Topologically Massive Gravity and the AdS/CFT Correspondence

We set up the AdS/CFT correspondence for topologically massive gravity in three dimensions. We discuss in detail the asymptotic structure of the field equations, determine the map between bulk fields and CFT operators, obtain the appropriate counterterms needed for holographic renormalization and compute holographically oneand two-point functions at and away from the “chiral point” (μ = 1). The 2-point functions at the chiral point are those of a logarithmic CFT (LCFT) with cL = 0, cR = 3l/GN and b = −3l/GN , where b is a parameter characterizing different c = 0 LCFTs. The bulk correlators away from the chiral point (μ 6= 1) smoothly limit to the LCFT ones as μ → 1. Away from the chiral point, the CFT contains a state of negative norm and the expectation value of the energy momentum tensor in that state is also negative, reflecting a corresponding bulk instability due to negative energy modes.