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 anti de Sitter 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 nontrivial way.

• Received 7 December 2022
• Accepted 10 January 2023

DOI:https://doi.org/10.1103/PhysRevD.107.046001

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

Published by the American Physical Society