A CLASS OF FINITE 2-DIMENSIONAL SIGMA-MODELS AND STRING VACUA

We consider a two-dimensional Minkowski signature sigma model with a (2 + N)-dimensional target space metric having a null Killing vector. It is found that the model is finite to all orders of the loop expansion if the dependence of the "transverse" part of the metric g(ij)(u, x) on the light cone coordinate u is subject to the standard renormalization group equation of the N-dimensional sigma model, dg(ij)/du = beta(ij)g = R(ij)+.... In particular, we discuss the "one-coupling" case when g(ij)(u, x) is a metric of an N-dimensional symmetric space gamma(ij)(x) multiplied by a function f(u). The theory is finite if f (u) is equal to the "running" coupling of the symmetric space sigma model (with u playing the role of the RG "time"). For example, the geometry of space-time with gamma(ij) being the metric of the N-sphere is determined by the form of the beta-function of the O(N + 1) model. The "asymptotic freedom" limit of large u corresponds to the weak coupling limit of small (2 + N)-dimensional curvature. We show that there exists a dilaton field which together with the (2 + N)-dimensional metric solves the sigma model Weyl invariance conditions. The resulting backgrounds thus represent new tree-level string vacua. We remark on possible connections with some 2D quantum gravity models.