Field-Dependent BRST-antiBRST Lagrangian Transformations

TL;DR

This paper advances the understanding of finite BRST-antiBRST transformations in gauge theories, proving Jacobian correctness, deriving Ward identities, and exploring gauge dependence and symmetry breaking effects, with applications to Yang-Mills theories.

Contribution

It provides a rigorous proof of the Jacobian for finite field-dependent BRST-antiBRST transformations and explores gauge dependence and symmetry breaking in a unified framework.

Findings

Confirmed the correctness of the Jacobian in the partition function.

Derived Ward identities for field-dependent BRST-antiBRST parameters.

Analyzed gauge dependence and symmetry breaking effects in gauge theories.

Abstract

We continue our study of finite BRST-antiBRST transformations for general gauge theories in Lagrangian formalism, initiated in [arXiv:1405.0790[hep-th] and arXiv:1406.0179[hep-th]], with a doublet $\lambda_{a}$, $a=1,2$, 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 $\lambda_{a}=U_{a}\Lambda$ induced by a finite Bosonic functional $\Lambda(\phi,\pi,\lambda)$ and by the anticommuting generators $U_{a}$ of BRST-antiBRST transformations in the space of fields $\phi$ and auxiliary variables $\pi^{a},\lambda$. We obtain a Ward identity depending on the field-dependent parameters $\lambda_{a}$ and study the problem of gauge dependence, including the case of Yang--Mills theories. We examine a formulation with BRST-antiBRST symmetry breaking terms, additively introduced to 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-antiBRST settings. These concepts are applied to the average effective action in Yang--Mills theories within the functional renormalization group approach.