Slavnov-Taylor Parameterization for the Quantum Restoration of BRST Symmetries in Anomaly-Free Gauge Theories

TL;DR

This paper presents a method to systematically restore and parameterize Slavnov-Taylor identities at the quantum level in anomaly-free gauge theories, demonstrated through a BRST-invariant massive Yang-Mills model.

Contribution

It introduces a novel approach to parameterize the quantum effective action using ST functionals, applicable to all orders in loop expansion, ensuring symmetry restoration.

Findings

Method successfully applied to a BRST-invariant massive Yang-Mills model.

Derived the most general solution for the quantum effective action.

Explicit dependence on normalization conditions is provided.

Abstract

It is shown that the problem of the recursive restoration of the Slavnov-Taylor (ST) identities at the quantum level for anomaly-free gauge theories is equivalent to the problem of parameterizing the local approximation to the quantum effective action in terms of ST functionals, associated with the cohomology classes of the classical linearized ST operator. The ST functionals of dimension <=4 correspond to the invariant counterterms, those of dimension >4 generate the non-symmetric counterterms upon projection on the action-like sector. At orders higher than one in the loop expansion there are additional contributions to the non-invariant counterterms, arising from known lower order terms. They can also be parameterized by using the ST functionals. We apply the method to Yang-Mills theory in the Landau gauge with an explicit mass term introduced in a BRST-invariant way via a BRST doublet. Despite being non-unitary, this model provides a good example where the method devised in the paper can be applied to derive the most general solution for the action-like part of the quantum effective action, compatible with the fulfillment of the ST identities and the other relevant symmetries of the model, to all orders in the loop expansion. The full dependence of the solution on the normalization conditions is given.