Topologically Massive Gravity and Galilean Conformal Algebra: A Study of Correlation Functions

TL;DR

This paper demonstrates the correspondence between Topologically Massive Gravity and the Galilean Conformal Algebra by matching correlation functions, using holographic renormalization and non-relativistic energy-momentum tensors.

Contribution

It provides the first explicit matching of correlation functions between TMG and 2d GCA in a non-relativistic limit, confirming the holographic duality.

Findings

Correlation functions match on both gravity and field theory sides.

Constructed non-relativistic energy-momentum tensor for correlation analysis.

Utilized holographic renormalization techniques in TMG.

Abstract

The Galilean Conformal Algebra (GCA) arises from the relativistic conformal algebra in the non-relativistic limit. In two dimensions, one can view it as a limit of linear combinations of the two copies Virasoro algebra. Recently, it has been argued that Topologically Massive Gravity (TMG) realizes the quantum 2d GCA in a particular scaling limit of the gravitational Chern-Simons term. To add strength to this claim, we demonstrate a matching of correlation functions on both sides of this correspondence. A priori looking for spatially dependent correlators seems to force us to deal with high spin operators in the bulk. We get around this difficulty by constructing the non-relativistic Energy-Momentum tensor and considering its correlation functions. On the gravity side, our analysis makes heavy use of recent results of Holographic Renormalization in Topologically Massive Gravity.