Unimodular gravity and the gauge/gravity duality

TL;DR

This paper investigates the relationship between unimodular gravity and General Relativity within the gauge/gravity duality framework, focusing on two- and three-point functions and IR divergences in an AdS background.

Contribution

It demonstrates how unimodular gravity's two- and three-point functions relate to those of General Relativity, revealing their equivalence after IR divergence subtraction in the context of gauge/gravity duality.

Findings

IR divergent contact terms differ between theories

IR divergence subtraction yields equivalent finite results

Unimodular gravity and General Relativity are equivalent in gauge/gravity duality

Abstract

Unimodular gravity can be formulated so that transverse diffeomorphisms and Weyl transformations are symmetries of the theory. For this formulation of unimodular gravity, we work out the two-point and three-point $h_{\mu\nu}$ contributions to the on-shell classical gravity action in the leading approximation and for an Euclidean AdS background. We conclude that these contributions do not agree with those obtained by using General Relativity due to IR divergent contact terms. The subtraction of these IR divergent terms yields the same IR finite result for both unimodular gravity and General Relativity. Equivalence between unimodular gravity and General Relativity with regard to the gauge/gravity duality thus emerges in a non trivial way.