Equivalence of first and second order formulations of the Einstein-Hilbert theory

TL;DR

This paper demonstrates the quantum equivalence of first and second order formulations of Einstein-Hilbert gravity using background effective actions and explicit one-loop calculations.

Contribution

It establishes a general relation between background effective actions, proving the quantum equivalence of the two formulations of Einstein-Hilbert theory.

Findings

Background effective actions are related, confirming equivalence.

Explicit one-loop calculations support the theoretical proof.

The equivalence holds in a general background gauge.

Abstract

We derive a general relation between the background effective actions, which directly proves that the two formulations of the Einstein-Hilbert theory with background fields are equivalent at the quantum level. This basic result has been substantiated in a general background gauge, by explicit calculations at one-loop order of the corresponding counterterm Lagrangians.