell-Jackiw anomalies as non-ABJ gauge anomalies, which include Witten SU(2) global gauge anomalies. We introduce a notion of π-cohomology group, Hπ˙d+1(BG,R/Z), for the classifying space BG, which is an Abelian group and include Tor[Hd+1(G,R/Z)] and topological cohomology group Hd+1(BG,R/Z) as subgroups. We argue that Hπ˙d+1(BG,R/Z) classifies the bosonic non-ABJ gauge anomalies and partially classifies fermionic non-ABJ anomalies. Using the same approach that shows gauge anomalies to be connected to SPT phases, we can also show that gravitational anomalies are connected to topological orders (i.e., patterns of long-range entanglement) in one-higher dimension.
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.
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.
Non-abelian dynamics in first-order cosmological phase transitions
Johnson, Mikkel B.; Kisslinger, Leonard S.; Henley, Ernest M.; Hwang, P. W-Y.; Stevens, T.
2004-01-01
Bubble collisions in cosmological phase transitions are explored, taking the non-abelian character of the gauge fields into account. Both the QCD and electroweak phase transitions are considered. Numerical solutions of the field equations in several limits are presented. The investigations reported in this talk have been motivated by an interest in studying cosmological phase transitions quantitatively, taking the non-abelian character of the gauge fields into account. Ultimately, we hope to identify observable consequences of cosmological phase transitions. First-order phase transitions proceed by nucleation of bubbles of the broken phase in the background of the symmetric phase. Bubble collisions are of special interest, as they may lead to observable effects such as correlations in the cosmic microwave background (CMB) or as seeds of galactic and extra-galactic magnetic fields. The quantum chromodynamic (QCD) and the electroweak (EW) phase transitions are both candidates of interest in these respects. The Lagrangian driving both the QCD and the EW phase transitions are essentially known and make it possible to approach the physics of the phase transitions from first principles. However, a difficulty to making reliable predictions is that the fundamental guage fields in both these instances are non-abelian: the gluon field in QCD and the W and Z fields in the EW case. The quantitative role of non-abelian fields in cosmological phase transitions is poorly known and difficult to calculate due to the nonlinearities arising from the non-abelian character of the gauge fields.
Renormalization Group and Phase Transitions in Spin, Gauge, and QCD Like Theories
Liu, Yuzhi
2013-08-01
In this thesis, we study several different renormalization group (RG) methods, including the conventional Wilson renormalization group, Monte Carlo renormalization group (MCRG), exact renormalization group (ERG, or sometimes called functional RG), and tensor renormalization group (TRG).
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.
Coverings of topological semi-abelian algebras
NASA Astrophysics Data System (ADS)
Mucuk, Osman; Demir, Serap
2016-08-01
In this work, we study on a category of topological semi-abelian algebras which are topological models of given an algebraic theory T whose category of models is semi-abelian; and investigate some results on the coverings of topological models of such theories yielding semi-abelian categories. We also consider the internal groupoid structure in the semi-abelian category of T-algebras, and give a criteria for the lifting of internal groupoid structure to the covering groupoids.
Two-component Abelian sandpile models.
Alcaraz, F C; Pyatov, P; Rittenberg, V
2009-04-01
In one-component Abelian sandpile models, the toppling probabilities are independent quantities. This is not the case in multicomponent models. The condition of associativity of the underlying Abelian algebras imposes nonlinear relations among the toppling probabilities. These relations are derived for the case of two-component quadratic Abelian algebras. We show that Abelian sandpile models with two conservation laws have only trivial avalanches. PMID:19518280
The existence of self-dual vortices in a non-Abelian {Phi}{sup 2} Chern-Simons theory
Chen Shouxin; Wang Ying
2010-09-15
Applying the dynamic shooting method, we proved the existence of nontopological radially symmetric n-vortex solutions to the self-dual equation in non-Abelian Chern-Simons gauge theory with a {Phi}{sup 2}-type potential. Moreover, we obtained all possible radially symmetric nontopological bare (or 0-vortex) solutions in the non-Abelian Chern-Simons model. Meanwhile, we established the asymptotic behavior for the solutions as |x|{yields}{infinity}.
Abelian Hidden Sectors at a GeV
Morrissey, David E.; Poland, David; Zurek, Kathryn; /Fermilab /Michigan U.
2009-04-16
We discuss mechanisms for naturally generating GeV-scale hidden sectors in the context of weak-scale supersymmetry. Such low mass scales can arise when hidden sectors are more weakly coupled to supersymmetry breaking than the visible sector, as happens when supersymmetry breaking is communicated to the visible sector by gauge interactions under which the hidden sector is uncharged, or if the hidden sector is sequestered from gravity-mediated supersymmetry breaking. We study these mechanisms in detail in the context of gauge and gaugino mediation, and present specific models of Abelian GeV-scale hidden sectors. In particular, we discuss kinetic mixing of a U(1){sub x} gauge force with hypercharge, singlets or bi-fundamentals which couple to both sectors, and additional loop effects. Finally, we investigate the possible relevance of such sectors for dark matter phenomenology, as well as for low- and high-energy collider searches.
Gauge-covariant decomposition and magnetic monopole for G (2 ) Yang-Mills field
NASA Astrophysics Data System (ADS)
Matsudo, Ryutaro; Kondo, Kei-Ichi
2016-08-01
We provide a gauge-covariant decomposition of the Yang-Mills field with the exceptional gauge group G (2 ), which extends the field decomposition proposed by Cho, Duan-Ge, and Faddeev-Niemi for the S U (N ) Yang-Mills field. As an application of the decomposition, we derive a new expression of the non-Abelian Stokes theorem for the Wilson loop operator in an arbitrary representation of G (2 ). The resulting new form is used to define gauge-invariant magnetic monopoles in the G (2 ) Yang-Mills theory. Moreover, we obtain the quantization condition to be satisfied by the resulting magnetic charge. The method given in this paper is general enough to be applicable to any semisimple Lie group other than S U (N ) and G (2 ).
Nonabelian 2D gauge theories for determinantal Calabi-Yau varieties
NASA Astrophysics Data System (ADS)
Jockers, Hans; Kumar, Vijay; Lapan, Joshua M.; Morrison, David R.; Romo, Mauricio
2012-11-01
The two-dimensional supersymmetric gauged linear sigma model (GLSM) with abelian gauge groups and matter fields has provided many insights into string theory on Calabi-Yau manifolds of a certain type: complete intersections in toric varieties. In this paper, we consider two GLSM constructions with nonabelian gauge groups and charged matter whose infrared CFTs correspond to string propagation on determinantal Calabi-Yau varieties, furnishing another broad class of Calabi-Yau geometries in addition to complete intersections. We show that these two models — which we refer to as the PAX and the PAXY model — are dual descriptions of the same low-energy physics. Using GLSM techniques, we determine the quantum Kähler moduli space of these varieties and find no disagreement with existing results in the literature.
Light-induced gauge fields for ultracold atoms.
Goldman, N; Juzeliūnas, G; Öhberg, P; Spielman, I B
2014-12-01
Gauge fields are central in our modern understanding of physics at all scales. At the highest energy scales known, the microscopic universe is governed by particles interacting with each other through the exchange of gauge bosons. At the largest length scales, our Universe is ruled by gravity, whose gauge structure suggests the existence of a particle-the graviton-that mediates the gravitational force. At the mesoscopic scale, solid-state systems are subjected to gauge fields of different nature: materials can be immersed in external electromagnetic fields, but they can also feature emerging gauge fields in their low-energy description. In this review, we focus on another kind of gauge field: those engineered in systems of ultracold neutral atoms. In these setups, atoms are suitably coupled to laser fields that generate effective gauge potentials in their description. Neutral atoms 'feeling' laser-induced gauge potentials can potentially mimic the behavior of an electron gas subjected to a magnetic field, but also, the interaction of elementary particles with non-Abelian gauge fields. Here, we review different realized and proposed techniques for creating gauge potentials-both Abelian and non-Abelian-in atomic systems and discuss their implication in the context of quantum simulation. While most of these setups concern the realization of background and classical gauge potentials, we conclude with more exotic proposals where these synthetic fields might be made dynamical, in view of simulating interacting gauge theories with cold atoms. PMID:25422950
Gauge equivalence in QCD: The Weyl and Coulomb gauges
NASA Astrophysics Data System (ADS)
Haller, Kurt; Ren, Hai-Cang
2003-10-01
The Weyl-gauge (Aa0=0) QCD Hamiltonian is unitarily transformed to a representation in which it is expressed entirely in terms of gauge-invariant quark and gluon fields. In a subspace of gauge-invariant states we have constructed that implement the non-Abelian Gauss’s law, this unitarily transformed Weyl-gauge Hamiltonian can be further transformed and, under appropriate circumstances, can be identified with the QCD Hamiltonian in the Coulomb gauge. We demonstrate an isomorphism that materially facilitates the application of this Hamiltonian to a variety of physical processes, including the evaluation of S-matrix elements. This isomorphism relates the gauge-invariant representation of the Hamiltonian and the required set of gauge-invariant states to a Hamiltonian of the same functional form but dependent on ordinary unconstrained Weyl-gauge fields operating within a space of “standard” perturbative states. The fact that the gauge-invariant chromoelectric field is not Hermitian has important implications for the functional form of the Hamiltonian finally obtained. When this non-Hermiticity is taken into account, the “extra” vertices in the Christ-Lee’ Coulomb-gauge Hamiltonian are natural outgrowths of the formalism. When this non-Hermiticity is neglected, the Hamiltonian used in the earlier work of Gribov and others results.
Correlation-induced non-Abelian quantum holonomies
NASA Astrophysics Data System (ADS)
Johansson, Markus; Ericsson, Marie; Singh, Kuldip; Sjöqvist, Erik; Williamson, Mark S.
2011-04-01
In the context of two-particle interferometry, we construct a parallel transport condition that is based on the maximization of coincidence intensity with respect to local unitary operations on one of the subsystems. The dependence on correlation is investigated and it is found that the holonomy group is generally non-Abelian, but Abelian for uncorrelated systems. It is found that our framework contains the Lévay geometric phase (2004 J. Phys. A: Math. Gen. 37 1821) in the case of two-qubit systems undergoing local SU(2) evolutions.
Quirks in supersymmetry with gauge coupling unification
NASA Astrophysics Data System (ADS)
Martin, Stephen P.
2011-02-01
I investigate the phenomenology of supersymmetric models with extra vectorlike supermultiplets that couple to the standard model gauge fields and transform as the fundamental representation of a new confining non-Abelian gauge interaction. If perturbative gauge coupling unification is to be maintained, the new group can be SU(2), SU(3), or SO(3). The impact on the sparticle mass spectrum is explored, with particular attention to the gaugino mass dominated limit in which the supersymmetric flavor problem is naturally solved. The new confinement length scale is astronomical for SO(3), so the new particles are essentially free. For the SU(2) and SU(3) cases, the new vectorlike fermions are quirks; pair production at colliders yields quirk-antiquirk states bound by stable flux tubes that are microscopic but long compared to the new confinement scale. I study the reach of the Tevatron and LHC for the optimistic case that in a significant fraction of events the quirk-antiquirk bound state will lose most of its energy before annihilating as quirkonium.
NASA Astrophysics Data System (ADS)
Karndumri, Parinya
2016-08-01
We study various supersymmetric renormalization group (RG) flows of N =3 Chern-Simons-Matter theory in three dimensions by using four-dimensional N =3 gauged supergravity coupled to eight vector multiplets with S O (3 )×S U (3 ) gauge group. The AdS4 critical point preserving the full S O (3 )×S U (3 ) provides a gravity dual of N =3 superconformal field theory with flavor symmetry S U (3 ). We study the scalar potential and identify a new supersymmetric AdS4 critical point preserving the full N =3 supersymmetry and unbroken S O (3 )×U (1 ) symmetry. An analytic RG flow solution interpolating between S O (3 )×S U (3 ) and S O (3 )×U (1 ) critical points is explicitly given. We then investigate possible RG flows from these AdS4 critical points to nonconformal field theories in the IR. All of the singularities appearing in the IR turn out to be physically acceptable. Furthermore, we look for supersymmetric solutions of the form AdS2×Σ2 with Σ2 being a two-sphere or a two-dimensional hyperbolic space and find a number of AdS2 geometries preserving four supercharges with S O (2 )×S O (2 )×S O (2 ) and S O (2 )×S O (2 ) symmetries.
On discrete symmetries for a whole Abelian model
NASA Astrophysics Data System (ADS)
Chauca, J.; Doria, R.
2012-10-01
Considering the whole concept applied to gauge theory a nonlinear abelian model is derived. A next step is to understand on the model properties. At this work, it will be devoted to discrete symmetries. For this, we will work based in two fields reference systems. This whole gauge symmetry allows to be analyzed through different sets which are the constructor basis {Dμ,Xiμ} and the physical basis {GμI}. Taking as fields reference system the diagonalized spin-1 sector, P, C, T and PCT symmetries are analyzed. They show that under this systemic model there are conservation laws driven for the parts and for the whole. It develops the meaning of whole-parity, field-parity and so on. However it is the whole symmetry that rules. This means that usually forbidden particles as pseudovector photons can be introduced through such whole abelian system. As result, one notices that the fields whole {GμI} manifest a quanta diversity. It involves particles with different spins, masses and discrete quantum numbers under a same gauge symmetry. It says that without violating PCT symmetry different possibilities on discrete symmetries can be accommodated.
On discrete symmetries for a whole Abelian model
Chauca, J.; Doria, R.
2012-09-24
Considering the whole concept applied to gauge theory a nonlinear abelian model is derived. A next step is to understand on the model properties. At this work, it will be devoted to discrete symmetries. For this, we will work based in two fields reference systems. This whole gauge symmetry allows to be analyzed through different sets which are the constructor basis {l_brace}D{sub {mu}},X{sup i}{sub {mu}}{r_brace} and the physical basis {l_brace}G{sub {mu}I}{r_brace}. Taking as fields reference system the diagonalized spin-1 sector, P, C, T and PCT symmetries are analyzed. They show that under this systemic model there are conservation laws driven for the parts and for the whole. It develops the meaning of whole-parity, field-parity and so on. However it is the whole symmetry that rules. This means that usually forbidden particles as pseudovector photons can be introduced through such whole abelian system. As result, one notices that the fields whole {l_brace}G{sub {mu}I}{r_brace} manifest a quanta diversity. It involves particles with different spins, masses and discrete quantum numbers under a same gauge symmetry. It says that without violating PCT symmetry different possibilities on discrete symmetries can be accommodated.
Köppl, Christoph; Werner, Hans-Joachim
2015-04-28
Electron correlation methods based on symmetry-adapted canonical Hartree-Fock orbitals can be speeded up significantly in the well known group theoretical manner, using the fact that integrals vanish unless the integrand is totally symmetric. In contrast to this, local electron correlation methods cannot benefit from such simplifications, since the localized molecular orbitals (LMOs) generally do not transform according to irreducible representations of the underlying point group symmetry. Instead, groups of LMOs become symmetry-equivalent and this can be exploited to accelerate local calculations. We describe an implementation of such a symmetry treatment for density-fitted local Møller-Plesset perturbation theory, using various types of virtual orbitals: Projected atomic orbitals, orbital specific virtuals, and pair natural orbitals. The savings by the symmetry treatment are demonstrated by calculations for several large molecules having different point group symmetries. Benchmarks for the parallel execution efficiency of our method are also presented.
Refined algebraic quantisation in a system with nonconstant gauge invariant structure functions
Martínez-Pascual, Eric
2013-08-15
In a previous work [J. Louko and E. Martínez-Pascual, “Constraint rescaling in refined algebraic quantisation: Momentum constraint,” J. Math. Phys. 52, 123504 (2011)], refined algebraic quantisation (RAQ) within a family of classically equivalent constrained Hamiltonian systems that are related to each other by rescaling one momentum-type constraint was investigated. In the present work, the first steps to generalise this analysis to cases where more constraints occur are developed. The system under consideration contains two momentum-type constraints, originally abelian, where rescalings of these constraints by a non-vanishing function of the coordinates are allowed. These rescalings induce structure functions at the level of the gauge algebra. Providing a specific parametrised family of real-valued scaling functions, the implementation of the corresponding rescaled quantum momentum-type constraints is performed using RAQ when the gauge algebra: (i) remains abelian and (ii) undergoes into an algebra of a nonunimodular group with nonconstant gauge invariant structure functions. Case (ii) becomes the first example known to the author where an open algebra is handled in refined algebraic quantisation. Challenging issues that arise in the presence of non-gauge invariant structure functions are also addressed.
Inverse avalanches on Abelian sandpiles
Chau, H.F. Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois 61801-3080 )
1994-11-01
A simple and computationally efficient way of finding inverse avalanches for Abelian sandpiles, called the inverse particle addition operator, is presented. In addition, the method is shown to be optimal in the sense that it requires the minimum amount of computation among methods of the same kind. The method is also conceptually succinct because avalanche and inverse avalanche are placed in the same footing.
Appearance of gauge structure in simple dynamical systems
NASA Technical Reports Server (NTRS)
Wilczek, F.; Zee, A.
1984-01-01
By generalizing a construction of Berry and Simon, it is shown that non-Abelian gauge fields arise in the adiabatic development of simple quantum mechanical systems. Characteristics of the gauge fields are related to energy splittings, which may be observable in real systems. Similar phenomena are found for suitable classical systems.
The Fock-Schwinger Gauge in the Bfv Formalism
NASA Astrophysics Data System (ADS)
Barcelos-Neto, J.; Galvão, Carlos A. P.; Gaete, P.
We consider the implementation of a properly modified form of the Fock-Schwinger gauge condition in a general non-Abelian gauge theory in the context of the BFV formalism. Arguments are presented to justify the necessity of modifying the original Fock-Schwinger condition. The free field propagator and the general Ward identity are also calculated.
Gauged Two Higgs Doublet Model confronts the LHC 750 GeV diphoton anomaly
NASA Astrophysics Data System (ADS)
Huang, Wei-Chih; Tsai, Yue-Lin Sming; Yuan, Tzu-Chiang
2016-08-01
In light of the recent 750 GeV diphoton anomaly observed at the LHC, we study the possibility of accommodating the deviation from the standard model prediction based on the recently proposed Gauged Two Higgs Doublet Model. The model embeds two Higgs doublets into a doublet of a non-abelian gauge group SU(2)H, while the standard model SU(2)L right-handed fermion singlets are paired up with new heavy fermions to form SU(2)H doublets, and SU(2)L left-handed fermion doublets are singlets under SU(2)H. An SU(2)H scalar doublet, which provides masses to the new heavy fermions as well as the SU(2)H gauge bosons, can be produced via gluon fusion and subsequently decays into two photons with the new fermions circulating the triangle loops to account for the deviation from the standard model prediction.
Decorated tensor network renormalization for lattice gauge theories and spin foam models
NASA Astrophysics Data System (ADS)
Dittrich, Bianca; Mizera, Sebastian; Steinhaus, Sebastian
2016-05-01
Tensor network techniques have proved to be powerful tools that can be employed to explore the large scale dynamics of lattice systems. Nonetheless, the redundancy of degrees of freedom in lattice gauge theories (and related models) poses a challenge for standard tensor network algorithms. We accommodate for such systems by introducing an additional structure decorating the tensor network. This allows to explicitly preserve the gauge symmetry of the system under coarse graining and straightforwardly interpret the fixed point tensors. We propose and test (for models with finite Abelian groups) a coarse graining algorithm for lattice gauge theories based on decorated tensor networks. We also point out that decorated tensor networks are applicable to other models as well, where they provide the advantage to give immediate access to certain expectation values and correlation functions.
NASA Astrophysics Data System (ADS)
Hidajatullah-Maksoed, Widastra
2015-04-01
Arthur Cayley at least investigate by creating the theory of permutation group[F:∖∖Group_theory.htm] where in cell elements addressing of the lattice Qmf used a Cayley tree, the self-afine object Qmf is described by the combination of the finite groups of rotation & inversion and the infinite groups of translation & dilation[G Corso & LS Lacena: ``Multifractal lattice and group theory'', Physica A: Statistical Mechanics &Its Applications, 2005, v 357, issue I, h 64-70; http://www.sciencedirect.com/science/articel/pii/S0378437105005005 ] hence multifractal can be related to group theory. Many grateful Thanks to HE. Mr. Drs. P. SWANTORO & HE. Mr. Ir. SARWONO KUSUMAATMADJA.
Universal attractor in a highly occupied non-Abelian plasma
NASA Astrophysics Data System (ADS)
Berges, J.; Boguslavski, K.; Schlichting, S.; Venugopalan, R.
2014-06-01
We study the thermalization process in highly occupied non-Abelian plasmas at weak coupling. The nonequilibrium dynamics of such systems is classical in nature and can be simulated with real-time lattice gauge theory techniques. We provide a detailed discussion of this framework and elaborate on the results reported in J. Berges, K. Boguslavski, S. Schlichting, and R. Venugopalan, Phys. Rev. D 89, 074011 (2014), 10.1103/PhysRevD.89.074011 along with novel findings. We demonstrate the emergence of universal attractor solutions, which govern the nonequilibrium evolution on large time scales both for nonexpanding and expanding non-Abelian plasmas. The turbulent attractor for a nonexpanding plasma drives the system close to thermal equilibrium on a time scale t ˜Q-1αs-7/4. The attractor solution for an expanding non-Abelian plasma leads to a strongly interacting albeit highly anisotropic system at the transition to the low-occupancy or quantum regime. This evolution in the classical regime is, within the uncertainties of our simulations, consistent with the "bottom up" thermalization scenario [R. Baier, A. H. Mueller, D. Schiff, and D. T. Son, Phys. Lett. B 502, 51 (2001), 10.1016/S0370-2693(01)00191-5]. While the focus of this paper is to understand the nonequilibrium dynamics in weak coupling asymptotics, we also discuss the relevance of our results for larger couplings in the early time dynamics of heavy ion collision experiments.
Vojta, Matthias; Mitchell, Andrew K; Zschocke, Fabian
2016-07-15
Kitaev's honeycomb-lattice compass model describes a spin liquid with emergent fractionalized excitations. Here, we study the physics of isolated magnetic impurities coupled to the Kitaev spin-liquid host. We reformulate this Kondo-type problem in terms of a many-state quantum impurity coupled to a multichannel bath of Majorana fermions and present the numerically exact solution using Wilson's numerical renormalization group technique. Quantum phase transitions occur as a function of Kondo coupling and locally applied field. At zero field, the impurity moment is partially screened only when it binds an emergent gauge flux, while otherwise it becomes free at low temperatures. We show how Majorana degrees of freedom determine the fixed-point properties, make contact with Kondo screening in pseudogap Fermi systems, and discuss effects away from the dilute limit. PMID:27472132
NASA Astrophysics Data System (ADS)
Vojta, Matthias; Mitchell, Andrew K.; Zschocke, Fabian
2016-07-01
Kitaev's honeycomb-lattice compass model describes a spin liquid with emergent fractionalized excitations. Here, we study the physics of isolated magnetic impurities coupled to the Kitaev spin-liquid host. We reformulate this Kondo-type problem in terms of a many-state quantum impurity coupled to a multichannel bath of Majorana fermions and present the numerically exact solution using Wilson's numerical renormalization group technique. Quantum phase transitions occur as a function of Kondo coupling and locally applied field. At zero field, the impurity moment is partially screened only when it binds an emergent gauge flux, while otherwise it becomes free at low temperatures. We show how Majorana degrees of freedom determine the fixed-point properties, make contact with Kondo screening in pseudogap Fermi systems, and discuss effects away from the dilute limit.
Heterotic non-Abelian string of a finite length
NASA Astrophysics Data System (ADS)
Monin, S.; Shifman, M.; Yung, A.
2016-06-01
We consider non-Abelian strings in N =2 supersymmetric quantum chromodynamics (QCD) with the U (N ) gauge group and Nf=N quark flavors deformed by a mass term for the adjoint matter. This deformation breaks N =2 supersymmetry down to N =1 . Dynamics of orientational zero modes on the string world sheet are described then by C P (N -1 ) model with N =(0 ,2 ) supersymmetry. We study the string of a finite length L assuming compactification on a cylinder (periodic boundary conditions). The world-sheet theory is solved in the large-N approximation. At N =∞ we find a rich phase structure in the (L ,u ) plane where u is a deformation parameter. At large L and intermediate u we find a phase with broken Z2 N symmetry, N vacua and a mass gap. At large values of L and u still larger we have the Z2 N-symmetric phase with a single vacuum and massless fermions. In both phases N =(0 ,2 ) supersymmetry is spontaneously broken. We also observe a phase with would-be broken SU (N ) symmetry at small L (it is broken only for N =∞ ). In the latter phase the mass gap vanishes and the vacuum energy is zero in the leading 1 /N approximation. We expect that at large but finite N corrections O (1 /N ) will break N =(0 ,2 ) supersymmetry. Simultaneously, the phase transitions will become rapid crossovers. Finally we discuss how the observed rich phase structure matches the N =(2 ,2 ) limit in which the world-sheet theory has a single phase with the mass gap independent of L .
ERIC Educational Resources Information Center
Kohl, Timothy
2012-01-01
A pair of elementary exercises, one from topology, the other from group theory are such that if one replaces three words in the topology problem, you get the group theory problem and vice-versa. This suggests connections between the two that are explored here.
Fun with the Abelian Higgs model
NASA Astrophysics Data System (ADS)
Malinský, Michal
2013-05-01
In calculations of the elementary scalar spectra of spontaneously broken gauge theories there are a number of subtleties which, though it is often unnecessary to deal with them in the order-of-magnitude type of calculations, have to be taken into account if fully consistent results are sought for. Within the "canonical" effective-potential approach these are, for instance: the need to handle infinite series of nested commutators of derivatives of field-dependent mass matrices, the need to cope with spurious IR divergences emerging in the consistent leading-order approximation and, in particular, the need to account for the fine interplay between the renormalization effects in the one- and two-point Green functions which, indeed, is essential for the proper stable vacuum identification and, thus, for the correct interpretation of the results. In this note we illustrate some of these issues in the realm of the minimal Abelian Higgs model and two of its simplest extensions including extra heavy scalars in the spectrum in attempt to exemplify the key aspects of the usual "hierarchy problem" lore in a very specific and simple setting. We emphasize that, regardless of the omnipresent polynomial cut-off dependence in the one-loop corrections to the scalar two-point function, the physical Higgs boson mass is always governed by the associated symmetry-breaking VEV and, as such, it is generally as UV-robust as all other VEV-driven masses in the theory.
Hattori, Chuichiro; Matsunaga, Mamoru; Matsuoka, Takeo
2011-01-01
In the standard model the hypercharges of quarks and leptons are not determined by the gauge group SU(3){sub c}xSU(2){sub L}xU(1){sub Y} alone. We show that, if we choose the semidirect product group [SU(3){sub c}xSU(2){sub L}]xU(1){sub Y} as its gauge group, the hyperchages are settled to be n/6 mod Z(n=0,1,3,4). In addition, the conditions for gauge-anomaly cancellation give strong constraints. As a result, the ratios of the hypercharges are uniquely determined and the gravitational anomaly is automatically canceled. The standard charge assignment to quarks and leptons can be properly reproduced. For exotic matter fields their hypercharges are also discussed.
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.
Gauge-flation and cosmic no-hair conjecture
Maleknejad, A.; Sheikh-Jabbari, M.M.; Soda, Jiro E-mail: jabbari@theory.ipm.ac.ir
2012-01-01
Gauge-flation, inflation from non-Abelian gauge fields, was introduced in [1, 2]. In this work, we study the cosmic no-hair conjecture in gauge-flation. Starting from Bianchi-type I cosmology and through analytic and numeric studies we demonstrate that the isotropic FLRW inflation is an attractor of the dynamics of the theory and that the anisotropies are damped within a few e-folds, in accord with the cosmic no-hair conjecture.
Classical gauged massless Rarita-Schwinger fields
NASA Astrophysics Data System (ADS)
Adler, Stephen L.
2015-10-01
We show that, in contrast to known results in the massive case, a minimally gauged massless Rarita-Schwinger field yields a consistent classical theory, with a generalized fermionic gauge invariance realized as a canonical transformation. To simplify the algebra, we study a two-component left chiral reduction of the massless theory. We formulate the classical theory in both Lagrangian and Hamiltonian form for a general non-Abelian gauging and analyze the constraints and the Rarita-Schwinger gauge invariance of the action. An explicit wave front calculation for Abelian gauge fields shows that wavelike modes do not propagate with superluminal velocities. An analysis of Rarita-Schwinger spinor scattering from gauge fields shows that adiabatic decoupling fails in the limit of zero gauge field amplitude, invalidating various "no-go" theorems based on "on-shell" methods that claim to show the impossibility of gauging Rarita-Schwinger fields. Quantization of Rarita-Schwinger fields, using many formulas from this paper, is taken up in the following paper.
Gauge coupling unification in gauge-Higgs grand unification
NASA Astrophysics Data System (ADS)
Yamatsu, Naoki
2016-04-01
We discuss renormalization group equations for gauge coupling constants in gauge-Higgs grand unification on five-dimensional Randall-Sundrum warped space. We show that all four-dimensional Standard Model gauge coupling constants are asymptotically free and are effectively unified in SO(11) gauge-Higgs grand unified theories on 5D Randall-Sundrum warped space.
Non-Abelian vortices and non-Abelian statistics
Lo, H.; Preskill, J. )
1993-11-15
We study the interactions of non-Abelian vortices in two spatial dimensions. These interactions have novel features, because the Aharonov-Bohm effect enables a pair of vortices to exchange quantum numbers. The cross section for vortex-vortex scattering is typically a multivalued function of the scattering angle. There can be an exchange contribution to the vortex-vortex scattering amplitude that adds coherently with the direct amplitude, even if the two vortices have distinct quantum numbers. Thus two vortices can be indistinguishable'' even though they are not the same.
Properties of a consistent Lorentz-violating Abelian gauge theory
Alexandre, J.; Vergou, A.
2011-06-15
A Lorentz-violating modification of massless QED is proposed, with higher-order space derivatives for the photon field. The fermion dynamical mass generation is studied with the Schwinger-Dyson approach. Perturbative properties of the model are calculated at one-loop and discussed at higher-order loops, showing the consistency of the model. We explain that there is no contradiction with the definition of the speed of light c, although fermions see an effective light cone, with a maximum speed smaller than c.
Competing Abelian and non-Abelian topological orders in ν =1 /3 +1 /3 quantum Hall bilayers
NASA Astrophysics Data System (ADS)
Geraedts, Scott; Zaletel, Michael P.; Papić, Zlatko; Mong, Roger S. K.
2015-05-01
Bilayer quantum Hall systems, realized either in two separated wells or in the lowest two subbands of a wide quantum well, provide an experimentally realizable way to tune between competing quantum orders at the same filling fraction. Using newly developed density matrix renormalization group techniques combined with exact diagonalization, we return to the problem of quantum Hall bilayers at filling ν =1 /3 +1 /3 . We first consider the Coulomb interaction at bilayer separation d , bilayer tunneling energy ΔSAS, and individual layer width w , where we find a phase diagram which includes three competing Abelian phases: a bilayer Laughlin phase (two nearly decoupled ν =1 /3 layers), a bilayer spin-singlet phase, and a bilayer symmetric phase. We also study the order of the transitions between these phases. A variety of non-Abelian phases has also been proposed for these systems. While absent in the simplest phase diagram, by slightly modifying the interlayer repulsion we find a robust non-Abelian phase which we identify as the "interlayer-Pfaffian" phase. In addition to non-Abelian statistics similar to the Moore-Read state, it exhibits a novel form of bilayer-spin charge separation. Our results suggest that ν =1 /3 +1 /3 systems merit further experimental study.
Investigations in gauge theories, topological solitons and string theories. Final report
Not Available
1993-06-01
This is the Final Report on a supported research project on theoretical particle physics entitled ``Investigations in Gauge Theories, Topological Solitons and String Theories.`` The major theme of particle theory pursued has been within the rubric of the standard model, particularly on the interplay between symmetries and dynamics. Thus, the research has been carried out primarily in the context of gauge with or without chiral fermions and in effective chiral lagrangian field theories. The topics studied include the physical implications of abelian and non-abelian anomalies on the spectrum and possible dynamical symmetry breaking in a wide range of theories. A wide range of techniques of group theory, differential geometry and function theory have been applied to probe topological and conformal properties of quantum field theories in two and higher dimensions, the breaking of global chiral symmetries by vector-like gauge theories such as QCD,the phenomenology of a possibly strongly interacting Higgs sector within the minimal standard model, and the relevance of solitonic ideas to non-perturbative phenomena at SSC energies.
Lieber, Bryan A; Wilson, Taylor A; Bell, Randy S; Ashley, William W; Barrow, Daniel L; Wolfe, Stacey Quintero
2014-11-01
Indirect costs of the interview tour can be prohibitive. The authors sought to assess the desire of interviewees to mitigate these costs through ideas such as sharing hotel rooms and transportation, willingness to stay with local students, and the preferred modality to coordinate this collaboration. A survey link was posted on the Uncle Harvey website and the Facebook profile page of fourth-year medical students from 6 different medical schools shortly after the 2014 match day. There were a total of 156 respondents to the survey. The majority of the respondents were postinterview medical students (65.4%), but preinterview medical students (28.2%) and current residents (6.4%) also responded to the survey. Most respondents were pursuing a field other than neurosurgery (75.0%) and expressed a desire to share a hotel room and/or transportation (77.4%) as well as stay in the dorm room of a medical student at the program in which they are interviewing (70.0%). Students going into neurosurgery were significantly more likely to be interested in sharing hotel/transportation (89.2% neurosurgery vs 72.8% nonneurosurgery; p = 0.040) and in staying in the dorm room of a local student when on interviews (85.0% neurosurgery vs 57.1% nonneurosurgery; p = 0.040) than those going into other specialties. Among postinterview students, communication was preferred to be by private, email identification-only chat room. Given neurosurgery resident candidates' interest in collaborating to reduce interview costs, consideration should be given to creating a system that could allow students to coordinate cost sharing between interviewees. Moreover, interviewees should be connected to local students from neurosurgery interest groups as a resource. PMID:25363428
Bilayer quantum Hall phase transitions and the orbifold non-Abelian fractional quantum Hall states
Barkeshli, Maissam; Wen Xiaogang
2011-09-15
We study continuous quantum phase transitions that can occur in bilayer fractional quantum Hall (FQH) systems as the interlayer tunneling and interlayer repulsion are tuned. We introduce a slave-particle gauge theory description of a series of continuous transitions from the (ppq) Abelian bilayer states to a set of non-Abelian FQH states, which we dub orbifold FQH states, of which the Z{sub 4} parafermion (Read-Rezayi) state is a special case. This provides an example in which Z{sub 2} electron fractionalization leads to non-Abelian topological phases. The naive ''ideal'' wave functions and ideal Hamiltonians associated with these orbifold states do not in general correspond to incompressible phases but, instead, lie at a nearby critical point. We discuss this unusual situation from the perspective of the pattern-of-zeros/vertex algebra frameworks and discuss implications for the conceptual foundations of these approaches. Due to the proximity in the phase diagram of these non-Abelian states to the (ppq) bilayer states, they may be experimentally relevant, both as candidates for describing the plateaus in single-layer systems at filling fractions 8/3 and 12/5 and as a way to tune to non-Abelian states in double-layer or wide quantum wells.
Abelian and non-abelian D-brane effective actions
NASA Astrophysics Data System (ADS)
Koerber, P.
2004-09-01
In this Ph.D. thesis, accepted at the Vrije Universiteit Brussel, we review and elaborate on a method to find the D-brane effective action, based on BPS equations. Firstly, both for the Yang-Mills action and the Born-Infeld action it is shown that these configurations are indeed BPS, i.e. solutions to these equations saturate a Bogomolny bound and leave some supersymmetry unbroken. Next, we use the BPS equations as a tool to construct the D-brane effective action and require that (a deformation of) these equations should still imply the equations of motion in more general cases. In the abelian case we managed to calculate all order in four-derivative corrections to the effective action and the BPS equations while in the non-abelian case we obtained the effective action up to order 4. Furthermore, we discuss a check based on the spectrum of strings stretching between intersecting branes. Finally, this Ph.D. thesis also discusses the construction of a boundary superspace which would be the first step to use the method of Weyl invariance in N = 2 superspace in order to again construct the D-brane effective action. A more detailed summary of each section can be found in the introduction.
Topologically Massive Non-Abelian Theory:. Superfield Approach
NASA Astrophysics Data System (ADS)
Krishna, S.; Shukla, A.; Malik, R. P.
We apply the well-established techniques of geometrical superfield approach to Becchi-Rouet-Stora-Tyutin (BRST) formalism in the context of four (3+1)-dimensional (4D) dynamical non-Abelian 2-form gauge theory by exploiting its inherent "scalar" and "vector" gauge symmetry transformations and derive the corresponding off-shell nilpotent and absolutely anticommuting BRST and anti-BRST symmetry transformations. Our approach leads to the derivation of three (anti-)BRST invariant Curci-Ferrari (CF)-type restrictions that are found to be responsible for the absolute anticommutativity of the BRST and anti-BRST symmetry transformations. We derive the coupled Lagrangian densities that respect the (anti-)BRST symmetry transformations corresponding to the "vector" gauge transformations. We also capture the (anti-)BRST invariance of the CF-type restrictions and coupled Lagrangian densities within the framework of our superfield approach. We obtain, furthermore, the off-shell nilpotent (anti-)BRST symmetry transformations when the (anti-)BRST symmetry transformations corresponding to the "scalar" and "vector" gauge symmetries are merged together. These off-shell nilpotent "merged" (anti-)BRST symmetry transformations are, however, found to be non-anticommuting in nature.
NASA Astrophysics Data System (ADS)
Ortín, Tomás; Ramírez, Pedro F.
2016-09-01
We construct a supersymmetric black ring solution of SU (2) N = 1, d = 5 Super-Einstein-Yang-Mills (SEYM) theory by adding a distorted BPST instanton to an Abelian black ring solution of the same theory. The change cannot be observed from spatial infinity: neither the mass, nor the angular momenta or the values of the scalars at infinity differ from those of the Abelian ring. The entropy is, however, sensitive to the presence of the non-Abelian instanton, and it is smaller than that of the Abelian ring, in analogy to what happens in the supersymmetric colored black holes recently constructed in the same theory and in N = 2, d = 4 SEYM. By taking the limit in which the two angular momenta become equal we derive a non-Abelian generalization of the BMPV rotating black-hole solution.
G2HDM: Gauged Two Higgs Doublet Model
NASA Astrophysics Data System (ADS)
Huang, Wei-Chih; Tsai, Yue-Lin Sming; Yuan, Tzu-Chiang
2016-04-01
A novel model embedding the two Higgs doublets in the popular two Higgs doublet models into a doublet of a non-abelian gauge group SU(2) H is presented. The Standard Model SU(2) L right-handed fermion singlets are paired up with new heavy fermions to form SU(2) H doublets, while SU(2) L left-handed fermion doublets are singlets under SU(2) H . Distinctive features of this anomaly-free model are: (1) Electroweak symmetry breaking is induced from spontaneous symmetry breaking of SU(2) H via its triplet vacuum expectation value; (2) One of the Higgs doublet can be inert, with its neutral component being a dark matter candidate as protected by the SU(2) H gauge symmetry instead of a discrete Z 2 symmetry in the usual case; (3) Unlike Left-Right Symmetric Models, the complex gauge fields ( W 1 ' ∓ W 2 ' ) (along with other complex scalar fields) associated with the SU(2) H do not carry electric charges, while the third component W 3 ' can mix with the hypercharge U(1) Y gauge field and the third component of SU(2) L ; (4) Absence of tree level flavour changing neutral current is guaranteed by gauge symmetry; and etc. In this work, we concentrate on the mass spectra of scalar and gauge bosons in the model. Constraints from previous Z' data at LEP and the Large Hadron Collider measurements of the Standard Model Higgs mass, its partial widths of γγ and Zγ modes are discussed.
NASA Astrophysics Data System (ADS)
Khan, Mayukh; Teo, Jeffrey; Hughes, Taylor
2014-03-01
We consider bosonic abelian Fractional Quantum Hall (FQH) and Fractional Quantum Spin Hall (FQSH) states with edge theories drawn from the ADE Kac Moody algebras at level 1 . This set of systems have `anyonic' symmetries that leave braiding and fusion invariant Remarkably, the group of anyonic symmetries for this class of models is isomorphic to the symmetries of the Dynkin diagrams of the particular ADE Lie Algebra under consideration. The triality symmetry of the Dynkin diagram of so(8) leads to the largest anyonic symmetry group S3 (the permutation group on 3 elements). Each element of the anyonic symmetry group corresponds to a distinct way of gapping out the edge (i.e., each element corresponds to a Lagrangian subgroup). Junctions between two distinct gapped edges host non abelian twist defects with quantum dimensions (> 1). In the case of so(8) we have more exotic twist defects with non-abelian fusion. We acknowledge support from the U.S. Department of Energy, Division of Materials Sciences under Award No. DE-FG02- 07ER46453 (MK, TLH) and the Simons Foundation (JT).
Gauge bosons at zero and finite temperature
NASA Astrophysics Data System (ADS)
Maas, Axel
2013-03-01
Gauge theories of the Yang-Mills type are the single most important building block of the standard model of particle physics and beyond. They are an integral part of the strong and weak interactions, and in their Abelian version of electromagnetism. Since Yang-Mills theories are gauge theories their elementary particles, the gauge bosons, cannot be described without fixing a gauge. Therefore, to obtain their properties a quantized and gauge-fixed setting is necessary. Beyond perturbation theory, gauge-fixing in non-Abelian gauge theories is obstructed by the Gribov-Singer ambiguity, which requires the introduction of non-local constraints. The construction and implementation of a method-independent gauge-fixing prescription to resolve this ambiguity is the single most important first step to describe gauge bosons beyond perturbation theory. Proposals for such a procedure, generalizing the perturbative Landau gauge, are described here. Their implementation are discussed for two example methods, lattice gauge theory and the quantum equations of motion. After gauge-fixing, it is possible to study gauge bosons in detail. The most direct access is provided by their correlation functions. The corresponding two- and three-point correlation functions are presented at all energy scales. These give access to the properties of the gauge bosons, like their absence from the asymptotic physical state space, particle-like properties at high energies, and the running coupling. Furthermore, auxiliary degrees of freedom are introduced during gauge-fixing, and their properties are discussed as well. These results are presented for two, three, and four dimensions, and for various gauge algebras. Finally, the modifications of the properties of gauge bosons at finite temperature are presented. Evidence is provided that these reflect the phase structure of Yang-Mills theory. However, it is found that the phase transition is not deconfining the gauge bosons, although the bulk
Constraints on abelian extensions of the Standard Model from two-loop vacuum stability and U(1) B- L
NASA Astrophysics Data System (ADS)
Corianò, Claudio; Rose, Luigi Delle; Marzo, Carlo
2016-02-01
We present a renormalization group study of the scalar potential in a minimal U(1) B- L extension of the Standard Model involving one extra heavier Higgs and three heavy right-handed neutrinos with family universal B-L charge assignments. We implement a type-I seesaw for the masses of the light neutrinos of the Standard Model. In particular, compared to a previous study, we perform a two-loop extension of the evolution, showing that two-loop effects are essential for the study of the stability of the scalar potential up to the Planck scale. The analysis includes the contribution of the kinetic mixing between the two abelian gauge groups, which is radiatively generated by the evolution, and the one-loop matching conditions at the electroweak scale. By requiring the stability of the potential up to the Planck mass, significant constraints on the masses of the heavy neutrinos, on the gauge couplings and the mixing in the Higgs sector are identified.
On Geometrical Interpretation of Non-Abelian D and F-Flat Direction Constraints
NASA Astrophysics Data System (ADS)
Walker, Joel; Cleaver, Gerald; Nanopoulos, Dimitri; Perkins, John
2004-10-01
In order to produce a low energy effective field theory from a string model, it is necessary to specify a vacuum state. In order that this vacuum be supersymmetric, it is well known that all field expectation values must be along so-called flat directions, leaving the F- and D-terms of the scalar potential to be zero. The situation becomes particularly interesting when one attempts to realize such directions while assigning VEVS to fields transforming under non-Abelian representations of the gauge group. Since the expectation value is now shared among multiple components of a field, satisfaction of flatness becomes an inherently geometrical problem in the group space. Furthermore, the possibility emerges that a single seemingly dangerous F-term might experience a self-cancellation among its components. The hope exists that the geometric language can provide an intuitive and immediate recognition of when the D and F conditions are simultaneously compatible, as well as a powerful tool for their comprehensive classification. This is the avenue explored in this study, and applied to the cases of SU(2) and SO(2N), relevant respectively to previous attempts at reproducing the MSSM and the flipped SU(5) GUT. It is hoped that the techniques encountered will be of benefit in extending the viability of the quasi-realistic phenomenologies already developed.
The Abelian Higgs model and a minimal length in an un-particle scenario
NASA Astrophysics Data System (ADS)
Gaete, Patricio; Spallucci, Euro
2014-01-01
We consider both the Abelian Higgs model and the impact of a minimal length in the un-particle sector. It is shown that even if the Higgs field takes a non-vanishing vacuum expectation value (v.e.v.), gauge interaction keeps its long-range character leading to an effective gauge symmetry restoration. The effect of a quantum-gravity-induced minimal length on a physical observable is then estimated by using a physically based alternative to the usual Wilson loop approach. Interestingly, we obtain an ultraviolet finite interaction energy described by a confluent hypergeometric function, which shows a remarkable richness of behavior.
On the zero modes of the Faddeev-Popov operator in the Landau gauge
Landim, R. R.; Vilar, L. C. Q. Lemes, V. E. R.; Ventura, O. S.
2014-02-15
Following Henyey procedure [Phys. Rev. D 20, 1460 (1979)], we construct examples of zero modes of the Faddeev-Popov operator in the Landau gauge in Euclidean space in D dimensions, for both SU(2) and SU(3) groups. We obtain gauge field configurations A{sub μ}{sup a} which give rise to a field strength, F{sub μν}{sup a}=∂{sub μ}A{sub ν}{sup a}−∂{sub ν}A{sub μ}{sup a}+f{sup abc}A{sub μ}{sup b}A{sub ν}{sup c}, whose nonlinear term, f{sup abc}A{sub μ}{sup b}A{sub ν}{sup c}, turns out to be non-vanishing. To our knowledge, this is the first time where such a non-abelian configuration is explicitly obtained in the case of SU(3) in 4D.
Instanton-mediated baryon number violation in non-universal gauge extended models
NASA Astrophysics Data System (ADS)
Fuentes-Martín, J.; Portolés, J.; Ruiz-Femenía, P.
2015-01-01
Instanton solutions of non-abelian Yang-Mills theories generate an effective action that may induce lepton and baryon number violations, namely Δ B = Δ L = n f , being n f the number of families coupled to the gauge group. In this article we study instanton mediated processes in a SU(2) ℓ ⊗SU(2) h ⊗U(1) extension of the Standard Model that breaks universality by singularizing the third family. In the construction of the instanton Green functions we account systematically for the inter-family mixing. This allows us to use the experimental bounds on proton decay in order to constrain the gauge coupling of SU(2) h . Tau lepton non-leptonic and radiative decays with Δ B = Δ L = 1 are also analysed.
Abelian and non-Abelian bosonization: The operator solution of the WZW. sigma. model
do Amaral, R.L.P.G. ); Stephany Ruiz, J.E. )
1991-03-15
The complete equivalence between the Abelian and the non-Abelian bosonization formalisms for the treatment of SU({ital N}) fermions in two dimensions is analyzed and the operator solution of the Wess-Zumino-Witten nonlinear {sigma} model, written in terms of the scalar fields of the non-Abelian construction, is obtained. The importance of the order and disorder operators is stressed. In particular, they are used to show that an adequate reinterpretation of Mandelstam's formula gives the fermion representation in the non-Abelian bosonization formalism.
NASA Astrophysics Data System (ADS)
Markov, Yuri A.; Markova, Margaret A.; Shishmarev, Alexey A.
2010-10-01
Based on the most general principles of reality, gauge and reparametrization invariance, a problem of constructing the action describing dynamics of a classical color-charged particle interacting with background non-Abelian gauge and fermion fields is considered. The cases of the linear and quadratic dependence of a Lagrangian on background Grassmann fermion field are discussed. It is shown that in both cases in general there exists an infinite number of interaction terms, which should be included in the Lagrangian in question. Employing a simple iteration scheme, examples of the construction of the first few gauge-covariant currents and sources induced by a moving particle with non-Abelian charge are given. It is found that these quantities, by a suitable choice of parameters, exactly reproduce additional currents and sources previously obtained in Markov and Markova (2007 Nucl. Phys. A 784 443) on the basis of heuristic considerations.
Non-abelian dark matter solutions for Galactic gamma-ray excess and Perseus 3.5 keV X-ray line
Cheung, Kingman; Huang, Wei-Chih; Tsai, Yue-Lin Sming
2015-05-26
We attempt to explain simultaneously the Galactic center gamma-ray excess and the 3.5 keV X-ray line from the Perseus cluster based on a class of non-abelian SU(2) DM models, in which the dark matter and an excited state comprise a “dark” SU(2) doublet. The non-abelian group kinetically mixes with the standard model gauge group via dimensions-5 operators. The dark matter particles annihilate into standard model fermions, followed by fragmentation and bremsstrahlung, and thus producing a continuous spectrum of gamma-rays. On the other hand, the dark matter particles can annihilate into a pair of excited states, each of which decays back into the dark matter particle and an X-ray photon, which has an energy equal to the mass difference between the dark matter and the excited state, which is set to be 3.5 keV. The large hierarchy between the required X-ray and γ-ray annihilation cross-sections can be achieved by a very small kinetic mixing between the SM and dark sector, which effectively suppresses the annihilation into the standard model fermions but not into the excited state.
NASA Astrophysics Data System (ADS)
Escobar, C. A.; Urrutia, L. F.
2015-07-01
After imposing current conservation together with the Gauss law as initial conditions on the Abelian Nambu model, we prove that the resulting theory is equivalent to standard QED in the nonlinear gauge (AμAμ-n2M2) =0 , to all orders in perturbation theory. We show this by writing both models in terms of the same variables, which produce identical Feynman rules for the interactions and propagators. A crucial point is to verify that the Faddeev-Popov ghosts arising from the gauge fixing procedure in the QED sector decouple to all orders. We verify this decoupling by following a method like that employed in Yang-Mills theories when investigating the behavior of axial gauges. The equivalence between the two theories supports the idea that gauge particles can be envisaged as the Goldstone bosons originating from spontaneous Lorentz symmetry breaking.
Quantum Hall effects in a non-Abelian honeycomb lattice
NASA Astrophysics Data System (ADS)
Li, Ling; Hao, Ningning; Liu, Guocai; Bai, Zhiming; Li, Zai-Dong; Chen, Shu; Liu, W. M.
2015-12-01
We study the tunable quantum Hall effects in a non-Abelian honeycomb optical lattice which is a multi-Dirac-point system. We find that the quantum Hall effects present different features with the change in relative strengths of several perturbations. Namely, the quantum spin Hall effect can be induced by gauge-field-dressed next-nearest-neighbor hopping, which, together with a Zeeman field, can induce the quantum anomalous Hall effect characterized by different Chern numbers. Furthermore, we find that the edge states of the multi-Dirac-point system represent very different features for different boundary geometries, in contrast with the generic two-Dirac-point system. Our study extends the borders of the field of quantum Hall effects in a honeycomb optical lattice with multivalley degrees of freedom.
Minimal non-Abelian model of atomic dark matter
NASA Astrophysics Data System (ADS)
Choquette, Jeremie; Cline, James M.
2015-12-01
A dark sector resembling the Standard Model, where the abundance of matter is explained by baryon and lepton asymmetries and stable constituents bind to form atoms, is a theoretically appealing possibility. We show that a minimal model with a hidden SU(2) gauge symmetry broken to U(1), with a Dirac fermion doublet, suffices to realize this scenario. Supplemented with a dark Higgs doublet that gets no vacuum expectation value, we readily achieve the dark matter asymmetry through leptogenesis. The model can simultaneously have three portals to the Standard Model, through the Higgs, non-Abelian kinetic mixing, and the heavy neutrino, with interesting phenomenology for direct and collider searches, as well as cosmologically relevant dark matter self-interactions. Exotic bound states consisting of two fermions and a doubly charged vector boson can exist in one phase of the theory.
Cold-atom quantum simulator for SU(2) Yang-Mills lattice gauge theory.
Zohar, Erez; Cirac, J Ignacio; Reznik, Benni
2013-03-22
Non-Abelian gauge theories play an important role in the standard model of particle physics, and unfold a partially unexplored world of exciting physical phenomena. In this Letter, we suggest a realization of a non-Abelian lattice gauge theory-SU(2) Yang-Mills in (1 + 1) dimensions, using ultracold atoms. Remarkably, and in contrast to previous proposals, in our model gauge invariance is a direct consequence of angular momentum conservation and thus is fundamental and robust. Our proposal may serve as well as a starting point for higher-dimensional realizations. PMID:25166817
Studying critical string emerging from non-Abelian vortex in four dimensions
NASA Astrophysics Data System (ADS)
Koroteev, P.; Shifman, M.; Yung, A.
2016-08-01
Recently a special vortex string was found [5] in a class of soliton vortices supported in four-dimensional Yang-Mills theories that under certain conditions can become infinitely thin and can be interpreted as a critical ten-dimensional string. The appropriate bulk Yang-Mills theory has the U (2) gauge group and the Fayet-Iliopoulos term. It supports semilocal non-Abelian vortices with the world-sheet theory for orientational and size moduli described by the weighted CP (2 , 2) model. The full target space is R4 ×Y6 where Y6 is a non-compact Calabi-Yau space. We study the above vortex string from the standpoint of string theory, focusing on the massless states in four dimensions. In the generic case all massless modes are non-normalizable, hence, no massless gravitons or vector fields are predicted in the physical spectrum. However, at the selfdual point (at strong coupling) weighted CP (2 , 2) admits deformation of the complex structure, resulting in a single massless hypermultiplet in the bulk. We interpret it as a composite "baryon."
Exponentiation of eikonal cross sections in nonabelian gauge theories
NASA Astrophysics Data System (ADS)
Gatheral, J. G. M.
1983-12-01
A theorem is presented which generalises the well-known exponentiation property of eikonal cross sections in abelian gauge theories to the nonabelian case. Address after September 1, 1983: Bank of America, 25 Cannon Street, London EC4P 4HN, UK.
Aspects of entanglement entropy for gauge theories
NASA Astrophysics Data System (ADS)
Soni, Ronak M.; Trivedi, Sandip P.
2016-01-01
A definition for the entanglement entropy in a gauge theory was given recently in arXiv:1501.02593. Working on a spatial lattice, it involves embedding the physical state in an extended Hilbert space obtained by taking the tensor product of the Hilbert space of states on each link of the lattice. This extended Hilbert space admits a tensor product decomposition by definition and allows a density matrix and entanglement entropy for the set of links of interest to be defined. Here, we continue the study of this extended Hilbert space definition with particular emphasis on the case of Non-Abelian gauge theories.
Gauged WZW Models via Equivariant Cohomology
NASA Astrophysics Data System (ADS)
García-Compeán, Hugo; Paniagua, Pablo
The problem of finding a systematic computation of the gauge-invariant extension of WZW term by using equivariant cohomology is addressed. Witten's analysis for the two-dimensional case is extended to higher dimensions, in particular to four dimensions. It is shown that Cartan's model is used to find the anomaly cancellation condition while Weil's model is more appropriated to express the gauge-invariant extension of the WZW term. In the process we point out that both models are also useful to emphasize some nice relations with the Abelian anomaly.
Gauge interaction as periodicity modulation
NASA Astrophysics Data System (ADS)
Dolce, Donatello
2012-06-01
The paper is devoted to a geometrical interpretation of gauge invariance in terms of the formalism of field theory in compact space-time dimensions (Dolce, 2011) [8]. In this formalism, the kinematic information of an interacting elementary particle is encoded on the relativistic geometrodynamics of the boundary of the theory through local transformations of the underlying space-time coordinates. Therefore gauge interactions are described as invariance of the theory under local deformations of the boundary. The resulting local variations of the field solution are interpreted as internal transformations. The internal symmetries of the gauge theory turn out to be related to corresponding space-time local symmetries. In the approximation of local infinitesimal isometric transformations, Maxwell's kinematics and gauge invariance are inferred directly from the variational principle. Furthermore we explicitly impose periodic conditions at the boundary of the theory as semi-classical quantization condition in order to investigate the quantum behavior of gauge interaction. In the abelian case the result is a remarkable formal correspondence with scalar QED.
Standard model with partial gauge invariance
NASA Astrophysics Data System (ADS)
Chkareuli, J. L.; Kepuladze, Z.
2012-03-01
We argue that an exact gauge invariance may disable some generic features of the Standard Model which could otherwise manifest themselves at high energies. One of them might be related to the spontaneous Lorentz invariance violation (SLIV), which could provide an alternative dynamical approach to QED and Yang-Mills theories with photon and non-Abelian gauge fields appearing as massless Nambu-Goldstone bosons. To see some key features of the new physics expected we propose partial rather than exact gauge invariance in an extended SM framework. This principle applied, in some minimal form, to the weak hypercharge gauge field B μ and its interactions, leads to SLIV with B field components appearing as the massless Nambu-Goldstone modes, and provides a number of distinctive Lorentz breaking effects. Being naturally suppressed at low energies they may become detectable in high energy physics and astrophysics. Some of the most interesting SLIV processes are considered in significant detail.
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.
Ultracold quantum gases and lattice systems: quantum simulation of lattice gauge theories
NASA Astrophysics Data System (ADS)
Wiese, U.-J.
2013-11-01
Abelian and non-Abelian gauge theories are of central importance in many areas of physics. In condensed matter physics, Abelian U(1) lattice gauge theories arise in the description of certain quantum spin liquids. In quantum information theory, Kitaev's toric code is a Z(2) lattice gauge theory. In particle physics, Quantum Chromodynamics (QCD), the non-Abelian SU(3) gauge theory of the strong interactions between quarks and gluons, is non-perturbatively regularized on a lattice. Quantum link models extend the concept of lattice gauge theories beyond the Wilson formulation, and are well suited for both digital and analog quantum simulation using ultracold atomic gases in optical lattices. Since quantum simulators do not suffer from the notorious sign problem, they open the door to studies of the real-time evolution of strongly coupled quantum systems, which are impossible with classical simulation methods. A plethora of interesting lattice gauge theories suggests itself for quantum simulation, which should allow us to address very challenging problems, ranging from confinement and deconfinement, or chiral symmetry breaking and its restoration at finite baryon density, to color superconductivity and the real-time evolution of heavy-ion collisions, first in simpler model gauge theories and ultimately in QCD.
Necessity of an energy barrier for self-correction of Abelian quantum doubles
NASA Astrophysics Data System (ADS)
Kómár, Anna; Landon-Cardinal, Olivier; Temme, Kristan
2016-05-01
We rigorously establish an Arrhenius law for the mixing time of quantum doubles based on any Abelian group Zd. We have made the concept of the energy barrier therein mathematically well defined; it is related to the minimum energy cost the environment has to provide to the system in order to produce a generalized Pauli error, maximized for any generalized Pauli errors, not only logical operators. We evaluate this generalized energy barrier in Abelian quantum double models and find it to be a constant independent of system size. Thus, we rule out the possibility of entropic protection for this broad group of models.
Non-Abelian vortices on a cylinder: Duality between vortices and walls
Eto, Minoru; Fujimori, Toshiaki; Isozumi, Youichi; Nitta, Muneto; Ohashi, Keisuke; Sakai, Norisuke; Ohta, Kazutoshi
2006-04-15
We investigate vortices on a cylinder in supersymmetric non-Abelian gauge theory with hypermultiplets in the fundamental representation. We identify moduli space of periodic vortices and find that a pair of wall-like objects appears as the vortex moduli is varied. Usual domain walls also can be obtained from the single vortex on the cylinder by introducing a twisted boundary condition. We can understand these phenomena as a T duality among D-brane configurations in type II superstring theories. Using this T-duality picture, we find a one-to-one correspondence between the moduli space of non-Abelian vortices and that of kinky D-brane configurations for domain walls.
Quaternion gauge fields. Pseudocolor
Govorkov, A.B.
1987-03-01
A simplified Guenaydin-Guersey model, in which a Majorana field constructed using quaternions combines a lepton and a color quark, is considered. Formulation of the gauge principle directly in the quaternions leads to the appearance of two vector quaternion gauge fields, these corresponding to the decomposition SO(4) approx. SO(3) x SO(3) of the invariance group. The diagonal subgroup SO(3) of automorphisms of the quarternions appears as a pseudocolor symmetry of the quarks, and the gauge field corresponding to it as the field of three color gluons. The other gauge field corresponds to lepton-quark transitions and in the presence of spontaneous breaking of the SO(4) gauge symmetry by the scalar quaternion field acquires a (large) finite mass.
Direct Sum Decomposition of Groups
ERIC Educational Resources Information Center
Thaheem, A. B.
2005-01-01
Direct sum decomposition of Abelian groups appears in almost all textbooks on algebra for undergraduate students. This concept plays an important role in group theory. One simple example of this decomposition is obtained by using the kernel and range of a projection map on an Abelian group. The aim in this pedagogical note is to establish a direct…
NASA Astrophysics Data System (ADS)
Iadecola, Thomas; Schuster, Thomas; Chamon, Claudio
2016-08-01
Many topological phenomena first proposed and observed in the context of electrons in solids have recently found counterparts in photonic and acoustic systems. In this work, we demonstrate that non-Abelian Berry phases can arise when coherent states of light are injected into "topological guided modes" in specially fabricated photonic waveguide arrays. These modes are photonic analogues of topological zero modes in electronic systems. Light traveling inside spatially well-separated topological guided modes can be braided, leading to the accumulation of non-Abelian phases, which depend on the order in which the guided beams are wound around one another. Notably, these effects survive the limit of large photon occupation, and can thus also be understood as wave phenomena arising directly from Maxwell's equations, without resorting to the quantization of light. We propose an optical interference experiment as a direct probe of this non-Abelian braiding of light.
Non-Abelian Braiding of Light.
Iadecola, Thomas; Schuster, Thomas; Chamon, Claudio
2016-08-12
Many topological phenomena first proposed and observed in the context of electrons in solids have recently found counterparts in photonic and acoustic systems. In this work, we demonstrate that non-Abelian Berry phases can arise when coherent states of light are injected into "topological guided modes" in specially fabricated photonic waveguide arrays. These modes are photonic analogues of topological zero modes in electronic systems. Light traveling inside spatially well-separated topological guided modes can be braided, leading to the accumulation of non-Abelian phases, which depend on the order in which the guided beams are wound around one another. Notably, these effects survive the limit of large photon occupation, and can thus also be understood as wave phenomena arising directly from Maxwell's equations, without resorting to the quantization of light. We propose an optical interference experiment as a direct probe of this non-Abelian braiding of light. PMID:27563965
Deconfinement on {{R}}^2× {S}_L^1× {S}_{β}^1 for all gauge groups and duality to double Coulomb gas
NASA Astrophysics Data System (ADS)
Teeple, Brett
2016-04-01
I study finite-temperature {N}=1 super Yang-Mills for any gauge group G = A N , B N , C N , D N , E 6,7,8, F 4, G 2, compactified from four dimensions on a torus, {{R}}^2× {S}_L^1× {S}_{β}^1 . I examine in particular the low temperature regime L ≪ β = 1/ T, where L is the length of the spatial circle with periodic boundary conditions and with anti-periodic boundary conditions for the adjoint gauginos along the thermal cycle S β 1 . For small such L we are in a regime were semiclassical calculations can be performed and a transition occurs at T c much smaller than 1/ NL. The transition is mediated by the competition between non-perturbative objects including `exotic' topological molecules: neutral and magnetic bions composed of BPS and KK monopole constituents, with r = rank( G) different charges in the co-root lattice of the gauge group G, and the perturbative electrically charged W-bosons (along with their wino superpartners).