Exactly solvable model of superstring in plane wave Ramond-Ramond background

We describe in detail the solution of type IIB superstring theory in the maximally supersymmetric plane-wave background with constant null Ramond-Ramond 5-form field strength. The corresponding light-cone Green-Schwarz action found by Metsaev is quadratic in both bosonic and fermionic coordinates. We obtain the light-cone Hamiltonian and the string representation of the corresponding supersymmetry algebra. The superstring Hamiltonian has a ``harmonic-oscillator'' form in both the string oscillator and the zero-mode parts and thus has a discrete spectrum. We analyze the structure of the zero-mode sector of the theory, establishing the precise correspondence between the lowest-lying ``massless'' string states and the type IIB supergravity fluctuation modes in the plane-wave background. The zero-mode spectrum has a certain similarity to the supergravity spectrum in AdS₅×S⁵ background of which the plane-wave background is a special limit. We also compare the plane-wave string spectrum with the expected form of the light-cone gauge spectrum of the AdS₅×S⁵ superstring.