Massive Gravity with Mass Term in Three Dimensions

TL;DR

This paper investigates the impact of the Pauli-Fierz mass term on a three-dimensional new massive gravity theory, revealing that it causes non-unitarity and cannot coexist with higher-derivative mass-generating terms.

Contribution

It demonstrates that the Pauli-Fierz mass term renders the new massive gravity theory non-unitary, even with the addition of the gravitational Chern-Simons term.

Findings

Pauli-Fierz mass term causes non-unitarity

Adding Chern-Simons term does not restore unitarity

Mass term cannot coexist with higher-derivative terms in this theory

Abstract

We analyze the effect of the Pauli-Fierz mass term on a recently established, new massive gravity theory in three space-time dimensions. We show that the Pauli-Fierz mass term makes the new massive gravity theory non-unitary. Moreover, although we add the gravitational Chern-Simons term to this model, the situation remains unchanged and the theory stays non-unitary in spite that structure of the graviton propagator is greatly changed. Thus, the Pauli-Fierz mass term is not allowed to coexist with mass-generating higher-derivative terms in the new massive gravity.