Dyonic BPS Saturated Black Holes of Heterotic String on a Six-Torus

TL;DR

This paper derives supersymmetric, dyonic black hole solutions in heterotic string theory compactified on a six-torus, highlighting their duality symmetries and supersymmetry preservation.

Contribution

It presents the first explicit derivation of BPS saturated black hole solutions with electric and magnetic charges invariant under duality symmetries in heterotic string theory.

Findings

Solutions exhibit $O(6,22)$ and $SL(2)$ duality invariance.

Configurations preserve 1/2 or 1/4 of $N=4$ supersymmetry.

Some solutions correspond to extreme Reissner-Nordström black holes.

Abstract

Within effective heterotic superstring theory compactified on a six-torus we derive minimum energy (supersymmetric), static, spherically symmetric solutions, which are manifestly invariant under the target space $O(6,22)$ and the strong-weak coupling $SL(2)$ duality symmetries with 28 electric and 28 magnetic charges subject to one constraint. The class of solutions with a constant axion corresponds to dyonic configurations subject to two charge constraints, with purely electric [or purely magnetic] and dyonic configurations preserving ${1\over 2}$ and ${1\over 4}$ of $N=4$ supersymmetry, respectively. General dyonic configurations in this class have a space-time of extreme Reissner-Nordstr\" om black holes while configurations with more constrained charges have a null or a naked singularity.