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.

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