4-DIMENSIONAL PLANE-WAVE STRING SOLUTIONS WITH COSET CFT DESCRIPTION

We present a number of D = 4 bosonic and heterotic string solutions wi th a covariantly constant null Killing vector which, like the solution of Nappi and Witten (NW), correspond to (gauged) WZW models and thus have a direct conformal field theory interpretation. A class of exact plane wave solutions (which includes the NW solution) is constructed b y 'boosting' the twisted products of two D = 2 'cosmological' or 'blac k-hole' cosets related to (G x G')/(H x H') (G, G' = SL(2, R) or SU(2) ; H, H'= SO(1, 1) or SO(2)) gauged WZW models. We describe a general l imiting procedure by which one can construct new solutions with a cova riantly constant null Killing vector starting with known string backgr ounds. By applying a non-abelian duality transformation to the NW mode l we find a D = 4 solution which admits a covariantly constant null Ki lling vector but is not a plane wave. Higher dimensional bosonic backg rounds with isometries can be interpreted as lower dimensional ones wi th extra gauge fields. Some of them are at the same time solutions of the heterotic string theory. In particular, the NW model represents al so a D = 3 gravi-electromagnetic heterotic string plane wave. In addit ion to the (1, 1) supersymmetric embeddings of bosonic solutions we co nstruct a number of non-trivial (1, 0) supersymmetric exact D = 4 hete rotic string plane wave solutions some of which are related (by a boos t and analytic continuation) to limiting cases of D = 4 heterotic blac k hole solutions.