Running coupling from gluon and ghost propagators in the Landau gauge: Yang-Mills theories with adjoint fermions

Abstract Supersymmetric Yang-Mills theories can be characterized by a non-local and non-linear transformation of the bosonic fields (Nicolai map) mapping the interacting functional measure to that of a free theory, such that the Jacobi determinant of the transformation equals the product of the fermionic determinants obtained by integrating out the gauginos and ghosts at least on the gauge hypersurface. While this transformation has been known so far only for the Landau gauge and to third order in the Yang-Mills coupling, we here extend the construction to a large class of (possibly non-linear and non-local) gauges, and exhibit the conditions for all statements to remain valid off the gauge hypersurface. Finally, we present explicit results to second order in the axial gauge and to fourth order in the Landau gauge.

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Infrared finiteness of the two-loop correction to the Chern–Simons term in the Yang–Mills–Chern–Simons theory

Canadian Journal of Physics ◽

10.1139/p95-048 ◽

1995 ◽

Vol 73 (5-6) ◽

pp. 344-348 ◽

Cited By ~ 2

Author(s):

Yeong-Chuan Kao ◽

Hsiang-Nan Li

Keyword(s):

Effective Action ◽

Background Field ◽

Landau Gauge ◽

Quantum Corrections ◽

Simons Theory ◽

Loop Correction ◽

Loop Contribution ◽

Yang Mills ◽

Chern Simons ◽

Chern Simons Theory

We show that the two-loop contribution to the coefficient of the Chern–Simons term in the effective action of the Yang–Mills–Chern–Simons theory is infrared finite in the background field Landau gauge. We also discuss the difficulties in verifying the conjecture, due to topological considerations, that there are no more quantum corrections to the Chern–Simons term other than the well-known one-loop shift of the coefficient.

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Spontaneous chiral symmetry breaking in the massive Landau gauge: Realistic running coupling

Physical Review D ◽

10.1103/physrevd.103.094035 ◽

2021 ◽

Vol 103 (9) ◽

Author(s):

Marcela Peláez ◽

Urko Reinosa ◽

Julien Serreau ◽

Matthieu Tissier ◽

Nicolás Wschebor

Keyword(s):

Symmetry Breaking ◽

Chiral Symmetry ◽

Chiral Symmetry Breaking ◽

Landau Gauge ◽

Spontaneous Chiral Symmetry Breaking ◽

Running Coupling

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On gauge independence for gauge models with soft breaking of BRST symmetry

International Journal of Modern Physics A ◽

10.1142/s0217751x1450184x ◽

2014 ◽

Vol 29 (30) ◽

pp. 1450184 ◽

Cited By ~ 10

Author(s):

Alexander Reshetnyak

Keyword(s):

Gauge Theories ◽

Brst Symmetry ◽

Landau Gauge ◽

Functional Integral ◽

Yang Mills ◽

Gauge Models ◽

S Matrix ◽

Gauge Fixing ◽

Dependent Parameter ◽

Quantum Treatment

A consistent quantum treatment of general gauge theories with an arbitrary gauge-fixing in the presence of soft breaking of the BRST symmetry in the field–antifield formalism is developed. It is based on a gauged (involving a field-dependent parameter) version of finite BRST transformations. The prescription allows one to restore the gauge-independence of the effective action at its extremals and therefore also that of the conventional S-matrix for a theory with BRST-breaking terms being additively introduced into a BRST-invariant action in order to achieve a consistency of the functional integral. We demonstrate the applicability of this prescription within the approach of functional renormalization group to the Yang–Mills and gravity theories. The Gribov–Zwanziger action and the refined Gribov–Zwanziger action for a many-parameter family of gauges, including the Coulomb, axial and covariant gauges, are derived perturbatively on the basis of finite gauged BRST transformations starting from Landau gauge. It is proved that gauge theories with soft breaking of BRST symmetry can be made consistent if the transformed BRST-breaking terms satisfy the same soft BRST symmetry breaking condition in the resulting gauge as the untransformed ones in the initial gauge, and also without this requirement.

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