Holomorphic Factorization at the Quantum Horizon

TL;DR

This paper introduces a quantum horizon approach to analyze black hole thermodynamics, revealing a universal parameter linked to a 2D CFT central charge that reproduces black hole thermodynamics across various types.

Contribution

It demonstrates that a single real parameter, interpreted as a 2D CFT central charge, can unify the thermodynamics of diverse black holes without relying on asymptotic symmetries.

Findings

The UV inputs can be combined into a single real parameter.

Choosing the parameter as the Kerr-CFT value reproduces thermodynamics.

The approach applies to non-extremal, non-BPS black holes.

Abstract

We identify a horizon-skimming limit under which wave equations around large classes of black holes allow a determination of their low-lying (quasi-)degenerate normal modes. Building on our recent work, we use these ``quantum horizon" normal modes to study the thermodynamics of the parent black holes. A key observation is that the UV inputs (the location of the UV regulator, the number of species, and the cut-off in the angular Casimir quantum number) can all be combined into the freedom in a single real parameter. Remarkably, this parameter has an interpretation as the central charge of a holomorphically factorized 2D CFT, and choosing it to be the Kerr-CFT value reproduces the black hole's detailed thermodynamics from the statistical mechanics of normal modes. This perspective provides a heuristic understanding for why the Kerr-CFT central charge is related to the angular momentum of the black hole. The black holes we consider include Kerr-Newman in 3+1 dimensions and Cvetic-Youm in 4+1 dimensions (with all six charges), and they need not be BPS or extremal. Our results show that a refined version of the 't Hooftian quantum gas can be made fully consistent with the thermodynamics of very general black holes. This ``mechanical" approach to the central charge is not directly reliant on asymptotic symmetries in the extremal limit, where the black hole is often unstable.