Topologically massive AdS gravity

Abstract

We analyze (2+1)-dimensional gravity with a Chern–Simons term and a negative cosmological constant, primarily at the weak field level. The full theory is expressible as the sum of two higher derivative SL(2,R) “vector” Chern–Simons terms, while the physical bulk degrees of freedom correspond to a single massive scalar field, just as for Λ=0. The interplay of Λ and the mass parameter μ can be studied, and any physical mass—including the conformal value with null propagation—is accessible by tuning μ. The single bulk mode yields a complete set of normalizable positive energy wave packets, as long as one chooses the usual, “wrong” sign of G necessary to connect smoothly with the known Λ=0 limit. The chiral Chern–Simons coupling leads to gauge invariant linearized curvatures propagating with chirality-dependent masses. Linearized metric fluctuations have a finite asymptotic Fefferman–Graham expansion about the Poincaré metric for any mass value greater or equal to a “critical” one, where various amusing effects appear, such as vanishing of one of the two “vector” Chern–Simons terms and an equivalence between tensor and vector excitations. We also find a set of chiral, pp-wave metrics that exactly solve the full nonlinear equations.