The Constraint Algebra of Topologically Massive AdS Gravity

TL;DR

This work provides a nonperturbative, constraint-based analysis of three-dimensional topologically massive AdS gravity, resolving the previously opaque constraint algebra by introducing a new variable set that diagonalizes the canonical structure. It demonstrates that there is a single local propagating degree of freedom for all values of the mass parameter $\mu$ and AdS scale $\ell$, and it derives the boundary Virasoro algebras with central charges $c_\pm = \frac{3\ell}{2G}\left(1\pm\frac{1}{\mu\ell}\right)$ from the asymptotic symmetry analysis. At the chiral points $\mu\ell=\pm1$, one chiral sector becomes a boundary gauge symmetry, yielding a chiral boundary theory, while the total central charge remains unchanged. These results illuminate the nonperturbative structure of TMG in AdS, with implications for AdS/CFT and questions about stability and the interpretation of bulk versus boundary degrees of freedom.

Abstract

Three-dimensional topologically massive AdS gravity has a complicated constraint algebra, making it difficult to count nonperturbative degrees of freedom. I show that a new choice of variables greatly simplifies this algebra, and confirm that the theory contains a single propagating mode for all values of the mass parameter and the cosmological constant. As an added benefit, I rederive the central charges and conformal weights of the boundary conformal field theory from an explicit analysis of the asymptotic algebra of constraints.