Superstring gravitational wave backgrounds with spacetime supersymmetry

We analyze the stringy gravitational wave background based on the current algebra E2c. We determine its exact spectrum and construct the modular invariant vacuum energy. The corresponding N = 1 extension is also constructed. The algebra is again mapped to free bosons and fermions and we show that this background has N = 4 (N = 2) unbroken spacetime supersymmetry in the type II (heterotic case).