Breaking Of BRST Symmetry Research Articles

From SL(5, ℝ) Yang–Mills theory to induced gravity

From pure Yang–Mills action for the [Formula: see text] group in four Euclidean dimensions we obtain a gravity theory in the first order formalism. Besides the Einstein–Hilbert term, the effective gravity has a cosmological constant term, a curvature squared term, a torsion squared term and a matter sector. To obtain such geometrodynamical theory, asymptotic freedom and the Gribov parameter (soft BRST symmetry breaking) are crucial. Particularly, Newton and cosmological constant are related to these parameters and they also run as functions of the energy scale. One-loop computations are performed and the results are interpreted.

Some Developments in Gribov’s Approach to QCD

We review several developments in the formulation of QCD provided by the GZ action. These include the GZ-action at finite temperature, the relation of the horizon condition and the Kugo-Ojima confinement criterion, the relation of the horizon condition and the dual-Meisssner effect, the alternative derivation of the GZ action provided by the Maggiore-Schaden shift, and the spontaneous breaking of BRST symmetry. We conclude with a proposal for the definition of physical states in the presence of BRST breaking.

Numerical evaluation of the Bose-ghost propagator in minimal Landau gauge on the lattice

We present numerical details of the evaluation of the so-called Bose-ghost propagator in lattice minimal Landau gauge, for the SU(2) case in four Euclidean dimensions. This quantity has been proposed as a carrier of the confining force in the Gribov-Zwanziger approach and, as such, its infrared behavior could be relevant for the understanding of color confinement in Yang-Mills theories. Also, its nonzero value can be interpreted as direct evidence of BRST-symmetry breaking, which is induced when restricting the functional measure to the first Gribov region Omega. Our simulations are done for lattice volumes up to 120^4 and for physical lattice extents up to 13.5 fm. We investigate the infinite-volume and continuum limits.

Spontaneous breaking of nilpotent symmetry in boundary BLG theory

We exploit boundary term to preserve the supersymmetric gauge invariance of Bagger–Lambert–Gustavsson (BLG) theory. The fermionic rigid BRST and anti-BRST symmetries are studied in linear and nonlinear gauges. Remarkably, for Delbourgo–Jarvis–Baulieu–Thierry–Mieg (DJBTM) type gauge the spontaneous breaking of BRST symmetry occurs in the BLG theory. The responsible guy for such spontaneous breaking is ghost–antighost condensation. Further, we discuss the ghost–antighost condensates in the modified maximally Abelian (MMA) gauge in the BLG theory.

Living with spontaneously broken BRST symmetry. I. Physical states and cohomology

We address the issue of BRST symmetry breaking in the GZ model, a local, renormalizable, non-perturbative approach to QCD. Explicit calculation of several examples reveals that BRST symmetry breaking apparently afflicts the unphysical sector of the theory, but may be unbroken where needed, in cases of physical interest. Specifically, the BRST-exact part of the conserved energy-momentum tensor and the BRST-exact term in the Kugo-Ojima confinement condition both have vanishing expectation value. We analyze the origin of the breaking of BRST symmetry in the GZ model, and obtain a useful sufficient condition that determines which operators preserve BRST. Observables of the GZ theory are required to be invariant under a certain group of symmetries that includes not only BRST but also others. The definition of observables is thereby sharpened, and excludes all operators known to us that break BRST invariance. We take as a hypothesis that BRST symmetry is unbroken by this class of observables. If the hypothesis holds, BRST breaking is relegated to the unphysical sector of the GZ theory, and its physical states are obtained by the usual cohomological BRST construction. The fact that the horizon condition and the Kugo-Ojima confinement criterion coincide assures that color is confined in the GZ theory.

Field-dependent BRST–anti-BRST Lagrangian transformations

We continue our study of finite BRST–anti-BRST transformations for general gauge theories in Lagrangian formalism, initiated in [arXiv:1405.0790 [hep-th] and arXiv:1406.0179 [hep-th]], with a doublet λa, a = 1, 2, of anticommuting Grassmann parameters, and prove the correctness of the explicit Jacobian in the partition function announced in [arXiv:1406.0179 [hep-th]], which corresponds to a change of variables with functionally dependent parameters λa = UaΛ induced by a finite Bosonic functional Λ(ϕ, π, λ) and by the anticommuting generators Ua of BRST–anti-BRST transformations in the space of fields ϕ and auxiliary variables πa, λ. We obtain a Ward identity depending on the field-dependent parameters λa and study the problem of gauge dependence, including the case of Yang–Mills theories. We examine a formulation with BRST–anti-BRST symmetry breaking terms, additively introduced into the quantum action constructed by the Sp(2)-covariant Lagrangian rules, obtain the Ward identity and investigate the gauge independence of the corresponding generating functional of Green's functions. A formulation with BRST symmetry breaking terms is developed. It is argued that the gauge independence of the above generating functionals is fulfilled in the BRST and BRST–anti-BRST settings. These concepts are applied to the average effective action in Yang–Mills theories within the functional renormalization group approach.

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

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.

BRST-symmetry breaking and Bose-ghost propagator in lattice minimal Landau gauge

The Bose-ghost propagator has been proposed as a carrier of the confining force in Yang-Mills theories in minimal Landau gauge. We present the first numerical evaluation of this propagator, using lattice simulations for the SU(2) gauge group in the scaling region. Our data are well described by a simple fitting function, which is compatible with an infrared-enhanced Bose-ghost propagator. This function can also be related to a massive gluon propagator in combination with an infrared-free (Faddeev-Popov) ghost propagator. Since the Bose-ghost propagator can be written as the vacuum expectation value of a BRST-exact quantity and should therefore vanish in a BRST-invariant theory, our results provide the first numerical manifestation of BRST-symmetry breaking due to restriction of gauge-configuration space to the Gribov region.

Spontaneous breaking of the BRST symmetry in the ABJM theory

In this paper, we will analyze the ghost condensation in the ABJM theory. We will perform our analysis in N=1 superspace. We show that in the Delbourgo–Jarvis–Baulieu–Thierry–Mieg gauge the spontaneous breaking of BRST symmetry can occur in the ABJM theory. This spontaneous breaking of BRST symmetry is caused by ghost–anti-ghost condensation. We will also show that in the ABJM theory, the ghost–anti-ghost condensates remain present in the modified abelian gauge. Thus, the spontaneous breaking of BRST symmetry in ABJM theory can even occur in the modified abelian gauge.

Notes on Soft BRST Symmetry Breaking within the Batalin–Vilkovisky Formalism

Nilpotency of the operators used to describe a dependence of generating functionals of the Green’s functions with soft BRST symmetry breaking within the Batalin–Vilkovisky formalism is proved.

SOFT BREAKING OF BRST SYMMETRY AND GAUGE DEPENDENCE

We continue investigation of soft breaking of BRST symmetry in the Batalin–Vilkovisky (BV) formalism beyond regularizations like dimensional ones used in our previous paper [JHEP 1110, 043 (2011)]. We generalize a definition of soft breaking of BRST symmetry valid for general gauge theories and arbitrary gauge fixing. The gauge dependence of generating functionals of Green's functions is investigated. It is proved that such introduction of a soft breaking of BRST symmetry into gauge theories leads to inconsistency of the conventional BV formalism.

Is soft breaking of BRST symmetry consistent?

A definition of soft breaking of BRST symmetry in the field-antifield formalism is proposed, valid for general gauge theories and arbitrary gauge fixing. The Ward identities for the generating functionals of Green's functions are derived, and their gauge dependence is investigated. We discuss the Gribov-Zwanziger action for the one-parameter family of R_xi gauges. It is argued that gauge theories with a soft breaking of BRST symmetry are inconsistent.

Global aspects of covariant quantization of gauge theories

A global analysis of the covariant formulation of gauge theories shows that nonperturbative effects give rise to anomalous contributions to the Slavnov-Taylor identities. However, a global geometrical interpretation of BRST symmetry can be formulated and its relation with Slavnov-Taylor identities is clarified by means of this interpretation. In particular, we show that the existence of those non-perturbative anomalies in the Slavnov-Taylor identities does not imply a breaking of BRST symmetry. This opens the possibility of a BRST approach to the Osterwalder-Schrader construction of the physical states of the theory in the covariant formalism.