Israel--Wilson--Perj\'es Solutions in Heterotic String Theory

TL;DR

This paper introduces an algorithm to generate solutions in heterotic string theory that extend the Israel--Wilson--Perjés class, utilizing a map from Einstein--Maxwell theory, and explicitly constructs a dyonic solution with BPS-bound charges.

Contribution

It provides a novel, straightforward method to find solutions in heterotic string theory using matrix Ernst potentials and a mapping from Einstein--Maxwell theory, including explicit dyonic solutions.

Findings

Derived explicit dyonic solution in heterotic string theory.

Established charges satisfy the BPS bound.

Developed an algorithm for generating generalized solutions.

Abstract

We present a simple algorithm to obtain solutions that generalize the Israel--Wilson--Perj\'es class for the low-energy limit of heterotic string theory toroidally compactified from D=d+3 to three dimensions. A remarkable map existing between the Einstein--Maxwell (EM) theory and the theory under consideration allows us to solve directly the equations of motion making use of the matrix Ernst potentials connected with the coset matrix of heterotic string theory. For the particular case d=1 (if we put n=6, the resulting theory can be considered as the bosonic part of the action of D=4, N=4 supergravity) we obtain explicitly a dyonic solution in terms of one real 2\times 2--matrix harmonic function and 2n real constants (n being the number of Abelian vector fields). By studying the asymptotic behaviour of the field configurations we define the charges of the system. They satisfy the Bogomol'nyi--Prasad--Sommmerfeld (BPS) bound.