Field-dependent BRST-antiBRST Transformations in Yang-Mills and Gribov-Zwanziger Theories

TL;DR

This paper develops finite BRST-antiBRST transformations, both global and field-dependent, in Yang-Mills and Gribov-Zwanziger theories, demonstrating gauge independence and extending the Gribov horizon functional.

Contribution

It introduces explicit finite field-dependent BRST-antiBRST transformations and applies them to gauge fixing and Gribov horizon extension in Yang-Mills theories.

Findings

Finite transformations are quadratic in parameters.

Gauge independence of the vacuum functional is proven.

Extension of Gribov horizon functional in a gauge-consistent manner.

Abstract

We introduce the notion of finite BRST-antiBRST transformations, both global and field-dependent, with a doublet $\lambda_{a}$, $a=1,2$, of anticommuting Grassmann parameters and find explicit Jacobians corresponding to these changes of variables in Yang-Mills theories. It turns out that the finite transformations are quadratic in their parameters. At the same time, exactly as in the case of finite field-dependent BRST transformations for the Yang-Mills vacuum functional, special field-dependent BRST-antiBRST transformations, with $s_{a}$-potential parameters $\lambda_{a}=s_{a}\Lambda$ induced by a finite even-valued functional $\Lambda$ and by the anticommuting generators $s_{a}$ of BRST-antiBRST transformations, amount to a precise change of the gauge-fixing functional. This proves the independence of the vacuum functional under such BRST-antiBRST transformations. We present the form of transformation parameters that generates a change of the gauge in the path integral and evaluate it explicitly for connecting two arbitrary $R_{\xi }$-like gauges. For arbitrary differentiable gauges, the finite field-dependent BRST-antiBRST transformations are used to generalize the Gribov horizon functional $h$, given in the Landau gauge, and being an additive extension of the Yang-Mills action by the Gribov horizon functional in the Gribov-Zwanziger model. This generalization is achieved in a manner consistent with the study of gauge independence. We also discuss an extension of finite BRST-antiBRST\ transformations to the case of general gauge theories and present an ansatz for such transformations.