Abstract
Three dimensional topologically massive gravity (TMG) with a negative cosmological constant ???2 and positive Newton constant G admits an AdS3 vacuum solution for any value of the graviton mass ?. These are all known to be perturbatively unstable except at the recently explored chiral point ?? = 1. However we show herein that for every value of ?? ? 3 there are two other (potentially stable) vacuum solutions given by SL(2,) ? U(1)-invariant warped AdS3 geometries, with a timelike or spacelike U(1) isometry. Critical behavior occurs at ?? = 3, where the warping transitions from a stretching to a squashing, and there are a pair of warped solutions with a null U(1) isometry. For 3$>?? > 3, there are known warped black hole solutions which are asymptotic to warped AdS3. We show that these black holes are discrete quotients of warped AdS3 just as BTZ black holes are discrete quotients of ordinary AdS3. Moreover new solutions of this type, relevant to any theory with warped AdS3 solutions, are exhibited. Finally we note that the black hole thermodynamics is consistent with the hypothesis that, for 3$>?? > 3, the warped AdS3 ground state of TMG is holographically dual to a 2D boundary CFT with central charges and .
Highlights
Introduction and summaryTopologically massive gravity [1, 2] is described by the action IT MG d3x√−g(R + 2/l2) 1 μ ICS (1.1)where ICS is the gravitational Chern-Simons action and we take both G and μ positive1
Massive gravity [1, 2] is described by the action where ICS is the gravitational Chern-Simons action and we take both G and μ positive1
Our story begins with the action for three dimensional topologically massive gravity with a negative cosmological constant
Summary
Where ICS is the gravitational Chern-Simons action (given explicitly below) and we take both G and μ positive. At the critical value μl = 1 the Compton wavelength of the massive graviton reaches the AdS3 radius and the linearized energy spectrum of asymptotically AdS3 excitations is non-negative.2 It was conjectured [10] that a consistent quantum theory of so-called chiral gravity can be defined at μl = 1. A similar exact match is found for warped black holes in warped AdS3 provided the central charges are As this picture fits together rather nicely we cannot resist conjecturing that μl > 3 TMG defined with suitable asymptotically warped boundary conditions exists and is dual to a 2D boundary CFT with central charges 1.2 and 1.3.3 Some non-trivial but far from definitive - evidence for the conjecture is given . After this work was completed several works appeared [30, 31] which overlap with section 3 as well as [32, 33, 34] which finds the null black holes of section 6.3 in the context of cold atoms
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