Exotic massive 3D gravities from truncation

TL;DR

This paper presents a systematic method to construct exotic massive gravity theories in 3D, introducing new models with higher-order derivatives and 'third way' consistency, expanding the landscape of 3D gravity theories.

Contribution

The authors develop a novel approach to generate 3D exotic massive gravity models via truncation and potential terms, including a sixth-order derivative model, with a focus on 'third way' consistency.

Findings

Re-derivation of known exotic theories using the new approach

Construction of an extended sixth-order exotic gravity model

Method for checking Bianchi identities in first order formulation

Abstract

We introduce a systematic way of constructing 3D exotic massive gravity theories in the first order formulation. Our method is based on truncating a single degree of freedom in the parity odd gravity models found earlier in arXiv:1405.6213 and supplementing it with appropriate potential terms such that the resulting models have well-defined metric equations but their Bianchi identities are satisfied only on-shell. Hence, they are `third way' consistent. We first re-derive two already known exotic theories using our approach and then construct an extended exotic massive gravity model whose metric field equation is sixth order in derivatives. We also explain how to check Bianchi identities using the first order formulation.