Non-trivial 2+1-Dimensional Gravity

TL;DR

This paper explores quantum gauge theory formulations of 2+1-dimensional gravity, revealing a non-trivial massive theory and deriving a topologically massive gravity model with additional ghost and vector fields.

Contribution

It introduces a non-trivial massive gravity model in 2+1 dimensions and derives a new topologically massive gravity theory with specific ghost and vector field couplings.

Findings

Einstein gravity in 2+1 dimensions has a trivial physical subspace.

Massive gravity in 2+1 dimensions is non-trivial and reduces to a different massless theory.

Derived a cosmological topologically massive gravity with additional ghost and vector fields.

Abstract

We analyze 2+1-dimensional gravity in the framework of quantum gauge theory. We find that Einstein gravity has a trivial physical subspace which reflects the fact that the classical solution in empty space is flat. Therefore we study massive gravity which is not trivial. In the limit of vanishing graviton mass we obtain a non-trivial massless theory different from Einstein gravity. We derive the interaction from descent equations and obtain the cosmological topologically massive gravity. However, in addition to Einstein and Chern-Simons coupling we need coupling to fermionic ghost and anti-ghost fields and to a vector-graviton field with the same mass as the graviton.