Finite BRST-antiBRST Transformations in Lagrangian Formalism

TL;DR

This paper extends the study of finite BRST-antiBRST transformations in gauge theories, deriving explicit Jacobians, Ward identities, and gauge-dependence analysis, with applications to non-Abelian tensor fields.

Contribution

It provides explicit Jacobians for finite BRST-antiBRST transformations, derives new Ward identities, and demonstrates gauge-fixing changes in a general gauge theory framework.

Findings

Explicit Jacobian formulas for finite BRST-antiBRST transformations.

New Ward identities involving transformation parameters.

Application to the Freedman--Townsend non-Abelian tensor model.

Abstract

We continue the study of finite BRST-antiBRST transformations for general gauge theories in Lagrangian formalism initiated in [arXiv:1405.0790[hep-th]], with a doublet $\lambda_{a}$, $a=1,2$, of anticommuting Grassmann parameters, and find an explicit Jacobian corresponding to this change of variables for constant $\lambda_{a}$. This makes it possible to derive the Ward identities and their consequences for the generating functional of Green's functions. We announce the form of the Jacobian [proved to be correct in [arXiv:1406.5086[hep-th]] for finite field-dependent BRST-antiBRST transformations with functionally-dependent parameters, $\lambda_{a}% =s_{a}\Lambda$, induced by a finite even-valued functional $\Lambda(\phi ,\pi,\lambda)$ and by the generators $s_{a}$ of BRST-antiBRST transformations acting in the space of fields $\phi$, antifields $\phi_{a}^{\ast}$, $\bar {\phi}$ and auxiliary variables $\pi^{a},\lambda$. On the basis of this Jacobian, we solve a compensation equation for $\Lambda$, which is used to achieve a precise change of the gauge-fixing functional for an arbitrary gauge theory. We derive a new form of the Ward identities containing the parameters $\lambda_{a}$ and study the problem of gauge-dependence. The general approach is exemplified by the Freedman--Townsend model of\ a non-Abelian antisymmetric tensor field.