FINITE SIGMA-MODELS AND EXACT STRING SOLUTIONS WITH MINKOWSKI SIGNATURE METRIC

We consider two-dimensional (2D) sigma models with a (D = 2 + N)-dimen sional Minkowski signature target space metric having a covariantly co nstant null Killing vector. These models are UV finite. The (2 + N)-di mensional target space metric can be explicitly determined for a class of supersymmetric sigma models with the N-dimensional ''transverse'' part of the target space being sigma homogeneous Kahler type. The corr esponding ''transverse'' subtheory is an n = 2 supersymmetric sigma mo del with the exact beta function coinciding with its one-loop expressi on. For example, the finite D = 4 model has the O(3) supersymmetric or model as its ''transverse'' part. Moreover, there exists a nontrivial dilaton field such that the Weyl invariance conditions are also satis fied; i.e., the resulting models correspond to string vacua. Generic s olutions are represented in terms of the renormalization group flow in ''transverse'' theory. We suggest a possible application of the const ructed Weyl-invariant sigma models to quantization of 2D gravity. They may be interpreted as ''effective actions'' of the quantum 2D dilaton gravity coupled to a (nonconformal) N-dimensional ''matter'' theory. The conformal factor of the 2D metric and 2D ''dilaton'' are identifie d with the light-cone coordinates of the (2 + N)-dimensional sigma mod el.