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

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.