Constraint Dynamics and Gravitons in Three Dimensions

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.