Field dependent nilpotent symmetry for gauge theories

TL;DR

This paper develops field-dependent mixed BRST transformations for gauge theories, demonstrating their nilpotency, invariance of the quantum master equation, and their role in maintaining symmetry in the path integral formulation.

Contribution

It introduces a novel construction of field-dependent mixed BRST transformations that preserve gauge symmetry and invariance of the quantum master equation.

Findings

Transformations are exact nilpotent symmetries of the effective action.

Jacobian contributions from BRST and anti-BRST parts cancel each other.

Quantum master equation solutions remain invariant under these transformations.

Abstract

We construct the field dependent mixed BRST (combination of BRST and anti-BRST) transformations for pure gauge theories. These are shown to be an exact nilpotent symmetry of both the effective action as well as the generating functional for certain choices of the field dependent parameters. We show that the Jacobian contributions for path integral measure in the definition of generating functional arising from BRST and anti-BRST part compensate each other. The field dependent mixed BRST transformations are also considered in field/antifield formulation to show that the solutions of quantum master equation remain invariant under these. Our results are supported by several explicit examples.