One-loop divergences in first order Einstein-Hilbert gravity

TL;DR

This paper calculates one-loop divergences in first order Einstein-Hilbert gravity with a scalar field, confirming previous results and demonstrating the divergence structure using heat kernel techniques.

Contribution

It provides an exact computation of off-shell one-loop divergences in the first order formalism, aligning with earlier findings by 't Hooft and Veltman.

Findings

Off-shell divergences match previous results

Heat kernel method effectively computes divergences

Results confirm consistency of first order formalism

Abstract

One-loop counterterms are computed in the first order formalism for the Einstein-Hilbert action with a minimally coupled scalar field using the background field method and the heat kernel technique. The {\em off-shell} divergent piece in the harmonic gauge is {\em exactly} the same as the one first found by 't Hooft and Veltman.