Finite field-dependent symmetries in perturbative quantum gravity

• The perturbative quantum gravity is treated as gauge theory.
• BRST and anti-BRST transformations are developed in linear and non-linear gauges.
• BRST transformation is generalized by making it finite and field dependent.
• Connection between linear and non-linear gauges is established.
• Using BV formulation the results are established at quantum level also.

In this paper we discuss the absolutely anticommuting nilpotent symmetries for perturbative quantum gravity in general curved spacetime in linear and non-linear gauges. Further, we analyze the finite field-dependent BRST (FFBRST) transformation for perturbative quantum gravity in general curved spacetime. The FFBRST transformation changes the gauge-fixing and ghost parts of the perturbative quantum gravity within functional integration. However, the operation of such symmetry transformation on the generating functional of perturbative quantum gravity does not affect the theory on physical ground. The FFBRST transformation with appropriate choices of finite BRST parameter connects non-linear Curci–Ferrari and Landau gauges of perturbative quantum gravity. The validity of the results is also established at quantum level using Batalin–Vilkovisky (BV) formulation.