General class of BPS saturated dyonic black holes as exact superstring solutions

Abstract

We show that a four-parameter generating solution for a general class of four-dimensional, spherically-symmetric, static, dyonic BPS saturated solutions of leading-order effective equations of toroidally compactified heterotic or type II superstring theory are exact string solutions. The corresponding ten-dimensional background defines a conformal sigma-model which is a particular case of a `chiral null model' with curved `transverse' part. The exact conformal invariance is a consequence of the chiral null structure of the `electric' part of the model and the N=4 world-sheet supersymmetry of its transverse `magnetic' part. The sigma-model action has a remarkable covariance under both target space and the electromagnetic $S$-duality transformations, and it illustrates the relation between string-string duality in six dimensions and $S$-duality in four dimensions. In general, there exists a large class of exact six-dimensional superstring solutions described by chiral null models with four-dimensional transverse parts represented by N=4 supersymmetric sigma-models with metrics conformal to hyper-Kahler ones.