Graviton 1-loop partition function for 3-dimensional massive gravity

TL;DR

This paper computes the graviton 1-loop partition function in 3D massive gravity, revealing non-holomorphic factorization and supporting the conjecture that the dual CFT is logarithmic, especially at the chiral point.

Contribution

It provides the first detailed calculation of the 1-loop partition function in topologically massive gravity and extends the analysis to new massive gravity, supporting the logarithmic CFT duality.

Findings

Partition function does not factorize holomorphically.

At the chiral point, the structure matches a logarithmic CFT.

Supports the duality between TMG and logarithmic CFT.

Abstract

The graviton 1-loop partition function in Euclidean topologically massive gravity (TMG) is calculated using heat kernel techniques. The partition function does not factorize holomorphically, and at the chiral point it has the structure expected from a logarithmic conformal field theory. This gives strong evidence for the proposal that the dual conformal field theory to TMG at the chiral point is indeed logarithmic. We also generalize our results to new massive gravity.