BRST Symmetry and the Convolutional Double Copy

TL;DR

This paper explores the convolutional double copy relating BRST-invariant formulations of gravity and gauge theories, demonstrating how supergravity solutions can be derived from Yang-Mills theories using superspace methods.

Contribution

It introduces a general BRST and anti-BRST invariant framework for linearised supergravity and illustrates its application to specific solutions like Schwarzschild black holes and black strings.

Findings

Supergravity can be obtained from Yang-Mills theories via convolutional double copy.

BRST invariance is maintained in the convolutional double copy framework.

Concrete examples demonstrate the practical application of the theoretical formulation.

Abstract

Motivated by the results of Anastasiou et al., we consider the convolutional double copy for BRST and anti-BRST covariant formulations of gravitational and gauge theories in more detail. We give a general BRST and anti-BRST invariant formulation of linearised $\mathcal{N}=0$ supergravity using superspace methods and show how this may be obtained from the square of linearised Yang-Mills theories. We demonstrate this relation for the Schwarzschild black hole and the ten-dimensional black string solution as two concrete examples.