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Probing sine dilaton gravity with flow central charge

Paramesh Mahapatra, Hemant Rathi, Dibakar Roychowdhury

TL;DR

This work constructs a holographic c-function for two-dimensional sine dilaton gravity (sDG) and establishes its UV dual description as two Liouville CFT sectors, yielding a total central charge $c=26$. The c-function is built via two complementary approaches: a superpotential flow and a null energy condition (NEC) analysis, which are shown to be mutually consistent and to converge to the UV central charge while vanishing in the IR. The IR limit corresponds to pure JT gravity, thereby providing a concrete holographic RG flow from DSSYK in the UV to JT/SYK in the IR. The results illuminate how LCFT structures encode the sDG degrees of freedom and offer a framework for exploring deformations and gauge couplings within 2D holography.

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.

Probing sine dilaton gravity with flow central charge

TL;DR

This work constructs a holographic c-function for two-dimensional sine dilaton gravity (sDG) and establishes its UV dual description as two Liouville CFT sectors, yielding a total central charge . The c-function is built via two complementary approaches: a superpotential flow and a null energy condition (NEC) analysis, which are shown to be mutually consistent and to converge to the UV central charge while vanishing in the IR. The IR limit corresponds to pure JT gravity, thereby providing a concrete holographic RG flow from DSSYK in the UV to JT/SYK in the IR. The results illuminate how LCFT structures encode the sDG degrees of freedom and offer a framework for exploring deformations and gauge couplings within 2D holography.

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.
Paper Structure (10 sections, 64 equations, 1 figure)

This paper contains 10 sections, 64 equations, 1 figure.

Table of Contents

  1. Overview and motivation
  2. Sine dilaton gravity in domain wall gauge
  3. The Liouville CFT and the central charge
  4. Review of LCFT
  5. Mapping sDG to LCFT
  6. c-function for sDG
  7. The superpotential approach
  8. The NEC approach
  9. Conclusion and future direction
  10. Asymptotics of the integral function

Figures (1)

  • Figure 1: In Figure (1a), $c_{sDG} = c^{(r)} + c^{(l)}$ corresponds to the central charge of sDG in the UV of the holographic RG flow. On the other hand, $c_{JT}$ is the central charge in JT gravity. Figure (1b) shows the RG flow from UV to IR and its holographic counterpart in the bulk.