HOMOGENEOUS CONFORMAL STRING BACKGROUNDS

We present exact solutions characterized by Bianchi-type I, II, III, V, VIo, VIh with a four-dimensional metric, space-independent dilaton, and vanishing torsion background, for the low-energy string effective action with zero central charge deficit. We show that, in such a context, curvature singularities cannot be avoided, except for the trivial case of flat spacetime and constant dilaton. We also provide a further example of the failure of the standard prescription for connecting conformal string backgrounds through duality transformations associated to nonsemisimple, non-Abelian isometry groups.