# Unitary Extension of Exotic Massive 3D Gravity from Bi-gravity

## TL;DR

This paper introduces a new 3D gravity model derived from bi-gravity theories, demonstrating its unitarity, degrees of freedom, and connections to exotic massive gravity, with potential applications in condensed matter physics.

## Contribution

The paper constructs a novel unitary 3D gravity model from parity-odd Einstein-Cartan theories, extending exotic massive gravity and analyzing its parameter space for unitarity.

## Key findings

- The model has two massive spin-2 modes as local degrees of freedom.
- Unitarity is achievable without fine-tuning in AdS and Minkowski backgrounds.
- A boundary crossing in parameter space yields a unitary model with one graviton and positive central charges.

## Abstract

We obtain a new 3D gravity model from two copies of parity-odd Einstein-Cartan theories. Using Hamiltonian analysis, we demonstrate that the only local degrees of freedom are two massive spin-2 modes. Unitarity of the model in anti-de Sitter and Minkowski backgrounds can be satisfied for vast choices of the parameters without fine-tuning. The recent "exotic massive 3D gravity" model arises as a limiting case of the new model. We also show that there exist trajectories on the parameter space of the new model which cross the boundary between unitary and non-unitary regions. At the crossing point, one massive graviton decouples resulting in a unitary model with just one bulk degree of freedom but two positive central charges at odds with the usual expectation that the critical model has at least one vanishing central charge. Given the fact that a suitable non-relativistic version of bi-gravity has been used as an effective theory for gapped spin-2 fractional quantum Hall states, our model may have interesting applications in condensed matter physics.