Matrix Dilaton-Axion for Heterotic String in Three Dimensions

Abstract

New and surprisingly simple representation is found for the heterotic string bosonic effective action in three dimensions in terms of complex potentials. The system is presented as a K\"ahler $\sigma$--model using complex symmetric $2\times 2$ matrix (matrix dilaton--axion) which depends linearly on three Ernst--type potentials and transforms under $U$--duality via matrix valued $SL(2,R)$. Two discrete automorphisms relating ten isometries of the target space (U--duality transformations) are found and used to generate the non--trivial Ehlers--Harrison sector by a map from the trivial gauge sector. Finite transformations are obtained in a simple form in terms of complex potentials. New solution generating technique is used to construct EMDA double--Kerr solution.