Multi--dimensional IWP Solutions for Heterotic String Theory

TL;DR

This paper develops a class of extremal, rotating solutions in heterotic string theory with multiple gauge fields, generalizing known solutions and analyzing their physical properties, including charges and BPS bounds.

Contribution

It introduces a new matrix Ernst potential formulation for extremal solutions in heterotic string theory with multiple U(1) fields, extending previous classes of solutions.

Findings

Derived a rotating dyonic solution expressed via matrix harmonic functions.

Established conditions for extremality and BPS saturation of charges.

Identified a subclass of black hole solutions with zero NUT charge.

Abstract

We present extremal stationary solutions that generalize the Israel-Wilson-Perjes class for the d+3-dimensional low-energy limit of heterotic string theory with n >= d+1 U(1) gauge fields compactified on a d-torus. A rotating axisymmetric dyonic solution is obtained using the matrix Ernst potential formulation and expressed in terms of a single d+1 X d+1-matrix harmonic function. By studying the asymptotic behaviour of the field configurations we define the physical charges of the field system. The extremality condition makes the charges to saturate the Bogomol'nyi-Prasad-Sommerfield (BPS) bound. The gyromagnetic ratios of the corresponding field configurations appear to have arbitrary values. A subclass of rotating dyonic black hole-type solutions arises when the NUT charges are set to zero. In the particular case d=1, n=6, which correspond to N=4, D=4 supergravity, the found dyon reproduces the supersymmetric dyonic solution constructed by Bergshoeff et al.