# A remarkably simple theory of 3d massive gravity

## TL;DR

This paper introduces a new, simple three-dimensional massive gravity theory that propagates a single massive graviton, confirmed through perturbative and Hamiltonian analyses, with a rich parameter space including massive and topological limits.

## Contribution

It presents a novel, simple action for 3D massive gravity that is explicitly shown to propagate a single massive degree of freedom, expanding the understanding of massive gravity models.

## Key findings

- The quadratic perturbation action matches self-dual massive gravity.
- Hamiltonian analysis confirms a single massive degree of freedom.
- The theory's parameter space includes various massive and topological limits.

## Abstract

We propose and study a new action for three-dimensional massive gravity. This action takes a very simple form when written in terms of connection and triad variables, but the connection can also be integrated out to obtain a triad formulation. The quadratic action for the perturbations around a Minkowski background reproduces the action of self-dual massive gravity, in agreement with the expectation that the theory propagates a massive graviton. We confirm this result at the non-linear level with a Hamiltonian analysis, and show that this new theory does indeed possess a single massive degree of freedom. The action depends on four coupling constants, and we identify the various massive and topological (or massless) limits in the space of parameters. This richness, along with the simplicity of the action, opens a very interesting new window onto massive gravity.