Duality invariant class of exact string backgrounds

Abstract

We consider a class of (2+ D)-dimensional string backgrounds with a target space metric having a covariantly constant null Killing vector and flat “transverse” part. The corresponding sigma models are invariant under D abelian isometries and are transformed by O( D, D) duality into models belonging to the same class. The leading-order solutions of the conformal invariance equations (metric, antisymmetric tensor and dilation), as well as the action of O( D, D) duality transformations on them, are exact, i.e. are not modified by α′-corrections. This makesa discussion of different space-time representations of the same string solution (related by the O(D,D| Z) duality subgroup) rather explicit. We show that the O( D, D) duality may connect curved (2+ D)-dimensional backgrounds with solutions having flat metric but, in general, non-trivial antisymmetric tensor and dilation. We discuss several particular examples including the (2+ D=4)-dimensional background that was recently interpreted in terms of a WZW model.