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 AdS3 × S supported by the NS-NS or R-R 3-form backgrounds. The NS-NS plane-wave string model is equivalent to a direct generalization of the NappiWitten 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 world-sheet theory reduces to a system of free fields: 4 massive and 4 massless copies of bosons and fermions. We describe the string spectra of the two models and study the associated asymptotic density of states. We also discuss a more general class of exactly solvable plane-wave models with reduced or completely broken supersymmetry which are obtained by adding twists in two spatial 2-planes. February 2002 ∗ e-mail address: [email protected] ⋆ e-mail address: [email protected] † Also at Lebedev Physics Institute, Moscow.