We study the superstring vacua constructed from the conformal field theories<br />
of the type H_4 x M, where H_4 denotes the super Nappi-Witten model (super WZW<br />
model on the 4-dimensional Heisenberg group H_4) and M denotes an arbitrary N=2<br />
rational superconformal field theory with c=9. We define (type II) superstring<br />
vacua with 8 supercharges, which are twice as many as those on the backgrounds<br />
of H_4 x CY_3. We explicitly construct as physical vertices the space-time SUSY<br />
algebra that is a natural extension of H_4 Lie algebra. The spectrum of<br />
physical states is classified into two sectors: (1) strings freely propagating<br />
along the transverse plane of pp-wave geometry and possessing the integral<br />
U(1)_R-charges in M sector, and (2) strings that do not freely propagate along<br />
the transverse plane and possess the fractional U(1)_R-charges in M. The former<br />
behaves like the string excitations in the usual Calabi-Yau compactification,<br />
but the latter defines new sectors without changing the physics in ``bulk&#039;&#039;<br />
space. We also analyze the thermal partition functions of these systems,<br />
emphasizing the similarity to the DLCQ string theory. As a byproduct we prove<br />
the supersymmetric cancellation of conformal blocks in an arbitrary unitary N=2<br />
SCFT of c=12 with the suitable GSO projection.