Renormalizability of Massive Gravity in Three Dimensions

TL;DR

This paper investigates whether a recently proposed three-dimensional massive gravity with higher-derivative terms can be both perturbatively renormalizable and unitary. By employing BRST quantization together with a BRST-invariant Pauli-Fierz regulator and dimensional regularization, it derives a graviton propagator that falls as a high-momentum regulator, enabling a concrete power-counting analysis. Slavnov-Taylor identities then constrain divergences so that only cosmological-constant and Einstein-Hilbert counterterms are needed, with higher-derivative sectors remaining unrenormalized; the regulator is removed by taking the regulator mass to zero at the end. The result provides a consistent, dynamical, renormalizable toy model of quantum gravity in three dimensions and offers a framework that could illuminate similar analyses in other massive gravity theories.

Abstract

We discuss renormalizability of a recently established, massive gravity theory with particular higher derivative terms in three space-time dimensions. It is shown that this massive gravity is certainly renormalizable as well as unitary, so it gives us a physically interesting toy model of perturbative quantum gravity in three dimensions.