AdS boundary conditions and the Topologically Massive Gravity/CFT correspondence

TL;DR

This work uses AdS/CFT to reframe boundary conditions and conserved charges in 3D gravity, focusing on Topologically Massive Gravity (TMG) with coupling $\mu$. By incorporating the holographic renormalization framework, it shows that for $\mu=1$ TMG is dual to a non-unitary logarithmic CFT with central charges $c_L=0$ and $c_R=3/G_N$, and a logarithmic partner operator $t_{ij}$ with new anomaly $b=-3/G_N$; for general $\mu$, the central charges are $c_L=\tfrac{3}{2G_N}(1-1/\mu)$ and $c_R=\tfrac{3}{2G_N}(1+1/\mu)$. The analysis reveals a rich LCFT structure arising from the dual of a higher-derivative bulk theory, including explicit two-point functions and Ward identities. The results highlight the non-unitarity and potential limits of chiral truncations, underscoring the need for a stringy completion to fully capture black hole microstates and a consistent dual description beyond pure gravity.

Abstract

The AdS/CFT correspondence provides a new perspective on recurrent questions in General Relativity such as the allowed boundary conditions at infinity and the definition of gravitational conserved charges. Here we review the main insights obtained in this direction over the last decade and apply the new techniques to Topologically Massive Gravity. We show that this theory is dual to a non-unitary CFT for any value of its parameter mu and becomes a Logarithmic CFT at mu = 1.