Generalised massive gravity one-loop partition function and AdS/(L)CFT

TL;DR

This paper computes the one-loop partition function for Euclidean generalised massive gravity in AdS space, demonstrating its consistency with AdS/CFT correspondence and exploring special limits like conformal Chern-Simons gravity.

Contribution

It provides the first detailed calculation of the GMG one-loop partition function and interprets the additional contributions in the conformal limit within the dual CFT framework.

Findings

Partition function fits the AdS/(L)CFT correspondence

Additional contributions from conformal ghost in Chern-Simons limit

Interpretation of ghost contributions as null vectors in CFT

Abstract

The graviton 1-loop partition function is calculated for Euclidean generalised massive gravity (GMG) using AdS heat kernel techniques. We find that the results fit perfectly into the AdS/(L)CFT picture. Conformal Chern-Simons gravity, a singular limit of GMG, leads to an additional contribution in the 1-loop determinant from the conformal ghost. We show that this contribution has a nice interpretation on the conformal field theory side in terms of a semi-classical null vector at level two descending from a primary with conformal weights (3/2,-1/2).