Superstring Vacua of 4-dimensional PP-Waves with Enhanced Supersymmetry

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We study the superstring vacua constructed from the conformal field theories of the type H₄ x M, where H₄ denotes the super Nappi-Witten model (super WZW model on the 4-dimensional Heisenberg group H₄) and M denotes an arbitrary N=2 rational superconformal field theory with c=9. We define (type II) superstring vacua with 8 supercharges, which are twice as many as those on the backgrounds of H₄ x CY₃. We explicitly construct as physical vertices the space-time SUSY algebra that is a natural extension of H₄ Lie algebra. The spectrum of physical states is classified into two sectors: (1) strings freely propagating along the transverse plane of pp-wave geometry and possessing the integral U(1)ᵣ-charges in M sector, and (2) strings that do not freely propagate along the transverse plane and possess the fractional U(1)ᵣ-charges in M. The former behaves like the string excitations in the usual Calabi-Yau compactification, but the latter defines new sectors without changing the physics in ``bulk'' space. We also analyze the thermal partition functions of these systems, emphasizing the similarity to the DLCQ string theory. As a byproduct we prove the supersymmetric cancellation of conformal blocks in an arbitrary unitary N=2 SCFT of c=12 with the suitable GSO projection.