Superstring Gravitational Wave Backgrounds with Spacetime Supersymmetry
  We analyse the stringy gravitational wave background based on the current algebra $E^{c}_{2}$. 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). 
E. Kiritsis, C. Kounnas and D. Luest