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

TL;DR

Within effective heterotic superstring theory compactified on a six-torus the authors 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.

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.