scholarly journals Comments on foliated gauge theories and dualities in 3+1d

2021 ◽  
Vol 11 (2) ◽  
Author(s):  
Po-Shen Hsin ◽  
Kevin Slagle
Keyword(s):  
Gauge Theories ◽  
Field Theories ◽  
Gauge Fields ◽  
Abelian Gauge ◽  
Codimension Two ◽  
Exactly Solvable ◽  
Hamiltonian Model ◽  
Ground State Degeneracy ◽  
Symmetry Protected ◽  
Particle Statistics

We investigate the properties of foliated gauge fields and construct several foliated field theories in 3+1d that describe foliated fracton orders both with and without matter, including the recent hybrid fracton models. These field theories describe Abelian or non-Abelian gauge theories coupled to foliated gauge fields, and they fall into two classes of models that we call the electric models and the magnetic models. We show that these two classes of foliated field theories enjoy a duality. We also construct a model (using foliated gauge fields and an exactly solvable lattice Hamiltonian model) for a subsystem-symmetry protected topological (SSPT) phase, which is analogous to a one-form symmetry protected topological phase, with the subsystem symmetry acting on codimension-two subregions. We construct the corresponding gauged SSPT phase as a foliated two-form gauge theory. Some instances of the gauged SSPT phase are a variant of the X-cube model with the same ground state degeneracy and the same fusion, but different particle statistics.

SPECTRAL FLOW OF HERMITIAN WILSON–DIRAC OPERATOR AND THE INDEX THEOREM IN ABELIAN GAUGE THEORIES ON FINITE LATTICES

2002 ◽  
Vol 16 (14n15) ◽  
pp. 1943-1950 ◽  
Author(s):  
T. FUJIWARA
Keyword(s):  
Dirac Operator ◽  
Gauge Theories ◽  
Index Theorem ◽  
Two Dimensions ◽  
Gauge Fields ◽  
Continuous Family ◽  
Spectral Flow ◽  
Abelian Gauge ◽  
Characteristic Structure ◽  
Finite Lattices

The spectral flows of the hermitian Wilson-Dirac operator for a continuous family of abelian gauge fields connecting different topological sectors are shown to have a characteristic structure leading to the lattice index theorem. The index of the overlap Dirac operator is shown to coincide with the topological charge for a wide class of gauge field configurations. It is also argued that in two dimensions the eigenvalue spectra for some special but nontrivial background gauge fields can be described by a set of universal polynomials and the index can be found exactly.

BLOCKSPIN AND MULTIGRID FOR STAGGERED FERMIONS IN NON-ABELIAN GAUGE FIELDS

1992 ◽  
Vol 03 (01) ◽  
pp. 121-147 ◽  
Author(s):  
T. KALKREUTER ◽  
G. MACK ◽  
M. SPEH
Keyword(s):  
Gauge Theories ◽  
Free Action ◽  
Real Space ◽  
Gauge Fields ◽  
Group Approach ◽  
Abelian Gauge ◽  
Staggered Fermions ◽  
Real Space Renormalization Group ◽  
Renormalization Group Approach ◽  
Definition Of

We discuss blockspins for staggered fermions, i. e. averaging and interpolation procedures which are needed in a real space renormalization group approach to gauge theories with staggered fermions and in a multigrid approach to the computation of gauge covariant propagators. The discussion starts from the requirement that the symmetries of the free action should be preserved by the blocking procedure in the limit of a pure gauge. A definition of an averaging kernel as a solution of a gauge covariant eigenvalue equation is proposed, and the properties of a corresponding interpolation kernel are examined in the light of general criteria for good choices of blockspins. Some results of multigrid computations of bosonic propagators in an SU(2) gauge field in 4 dimensions are also presented.

scholarly journals Finite field-dependent BRST–anti-BRST transformations: Jacobians and application to the Standard Model

2016 ◽  
Vol 31 (20n21) ◽  
pp. 1650111 ◽  
Author(s):  
Pavel Yu. Moshin ◽  
Alexander A. Reshetnyak
Keyword(s):  
Standard Model ◽  
Gauge Theories ◽  
Landau Gauge ◽  
Gauge Fields ◽  
Nontrivial Solutions ◽  
Abelian Gauge ◽  
The Standard Model ◽  
Field Dependent ◽  
Quantum Action ◽  
General Gauge

We continue our research[Formula: see text] and extend the class of finite BRST–anti-BRST transformations with odd-valued parameters [Formula: see text], [Formula: see text], introduced in these works. In doing so, we evaluate the Jacobians induced by finite BRST–anti-BRST transformations linear in functionally-dependent parameters, as well as those induced by finite BRST–anti-BRST transformations with arbitrary functional parameters. The calculations cover the cases of gauge theories with a closed algebra, dynamical systems with first-class constraints, and general gauge theories. The resulting Jacobians in the case of linearized transformations are different from those in the case of polynomial dependence on the parameters. Finite BRST–anti-BRST transformations with arbitrary parameters induce an extra contribution to the quantum action, which cannot be absorbed into a change of the gauge. These transformations include an extended case of functionally-dependent parameters that implies a modified compensation equation, which admits nontrivial solutions leading to a Jacobian equal to unity. Finite BRST–anti-BRST transformations with functionally-dependent parameters are applied to the Standard Model, and an explicit form of functionally-dependent parameters [Formula: see text] is obtained, providing the equivalence of path integrals in any 3-parameter [Formula: see text]-like gauges. The Gribov–Zwanziger theory is extended to the case of the Standard Model, and a form of the Gribov horizon functional is suggested in the Landau gauge, as well as in [Formula: see text]-like gauges, in a gauge-independent way using field-dependent BRST–anti-BRST transformations, and in [Formula: see text]-like gauges using transverse-like non-Abelian gauge fields.

scholarly journals Higher-form symmetries of 6d and 5d theories

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Lakshya Bhardwaj ◽  
Sakura Schäfer-Nameki
Keyword(s):  
Gauge Group ◽  
Gauge Theories ◽  
Matter Content ◽  
Gauge Fields ◽  
Symmetry Groups ◽  
Abelian Gauge ◽  
Superconformal Field Theories ◽  
Supersymmetric Gauge ◽  
Web Construction

Abstract We describe general methods for determining higher-form symmetry groups of known 5d and 6d superconformal field theories (SCFTs), and 6d little string theories (LSTs). The 6d theories can be described as supersymmetric gauge theories in 6d which include both ordinary non-abelian 1-form gauge fields and also abelian 2-form gauge fields. Similarly, the 5d theories can also be often described as supersymmetric non-abelian gauge theories in 5d. Naively, the 1-form symmetry of these 6d and 5d theories is captured by those elements of the center of ordinary gauge group which leave the matter content of the gauge theory invariant. However, an interesting subtlety is presented by the fact that some massive BPS excitations, which includes the BPS instantons, are charged under the center of the gauge group, thus resulting in a further reduction of the 1-form symmetry. We use the geometric construction of these theories in M/F-theory to determine the charges of these BPS excitations under the center. We also provide an independent algorithm for the determination of 1-form symmetry for 5d theories that admit a generalized toric construction (i.e. a 5-brane web construction). The 2-form symmetry group of 6d theories, on the other hand, is captured by those elements of the center of the abelian 2-form gauge group that leave all the massive BPS string excitations invariant, which is much more straightforward to compute as it is encoded in the Green-Schwarz coupling associated to the 6d theory.

scholarly journals An Exact Equation for Wilson Loops in Two-Dimensional Euclidean Space

2003 ◽  
Vol 18 (27) ◽  
pp. 1925-1929
Author(s):  
Mofazzal Azam
Keyword(s):  
Euclidean Space ◽  
Gauge Theories ◽  
Gauge Fields ◽  
Dimensional Euclidean Space ◽  
Exact Equation ◽  
Wilson Loops ◽  
Two Dimensional ◽  
Abelian Gauge

We derive an exact equation for simple self non-intersecting Wilson loops in non-Abelian gauge theories with gauge fields interacting with fermions in two-dimensional Euclidean space.

scholarly journals Thin-shell wormholes in AdS5 and string dioptrics

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Mariano Chernicoff ◽  
Edel García ◽  
Gaston Giribet ◽  
Emilio Rubín de Celis
Keyword(s):  
Thin Shell ◽  
Field Theories ◽  
Gauge Fields ◽  
Radial Coordinate ◽  
Thin Shells ◽  
Abelian Gauge ◽  
Codimension One ◽  
Higher Curvature Gravity ◽  
Thin Shell Wormholes ◽  
Small Separation

Abstract We consider string probes in a traversable wormhole geometry that connects two locally AdS5 asymptotic regions. Holographically, this describes two interacting copies of a 4-dimensional gauge theory. We consider string configurations whose endpoints are located either in the same boundary or in the two different boundaries of the wormhole. A string with both endpoints in the same boundary is dual to a quark-antiquark pair charged under the same gauge field, while a string extending through the wormhole describes a pair of colored particles charged under two different gauge fields. When one considers a quark-antiquark pair in each boundary, the system undergoes a phase transition: while for small separation each pair of charges exhibits Coulomb interaction, for large separation the charges in different field theories pair up. This behavior had previously been observed in other geometric realizations such as locally AdS5 wormhole solutions with hyperbolic throats. The geometries we consider here, in contrast, are stable thin-shell wormholes with flat codimension-one hypersurfaces at fixed radial coordinate. They appear as electrovacuum solutions of higher-curvature gravity theories coupled to Abelian gauge fields. The presence of the thin-shells produces a refraction of the string configurations in the bulk, leading to the presence of cusps in the phase space diagram. We discuss these and other features of the phase diagram, including the analogies and difference with other wormhole solutions considered in related contexts.

scholarly journals ONE-LOOP RENORMALIZATION OF NON-ABELIAN GAUGE THEORY AND β FUNCTION BASED ON LOOP REGULARIZATION METHOD

2008 ◽  
Vol 23 (19) ◽  
pp. 2861-2913 ◽  
Author(s):  
JIAN-WEI CUI ◽  
YUE-LIANG WU
Keyword(s):  
Gauge Theory ◽  
Regularization Method ◽  
Gauge Theories ◽  
Field Theories ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
Cutoff Energy ◽  
Original Field ◽  
Β Function ◽  
Renormalization Constants

All one-loop renormalization constants for non-Abelian gauge theory are computed in detail by using the symmetry-preserving loop regularization method proposed in Refs. 1 and 2. The resulting renormalization constants are manifestly shown to satisfy Ward–Takahaski–Slavnov–Taylor identities, and lead to the well-known one loop β function for non-Abelian gauge theory of QCD.3-5 The loop regularization method is realized in the dimension of original field theories, it maintains not only symmetries but also divergent behaviors of original field theories with the introduction of two energy scales. Such two scales play the roles of characterizing and sliding energy scales as well as ultraviolet and infrared cutoff energy scales. An explicit check of those identities provides a clear demonstration how the symmetry-preserving loop regularization method can consistently be applied to non-Abelian gauge theories.

scholarly journals Discretized Yang–Mills and Born–Infeld Actions on Finite Group Geometries

2003 ◽  
Vol 18 (20) ◽  
pp. 3555-3585 ◽  
Author(s):  
P. Aschieri ◽  
L. Castellani ◽  
A. P. Isaev
Keyword(s):  
Finite Group ◽  
Finite Groups ◽  
Gauge Theories ◽  
Consistency Condition ◽  
Field Theories ◽  
Product Spaces ◽  
Field Equations ◽  
Abelian Gauge ◽  
Yang Mills ◽  
Kaluza Klein

Discretized non-Abelian gauge theories living on finite group spaces G are defined by means of a geometric action ∫ Tr F ∧ *F. This technique is extended to obtain discrete versions of the Born–Infeld action. The discretizations are in 1–1 correspondence with differential calculi on finite groups. A consistency condition for duality invariance of the discretized field equations is derived for discretized U(1) actions S[F] living on a four-dimensional Abelian G. Discretized electromagnetism satisfies this condition and therefore admits duality rotations. Yang–Mills and Born–Infeld theories are also considered on product spaces MD×G, and we find the corresponding field theories on MD after Kaluza–Klein reduction on the G discrete internal spaces. We examine in detail the case G=ZN, and discuss the limit N→∞. A self-contained review on the noncommutative differential geometry of finite groups is included.

scholarly journals Volume independence for Yang–Mills fields on the twisted torus

2014 ◽  
Vol 29 (25) ◽  
pp. 1445001 ◽  
Author(s):  
Margarita García Pérez ◽  
Antonio González-Arroyo ◽  
Masanori Okawa
Keyword(s):  
Perturbation Theory ◽  
Boundary Conditions ◽  
Gauge Theories ◽  
Field Theories ◽  
Gauge Fields ◽  
Dimensional Torus ◽  
Loop Order ◽  
Yang Mills ◽  
Hooft Coupling ◽  
Twisted Boundary Conditions

We review some recent results related to the notion of volume independence in SU (N) Yang–Mills theories. The topic is discussed in the context of gauge theories living on a d-dimensional torus with twisted boundary conditions. After a brief introduction reviewing the formalism for introducing gauge fields on a torus, we discuss how volume independence arises in perturbation theory. We show how, for appropriately chosen twist tensors, perturbative results to all orders in the 't Hooft coupling depend on a specific combination of the rank of the gauge group (N) and the periods of the torus (l), given by lN2/d, for d even. We discuss the well-known relation to noncommutative field theories and address certain threats to volume independence associated to the occurrence of tachyonic instabilities at one-loop order. We end by presenting some numerical results in 2+1 dimensions that extend these ideas to the nonperturbative domain.

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