Chiral perturbation theory for GR

TL;DR

This paper introduces a novel perturbation theory for General Relativity based on the chiral Einstein-Cartan action, simplifying calculations by eliminating the connection-to-connection propagator and focusing on metric or tetrad propagations.

Contribution

It presents a new gauge-fixing method that removes the connection-to-connection propagator in first-order formalism, making perturbative calculations more efficient.

Findings

Eliminates the connection-to-connection propagator in the formalism

Results in only cubic and quartic vertices with special legs

Simplifies perturbative calculations in gravity similar to chiral Yang-Mills theory

Abstract

We describe a new perturbation theory for General Relativity, with the chiral first-order Einstein-Cartan action as the starting point. Our main result is a new gauge-fixing procedure that eliminates the connection-to-connection propagator. All other known first-order formalisms have this propagator non-zero, which significantly increases the combinatorial complexity of any perturbative calculation. In contrast, in the absence of the connection-to-connection propagator, our formalism leads to an effective description in which only the metric (or tetrad) propagates, there are only cubic and quartic vertices, but some vertex legs are special in that they cannot be connected by the propagator. The new formalism is the gravity analog of the well-known and powerful chiral description of Yang-Mills theory.