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

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 string theory is an exact string solution. 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 T-duality and the electro-magnetic S-duality transformations, and it illustrates the relationship 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 σ-models with metrics conformal to hyper-Kähler ones.