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 Poincar'e 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.

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