---
abstract: 'We calculate the 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.'
address: |
    Centre for Theoretical Physics, University of Groningen,\
    Nijenborgh 4, 9747 AG Groningen, The Netherlands
author:
- Thomas Zojer
title: 'On one-loop partition functions of three-dimensional critical gravities'
---

Introduction
============

Three-dimensional gravity has long been an interesting testing ground for theories of quantum gravity. But pure Einstein gravity, plus a cosmological constant, does not lead to propagating degrees of freedom in the bulk. Therefore modifications are sought. One natural way of extending the theory is to add massive gravitons. This can be achieved by adding higher-derivative terms to the action. Two concrete proposals in the literature are the parity 