Microscopic and Macroscopic Entropy of Extremal Black Holes in String Theory

TL;DR

The work surveys how microscopic counts of BPS black hole states in string theory compare with macroscopic entropy calculations that include higher-derivative and quantum corrections. It articulates a macroscopic framework based on an $AdS_2$ throat and Euclidean path integrals, yielding $S_{macro}$ that matches Wald entropy in the classical limit and reproduces quantum corrections. It reviews exact microscopic results expressed through Siegel modular and weak Jacobi forms, showing leading-order agreement with $S_{BH}$ and detailed matches for logarithmic and twisted-index corrections. The findings bolster string theory as a consistent quantum gravity framework and point to localization techniques as a promising path to exact macroscopic indices, with extensions to non-supersymmetric extremal black holes as a future direction.

Abstract

This is a short review summarizing the current status of the comparison between microscopic and macroscopic entropy of extremal BPS black holes in string theory.

Figures (1)

• Figure 1: Euclidean geometry described by the $(r,\theta)$ coordinates in (\ref{['euclid']}) with an IR cut-off $r\le r_0$.