Gravity as Gauge Theory Squared: A Ghost Story.

A Anastasiou,M J Duff,L Borsten,M Zoccali,S Nagy

doi:10.1103/physrevlett.121.211601

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 anticommute as a direct consequence of the formalism.

Highlights

The Becchi-Rouet-Stora-Tyutin (BRST) transformations and equations of motion of a gravity–twoform–dilaton system are derived from the product of two Yang-Mills theories in a BRST covariant form, to linear approximation
The resulting gravity–two-form–dilaton Lagrangian is anti-BRST invariant and the BRST and anti-BRST charges anticommute as a direct consequence of the formalism
These ambitions may be realized by adopting a Becchi-RouetStora-Tyutin (BRST) [33,34,35,36,37,38,39] formalism and paying due diligence to boundary conditions

Summary

Published by the American Physical Society

Physical and ghost fields of the graviton–two-form–dilaton system as the product of Yang-Mills fields using Eq (1). By exploiting the properties of the product (1), we are able to derive the BRST variation and equations of motion of the gravity theory from those of the Yang-Mills factors alone. The first concerns the domain of validity of the “derivative rule” of the convolution, which is not Leibniz, but rather satisfies This property is key to recovering both the BRST variations and equations of motion. Yang-Mills theories results in the states, physical as well as first- and second-level ghosts, of a graviton, two-form, and dilaton.

HμνρHμνρ þ

Qη mðdÞ ξðdÞ

AνÞ þ

Fρσ þ