Gravity as Gauge Theory Squared: A Ghost Story

TL;DR

This paper demonstrates how gravity theories with additional fields can be constructed from the product of two Yang-Mills theories using BRST symmetry, revealing new insights into gauge theory relationships.

Contribution

It derives the BRST transformations and equations of motion for a gravity-two-form-dilaton system from Yang-Mills theories, highlighting the role of ghost fields and gauge fixing.

Findings

Gravity-two-form-dilaton Lagrangian is anti-BRST invariant.

BRST and anti-BRST charges anti commute.

Gauge fixing terms are uniquely determined by Yang-Mills factors.

Abstract

The Becchi-Rouet-Stora-Tyutin (BRST) transformations and equations of motion of a gravity-two-form-dilaton system are derived from the product of two Yang-Mills theories in a BRST covariant form, to linear approximation. The inclusion of ghost fields facilitates the separation of the graviton and dilaton. The gravitational gauge fixing term is uniquely determined by those of the Yang-Mills factors which can be freely chosen. Moreover, the resulting gravity-two-form-dilaton Lagrangian is anti-BRST invariant and the BRST and anti-BRST charges anti commute as a direct consequence of the formalism.