A Calogero formulation for four-dimensional black-hole micro states

TL;DR

This paper models the microstates of a four-dimensional extremal black hole using a Calogero model, providing a new approach to compute its entropy via holography and conformal field theory.

Contribution

It introduces a Calogero model framework for describing black hole microstates in four dimensions, linking holography, CFT, and integrable systems.

Findings

Derives the entropy of the black hole from the Calogero model

Establishes a holographic duality between AdS2 geometry and Calogero system

Provides a counting formula for microstate degeneracies

Abstract

We extract the leading-order entropy of a four-dimensional extremal black hole in ${\cal N}{=}2$ ungauged supergravity by formulating the CFT$_1$ that is holographically dual to its near-horizon AdS$_2$ geometry, in terms of a rational Calogero model with a known counting formula for the degeneracy of states in its Hilbert space.