Black Hole Solutions in Heterotic String Theory on a Torus

TL;DR

The paper constructs the most general electrically charged rotating black hole in heterotic string theory compactified on T^6, parametrized by mass, angular momentum, and a 28-component electric charge vector, by exploiting duality symmetries (notably O(7,23)) to generate new solutions from the Kerr seed. It further develops a 58-parameter rotating dyonic extension by combining SL(2,R) dualities with O(7,23) and, more generally, O(8,24) transformations, identifying a Taub-NUT subset and imposing a single constraint to obtain a non-singular, no-hair-consistent 58-parameter space with 28 electric and 28 magnetic charges. Special charge configurations reproduce known dilaton-axion and Kaluza-Klein black holes, while generic cases reveal independent left- and right-handed gyromagnetic ratios and non-parallel electric and magnetic moments. The work also discusses extremal limits, Bogomol’nyi bounds, and connections to the spectrum of elementary string states, highlighting how black hole parameters mirror string-theoretic quantities in those limits.

Abstract

We construct the general electrically charged, rotating black hole solution in the heterotic string theory compactified on a six dimensional torus and study its classical properties. This black hole is characterized by its mass, angular momentum, and a 28 dimensional electric charge vector. We recover the axion-dilaton black holes and Kaluza-Klein black holes for special values of the charge vector. For a generic black hole of this kind, the 28 dimensional magnetic dipole moment vector is not proportional to the electric charge vector, and we need two different gyromagnetic ratios for specifying the relation between these two vectors. We also give an algorithm for constructing a 58 parameter rotating dyonic black hole solution in this theory, characterized by its mass, angular momentum, a 28 dimensional electric charge vector and a 28 dimensional magnetic charge vector. This is the most general asymptotically flat black hole solution in this theory consistent with the no-hair theorem.