An SLE approach to four dimensional black hole microstate entropy

TL;DR

This paper models the entropy of four-dimensional extremal black holes using SLE curves in AdS_2, connecting particle trajectories, conformal quantum gravity, and integrable models to compute black hole microstate degeneracy.

Contribution

It introduces a novel SLE-based framework to classify particle trajectories in AdS_2, linking boundary conditions to black hole entropy calculation.

Findings

Classifies particle trajectories using SLE in AdS_2.

Relates boundary conditions to singular vectors in conformal quantum gravity.

Provides a microscopic count of black hole entropy from first principles.

Abstract

In this note, we model the Bekenstein-Hawking entropy of a four dimensional extremal black hole in terms of classifying particles moving in its near horizon AdS_2 geometry. We use the framework of SLE curves in AdS_2 to classify these particle trajectories in terms of their boundary conditions. These turn out to be related to singular vectors in two-dimensional conformal quantum gravity theory in AdS_2 and the dynamics of these particles are governed by the Hamiltonians of the integrable Calogero-like models, for these boundary conditions. We use this classification to count the leading order Bekenstein-Hawking entropy of the black hole and arrive at a first principle microscopic computation of black hole degeneracy.