Exactly Solvable Model of Superstring in Plane-wave Background with Linear Null Dilaton

In this paper, we study an exactly solvable model of IIB superstring in a time-dependent plane-wave backgound with a constant self-dual Ramond-Ramond 5-form field strength and a linear dilaton in the light-like direction. This background keeps sixteen supersymmetries. In the light-cone gauge, the action is described by the two-dimensional free bosons and fermions with time-dependent masses. The model could be canonically quantized and its Hamiltonian is time-dependent with vanishing zero point energy. The spectrum of the excitations is symmetric between the bosonic and fermionic sector. The string mode creation turns out to be very small.