One-loop exactness of gravity partition function

Abstract

In a previous work, we showed that the two- and three-loop contributions to the partition function of three-dimensional gravity in flat space vanish. This is in agreement with the expected one-loop exactness dictated by the underlying symmetry at the quantum level. To highlight the distinctive nature of the =3 case, we extend the three-loop computation to arbitrary spacetime dimensions . In higher dimensions, the number of contributions increases substantially, reinforcing the view that one-loop exactness is a unique feature of three-dimensional gravity.