Quantum-Corrected Cardy Entropy for Generic 1+1-Dimensional Gravity

TL;DR

This paper applies Carlip's quantum correction to the Cardy entropy formula within generic 1+1-dimensional gravity models, revealing a logarithmic correction term consistent with thermodynamic derivations but with model-dependent discrepancies.

Contribution

It extends Carlip's quantum correction to the Cardy formula to generic 2D gravity models with dilaton coupling, highlighting model-specific differences in entropy corrections.

Findings

Corrected entropy includes a logarithmic term.

Discrepancy in the correction factor depends on the specific 2D model.

Agreement with thermodynamic results only in special models like Jackiw-Teitelboim.

Abstract

Various studies have explored the possibility of explaining the Bekenstein-Hawking (black hole) entropy by way of some suitable state-counting procedure. Notably, many of these treatments have used the well-known Cardy formula as an intermediate step. Our current interest is a recent calculation in which Carlip has deduced the leading-order quantum correction to the (otherwise) classical Cardy formula. In this paper, we apply Carlip's formulation to the case of a generic model of two-dimensional gravity with coupling to a dilaton field. We find that the corrected Cardy entropy includes the anticipated logarithmic ``area'' term. Such a term is also evident when the entropic correction is derived independently by thermodynamic means. However, there is an apparent discrepancy between the two calculations with regard to the factor in front of the logarithm. In fact, the two values of this prefactor can only agree for very specific two-dimensional models, such as that describing Jackiw-Teitelboim theory.