On Holographic Realization of Logarithmic GCA

TL;DR

This paper explores the holographic realization of 2D Logarithmic Galilean Conformal Algebra (LGCA) through a contraction of Topologically Massive Gravity at the critical point, revealing a method to obtain well-defined two-point functions.

Contribution

It demonstrates that contracting the theory near the critical point yields well-behaved two-point functions for LGCA, overcoming issues with naive contraction.

Findings

Naive contraction at the critical point fails to produce a well-defined theory.

Contracting near the critical point results in well-behaved two-point functions.

Provides a holographic approach to LGCA using TMG at criticality.

Abstract

We study 2-dimensional Logarithmic Galilean Conformal Algebra (LGCA) by making use of a contraction of Topologically Massive Gravity at critical point. We observe that using a naive contraction at the critical point fails to give a well defined theory, though contracting the theory while we are approaching the critical point leads to a well behaved expressions for two point functions of the energy-momentum tensors of LGCA.