Off-shell Diagrammatics for 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.

Algebraic Structures in the Coupling of Gravity to Gauge Theories

“…In particular, the cancellation identities for the Faddeev-Popov ghosts are quite involved: Cancellation identities are diagrammatic cancellations resulting from longitudinal projections, cf. [2,3,4,5,6,7,8]. Thus, this article is devoted to a proper derivation of symmetric ghost Lagrange densities using appropriate gauge fixing bosons, BRST and anti-BRST operators.…”

“…More precisely, we aim to show them graphically via so-called cancellation identities, cf. [15,16,17,18,19,20]. These identities will then be implemented on the algebra of Feynman graphs via a modified version of the Feynman graph cohomology introduced in [21,22].…”