One loop analysis of the cubic action for gravity

TL;DR

This paper investigates the cubic first-order (Palatini) action for gravity, analyzing its BRST invariance, one-loop quantum corrections, and comparing results with second-order formulations.

Contribution

It provides a detailed one-loop analysis of the cubic Palatini gravity action, including BRST invariance and comparison with second-order approaches.

Findings

BRST invariance of the cubic action confirmed

Explicit one-loop quantum corrections computed

Comparison with second-order gravity results made

Abstract

We analyze some aspects of the cubic action for gravity recently proposed by Cheung and Remmen, which is a particular instance of a first order (Palatini) action. In this approach both the spacetime metric and the connection are treated as independent fields. We discuss its BRST invariance and compute explicitly the one-loop contribution of quantum fluctuations around flat space, checking that the corresponding Slavnov-Taylor identities are fulfilled. Finally, our results on a first order action are compared with the existing ones corresponding to a second order action.