On the spontaneous break down of massive gravities in 2+1 dimensions

TL;DR

This paper investigates the symmetry breaking properties of different formulations of massive gravity in 2+1 dimensions, revealing that certain topological models cannot break down, while others reduce to a double massive spin-two system similar to a generalized Maxwell-Chern-Simons-Proca model.

Contribution

It demonstrates the breakdown behavior of locally diffeomorphism invariant massive gravity models and introduces a flat double massive spin-two system as a new effective theory.

Findings

Locally Lorentz invariant third order topological massive gravity cannot break down.

Locally diffeomorphism invariant second order massive triadic gravity reduces to a double massive spin-two system.

The resulting flat double massive action generalizes the Maxwell-Chern-Simons-Proca system.

Abstract

We show that locally Lorentz invariant, third order, topological massive gravity can not be broken down neither to the local diffeomorphism subgroup nor to the rigid Poincar\'e group. On the other hand, the recently formulated, locally diffeomorphism invariant, second order massive triadic (translational) Chern-Simons gravity breaks down on rigid Minkowski space to a double massive spin-two system. This flat double massive action is the uniform spin-two generalization of the Maxwell-Chern-Simons-Proca system which one is left with after U(1) abelian gauge invariance breaks down in the presence of a sextic Higgs potential.