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 HIGHER-SPIN GAUGE THEORIES IN FOUR, THREE AND TWO DIMENSIONS

1996 ◽  
Vol 05 (06) ◽  
pp. 763-797 ◽  
Author(s):  
M.A. VASILIEV
Keyword(s):  
Gauge Theories ◽  
Space Time ◽  
Two Dimensions ◽  
Gauge Fields ◽  
Higher Spin ◽  
Three Space ◽  
Matter Fields

We review the theory of higher-spin gauge fields in four and three space-time dimensions and present some new results on higher-spin gauge interactions of matter fields in two dimensions.

NON-COMPACT WZW MODELS AS MASSLESS (QCD)2 AT INFINITE COUPLING

1990 ◽  
Vol 05 (22) ◽  
pp. 4241-4255 ◽  
Author(s):  
Z. HABA
Keyword(s):  
Green's Functions ◽  
Green’S Functions ◽  
Functional Integration ◽  
Two Dimensions ◽  
Gauge Fields ◽  
Abelian Gauge ◽  
Left Handed ◽  
Scaling Dimension ◽  
Massless Fermions

Wess-Zumino-Witten (WZW) (compact and non-compact) coset Lagrangians arise as effective Lagrangians of Euclidean non-Abelian gauge fields coupled to (right- and left-handed) massless fermions in two dimensions. We choose coordinates on the non-compact coset in such a way that the WZW model becomes soluble through the functional integration. We interprete the model as a massless QCD (without the F2 gluon self-interaction). We discuss the fermionic Green's functions in this model. We show that the Fermi fields in (QCD) 2 become scale-invarient in the infinite coupling limit with a non-canonical scaling dimension.

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