DOES SIGMA-MODEL CONFORMAL-INVARIANCE IMPLY A ROBERTSON-WALKER UNIVERSE

Starting from the sigma-model conformal invariance conditions we find all four dimensional metrics when the dilaton field satisfies the condition del(mu)del(nu)phi=0. Such configurations have been previously employed in a flat D dimensional target space and naturally come out as solutions consistent with conformal invariance of the supersymmetric sigma-model beyond the two loop order. The four dimensional metrics emerging out are either of the Robertson-Walker type or a special kind of a generalized pp-wave metric. Of these solutions only the Robertson-Walker metric can be related to a noncritical string theory.