Black Hole Entropy in M-Theory

TL;DR

This paper computes the microscopic entropy of extremal black holes in M-theory using a two-dimensional sigma model and finds exact agreement with the macroscopic entropy calculations, confirming the microscopic origin of black hole entropy.

Contribution

It provides a detailed microscopic derivation of black hole entropy in M-theory, including quantum corrections, and compares it with macroscopic formulas.

Findings

Exact agreement between microscopic and macroscopic entropy calculations.

Inclusion of one-loop quantum corrections in the entropy.

Validation of the sigma model approach for black hole microstates.

Abstract

Extremal black holes in M-theory compactification on $M\times S^1$ are microscopically represented by fivebranes wrapping $P\times S^1$, where $M$ is a Calabi-Yau threefold and $P$ is a four-cycle in $M$. Additional spacetime charges arise from momentum around the $S^1$ and expectation values for the self-dual three-form field strength in the fivebrane. The microscopic entropy of the fivebrane as a function of all the charges is determined from a two-dimensional $(0,4)$ sigma model whose target space includes the fivebrane moduli space. This entropy is compared to the macroscopic formula. Precise agreement is found for both the tree-level and one-loop expressions.