Probing sine dilaton gravity with flow central charge

TL;DR

This paper develops a holographic c-function for sine dilaton gravity, demonstrating its equivalence to Liouville CFT and analyzing the flow of central charge from UV to IR, connecting to JT gravity.

Contribution

It introduces a holographic c-function for sine dilaton gravity and establishes its relation to Liouville CFT and JT gravity, providing insights into the flow of central charge.

Findings

Central charge matches Liouville CFT in UV limit.

Central charge flows to zero in IR limit, corresponding to JT gravity.

Holographic c-function captures the RG flow of the theory.

Abstract

We construct a holographic c-function for sine dilaton gravity (sDG) in the domain wall gauge. We show the equivalence between sDG and the two copies of Liouville conformal field theory (LCFT) and compute the associated central charge. We reproduce the central charge of LCFT from the holographic c-function of sDG corresponding to the UV limit. In contrast, in the deep IR limit, the c-function flows to the pure JT gravity, where the central charge becomes identically zero.