Canonical structure of topologically massive gravity with a cosmological constant

TL;DR

This paper analyzes the canonical structure of three-dimensional topologically massive gravity with a cosmological constant, revealing a single physical degree of freedom and a connection to 3D gravity with torsion in the asymptotic region.

Contribution

It provides a detailed canonical analysis of topologically massive gravity with a cosmological constant, highlighting its phase space structure and relation to 3D gravity with torsion.

Findings

Physical phase space dimension is two per spacetime point.

Single Lagrangian degree of freedom identified.

Asymptotic charges and symmetries match with 3D gravity with torsion in the torsionless limit.

Abstract

We study the canonical structure of three-dimensional topologically massive gravity with a cosmological constant, using the full power of Dirac's method for constrained Hamiltonian systems. It is found that the dimension of the physical phase space is two per spacetime point, which corresponds to a single Lagrangian degree of freedom. The analysis of the AdS asymptotic region reveals a remarkable relation to 3D gravity with torsion: in the limit of vanishing torsion, the conserved charges and asymptotic symmetries of the two theories become identical.