Constraint Dynamics and Gravitons in Three Dimensions

TL;DR

This paper analyzes three-dimensional Einstein gravity with a Chern-Simons term, revealing it has a single propagating graviton mode regardless of the cosmological constant, and discusses its relation to Chern-Simons gauge theory.

Contribution

It provides an explicit constraint algebra analysis showing the presence of one dynamical degree of freedom in 3D gravity with Chern-Simons term, independent of the cosmological constant.

Findings

Number of propagating graviton modes is one.

Constraint algebra is explicitly computed.

Standard Chern-Simons equivalence does not hold generally.

Abstract

The complete non-linear three-dimensional Einstein gravity with gravitational Chern-Simons term and cosmological constant are studied in dreibein formulation. The constraints and their algebras are computed in an explicit form. From counting the number of first and second class constraints, the number of dynamical degrees of freedom, which equals to the number of propagating graviton modes, is found to be 1, "regardless of" the value of cosmological constant. I note also that the usual equivalence with Chern-Simons gauge theory does "not" work for general circumstances.