Entropy and supersymmetry of $D$ dimensional extremal electric black holes versus string states

TL;DR

This paper explores the relationship between extremal black holes and string states in heterotic string theory, demonstrating that their entropies match at the stringy stretched horizon for supersymmetric solutions.

Contribution

It provides a detailed analysis of electrically charged extremal black holes in heterotic string theory, establishing their entropy correspondence with elementary string states, especially for supersymmetric cases.

Findings

Entropy of extremal black holes matches string state entropy at the stretched horizon.

Supersymmetric black holes exhibit properties consistent with string theory predictions.

The study extends the black hole-string correspondence to a range of dimensions D=4 to 9.

Abstract

Following the work of Sen, we consider the correspondence between extremal black holes and string states in the context of the entropy. We obtain and study properties of electrically charged black hole backgrounds of tree level heterotic string theory compactified on a $p$ dimensional torus, for $D=(10-p)=4 \ldots 9$. We study in particular a one--parameter extremal class of these black holes, the members of which are shown to be supersymmetric. We find that the entropy of such an extremal black hole, when calculated at the stringy stretched horizon, scales in such a way that it can be identified with the entropy of the elementary string state with the corresponding quantum numbers.