Unitarity Flow in 2+1 Dimensional Massive Gravity

TL;DR

This paper investigates the unitarity conditions of third-order Chern-Simons-like massive gravity theories in 2+1 dimensions, revealing boundary relationships between different order models and mechanisms for unitarity transitions.

Contribution

It provides a comprehensive analysis of unitarity regions in parameter space and explores the transition mechanisms between different order theories in 3D massive gravity.

Findings

Identified conditions for unitarity in parameter space.

Discovered boundary relationships between nth and (n-1)th order models.

Separated ghost and no-ghost regions using Chern-Simons theories.

Abstract

We analyze the most general case of third-order Chern-Simons-like theories of massive 3D gravity. Results show the conditions for finding the unitary regions on the parameter space. There exists $(n-1)$th order theories on the boundary of a unitary $n$th order model on parameter space under certain conditions, as the first example recently demonstrated from the bimetric generalization of exotic massive gravity. We investigated the mechanism that causes this type of transition for third-order models. Hamiltonian analysis of the theory also presents that ghost and no-ghost regions can be separated by Chern-Simons theories.