Extremal black hole entropy from conformal string sigma model

TL;DR

This paper derives the entropy of extremal dyonic black holes within string theory using a conformal sigma model, showing that the main contribution comes from string oscillations in four transverse dimensions, matching the Bekenstein-Hawking entropy.

Contribution

It provides a string-theoretic derivation of black hole entropy that resolves previous puzzles and identifies the universal dominant contribution from specific string oscillations.

Findings

The entropy matches the Bekenstein-Hawking formula.

String oscillations in four transverse dimensions dominate the entropy.

Subleading contributions come from internal compact dimensions.

Abstract

We present string-theory derivation of the semiclassical entropy of extremal dyonic black holes in the approach based on conformal sigma model (NS-NS embedding of the classical solution). We demonstrate (resolving some puzzles existed in previous related discussions) that the degeneracy responsible for the entropy is due to string oscillations in four transverse dimensions `intrinsic' to black hole: four non-compact directions of the D=5 black hole and three non-compact and one compact (responsible for embedding of magnetic charges) dimensions in the D=4 black hole case. Oscillations in other compact internal dimensions give subleading contributions to statistical entropy in the limit when all charges are large. The dominant term in the statistical entropy is thus universal (i.e. is the same in type II and heterotic string theory) and agrees with Bekenstein-Hawking expression.