On solvable models of type IIB superstring in NS-NS and R-R plane wave backgrounds

We consider type IIB string in the two plane-wave backgrounds which may be interpreted as special limits of the AdS_3 x S^3 metric supported by either the NS-NS or R-R 3-form field. The NS-NS plane-wave string model is equivalent to a direct generalization of the Nappi-Witten model, with its spectrum being similar to that of strings in constant magnetic field. The R-R model can be solved in the light-cone gauge, where the Green-Schwarz action describes 4 massive and 4 massless copies of free bosons and fermions. We find the spectra of the two string models and study the asymptotic density of states. We also discuss a more general class of exactly solvable plane-wave models with reduced supersymmetry which is obtained by adding twists in two spatial 2-planes.