Logarithmic Corrections to Black Hole Entropy from the Cardy Formula

TL;DR

This paper calculates the first-order quantum correction to black hole entropy using conformal field theory techniques, revealing a universal logarithmic correction term across various models.

Contribution

It derives a universal logarithmic correction to black hole entropy from the Cardy formula applicable to multiple theoretical models.

Findings

Logarithmic correction proportional to horizon size logarithm

Qualitative agreement with quantum geometry results

Potential universality of correction coefficient

Abstract

Many recent attempts to calculate black hole entropy from first principles rely on conformal field theory techniques. By examining the logarithmic corrections to the Cardy formula, I compute the first-order quantum correction to the Bekenstein-Hawking entropy in several models, including those based on asymptotic symmetries, horizon symmetries, and certain string theories. Despite very different physical assumptions, these models all give a correction proportional to the logarithm of the horizon size, and agree qualitatively with recent results from ``quantum geometry'' in 3+1 dimensions. There are some indications that even the coefficient of the correction may be universal, up to differences that depend on the treatment of angular momentum and conserved charges.