The one-loop unimodular graviton propagator in any dimension

Abstract

For unimodular gravity, we work out, by using dimensional regularization, the complete one-loop correction to the graviton propagator in any space-time dimension. The computation is carried out within the framework where unimodular gravity has Weyl invariance in addition to the transverse diffeomorphism gauge symmetry. Thus, no Lagrange multiplier is introduced to enforce the unimodularity condition. The quantization of the theory is carried out by using the BRST framework and there considering a large continuous family of gauge-fixing terms. The BRST formalism is developed in such a way that the set of ghost, {anti-ghost} and auxiliary fields and their BRST changes do not depend on the space-time dimension, as befits dimensional regularization. As an application of our general result, and at D=4, we obtain the renormalized one-loop graviton propagator in the dimensional regularization minimal {subtraction} scheme. We do so by considering two simplifying gauge-fixing choices.