We analyse the stringy gravitational wave background based on the curr
ent algebra E2c. We determine its exact spectrum and construct the mod
ular invariant vacuum energy. The corresponding N = 1 extension is als
o 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).