Topologically Massive Gravity and the AdS/CFT Correspondence

TL;DR

This paper establishes the AdS/CFT correspondence for topologically massive gravity in three dimensions, analyzing asymptotic structures, holographic renormalization, and correlators, revealing connections to logarithmic CFTs and bulk instabilities.

Contribution

It provides a detailed framework for applying AdS/CFT to TMG, including fall off conditions, operator mapping, and correlator calculations at and away from the chiral point.

Findings

2-point functions at the chiral point match LCFT predictions

Bulk correlators smoothly approach LCFT correlators as mu approaches 1

Negative energy modes indicate bulk instability

Abstract

We set up the AdS/CFT correspondence for topologically massive gravity (TMG) in three dimensions. The first step in this procedure is to determine the appropriate fall off conditions at infinity. These cannot be fixed a priori as they depend on the bulk theory under consideration and are derived by solving asymptotically the non-linear field equations. We discuss in detail the asymptotic structure of the field equations for TMG, showing that it contains leading and subleading logarithms, determine the map between bulk fields and CFT operators, obtain the appropriate counterterms needed for holographic renormalization and compute holographically one- and two-point functions at and away from the 'chiral point' (mu = 1). The 2-point functions at the chiral point are those of a logarithmic CFT (LCFT) with c_L = 0, c_R = 3l/G_N and b = -3l/G_N, where b is a parameter characterizing different c = 0 LCFTs. The bulk correlators away from the chiral point (mu \neq 1) smoothly limit to the LCFT ones as mu \to 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.