On one-loop partition functions of three-dimensional critical gravities

TL;DR

This paper computes the one-loop partition functions of three-dimensional critical gravities, finds agreement with dual logarithmic conformal field theories, and introduces a truncation method to isolate physical spectra.

Contribution

It provides the first detailed calculation of one-loop partition functions for tricritical gravity and proposes a truncation technique based on quasi-normal modes.

Findings

Agreement with logarithmic CFT partition functions

Discovery of a partially massless limit in linearized gravity

A new truncation method for physical spectrum isolation

Abstract

We calculate the gravity one-loop partition function of three-dimensional parity even tricritical gravity. Agreement with logarithmic conformal field theory single-particle partition functions on the field theory side is found and we furthermore discover a partially massless limit of linearized six-derivative parity even gravity. Then we define a "truncation" of the critical theory, at the level of the partition function, by calculating black hole determinants via summation over quasi-normal mode spectra and discriminating against those modes which are not present in the physical spectrum. This "truncation" is applied to critical new massive gravity and three-dimensional parity even tricritical gravity.