Master actions for linearized massive gravity models in 3-D

TL;DR

This paper unifies various 3D massive gravity models through a family of master actions, revealing dualities and connections between different formulations, including models with different orders and excitations.

Contribution

It introduces a unified framework of master actions that interpolate between multiple 3D massive gravity models, elucidating their dualities and relationships.

Findings

Identifies a family of first order actions linking different models.

Shows duality relations between models via master actions.

Connects higher-order models with second order Fierz-Pauli massive gravity.

Abstract

We present a unified analysis of the self-dual, second order, topologically massive and the recently introduced fourth order models of massive gravity in 3D. We show that there is a family of first order actions which interpolate between these different single excitation models. We show how the master actions are related by duality transformation. We construct by the same method the master action which relates the fourth order new massive model with two excitations and the usual second order model with Fierz-Pauli mass. We show that the more general model obtained by adding a Chern-Simons term to the new massive model is equivalent off shell to the second order spontaneously broken linearized massive gravity.