On the One-Loop Exactness of Gravity Partition Function

TL;DR

This paper demonstrates that the one-loop exactness of the gravity partition function, previously shown in 3D flat space, is a unique feature of three dimensions, as higher dimensions do not exhibit this property.

Contribution

The authors extend the three-loop computation of the gravity partition function to arbitrary dimensions, highlighting the special nature of three-dimensional gravity.

Findings

Two- and three-loop contributions vanish in 3D flat space

Higher dimensions do not exhibit one-loop exactness

One-loop exactness appears to be unique to three-dimensional gravity

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 $D=3$ case, we extend the three-loop computation to arbitrary spacetime dimensions $D$. In higher dimensions, the number of contributions increases substantially, reinforcing the view that one-loop exactness is a unique feature of three-dimensional gravity.