Canonical analysis of cosmological topologically massive gravity at the chiral point

TL;DR

This paper performs a canonical analysis of three-dimensional cosmological topologically massive gravity at the chiral point using a Chern-Simons formulation, revealing a local degree of freedom, the topologically massive graviton.

Contribution

It applies Wolfgang Kummer's philosophy to a 3D gravity model and introduces a new Chern-Simons representation for canonical analysis.

Findings

Physical phase space dimension is two per point.

The theory has a local physical degree of freedom, the topologically massive graviton.

The analysis confirms the presence of a propagating mode in the model.

Abstract

Wolfgang Kummer was a pioneer of two-dimensional gravity and a strong advocate of the first order formulation in terms of Cartan variables. In the present work we apply Wolfgang Kummer's philosophy, the `Vienna School approach', to a specific three-dimensional model of gravity, cosmological topologically massive gravity at the chiral point. Exploiting a new Chern-Simons representation we perform a canonical analysis. The dimension of the physical phase space is two per point, and thus the theory exhibits a local physical degree of freedom, the topologically massive graviton.