STRINGS ON CURVED SPACE-TIMES - BLACK-HOLES, TORSION, AND DUALITY

We present a general discussion of strings propagating on noncompact coset spaces G/H in terms of gauged WZW models, emphasizing the role played by isometries in the existence of target-space duality. Fixed points of the gauged transformations induce metric singularities and, in the case of abelian subgroups H, become horizons in a dual geometry. We also give a classification of models with a single timelike coordinate together with an explicit list for dimensions D less-than-or-equal-to 10. We study in detail the class of models described by the cosets SL(2, R) x SO(1, 1)D-2/SO(1, 1). For D greater-than-or-equal-to 2 each coset represents two different space-time geometries: (2d black hole) x R(D-2) and (3d black string) x R(D-3) with nonvanishing torsion. They are shown to be dual in such a way that the singularity of the former geometry (which is not due to a fixed point) is mapped to a regular surface (i.e. not even a horizon) in the latter. These cosets also lead to the conformal field theory description of known and new cosmological string models.