Strings on Plane Waves and AdS x S

We consider the RNS superstrings in $AdS_3 \times S^3 \times {\cal M}$, where $\cal M$ may be $K3$ or $T^4$, based on $SL(2,R)$ and SU(2) WZW models. We construct the physical states and calculate the spectrum. A subsector of this theory describes strings propagating in the six dimensional plane wave obtained by the Penrose limit of $AdS_3 \times S^3 \times {\cal M}$. We reproduce the plane wave spectrum by taking $J$ and the radius to infinity. We show that the plane wave spectrum actually coincides with the large $J$ spectrum at fixed radius, i.e. in $AdS_3 \times S^3$. Relation to some recent topics of interest such as the Frolov-Tseytlin string and strings with critical tension or in zero radius $AdS$ are discussed.