Off-shell Diagrammatics for Quantum Gravity

TL;DR

This paper develops diagrammatic identities for quantum gravity by translating Yang--Mills theory techniques to the Einstein--Hilbert action, expanding around Minkowski space, and constructing cancellation identities for graviton and ghost vertices.

Contribution

It introduces a novel diagrammatic framework for pure gravity based on Yang--Mills identities, extending the diagrammatics to higher valency vertices.

Findings

Derived cancellation identities for graviton and ghost vertices up to six valency.

Established a correspondence between Yang--Mills diagrammatics and gravity.

Provided a foundation for future diagrammatic calculations in quantum gravity.

Abstract

This article reports on how diagrammatic identities of Yang--Mills theory translate to diagrammatics for pure gravity. For this, we consider the Einstein--Hilbert action and follow the approach of Capper, Leibbrandt, and Medrano and expand the inverse metric density around the Minkowski metric. By analogy to Yang--Mills theory, cancellation identities are constructed for the graviton as well as the ghost vertices up to the valency of six.