STRING VACUUM BACKGROUNDS WITH COVARIANTLY CONSTANT NULL KILLING VECTOR AND 2-DIMENSIONAL QUANTUM-GRAVITY

We consider a two-dimensional sigma model with a (2 + N)-dimensional Minkowski signature target space metric having a covariantly constant null Killing vector. We study solutions of the conformal invariance conditions in 2 + N dimensions and find that generic solutions can be represented in terms of the RG flow in N-dimensional ''transverse space'' theory. The resulting conformal invariant sigma model is interpreted as a quantum action of the two-dimensional scalar (''dilaton'') quantum gravity model coupled to a (non-conformal) ''transverse'' sigma model. The conformal factor of the two-dimensional metric is identified with a light-cone coordinate of the (2 + N)-dimensional sigma model. We also discuss the case when the transverse theory is conformal (with or without the antisymmetric tensor background) and reproduce in a systematic way the solutions with flat transverse space known before.