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

TL;DR

This paper constructs and analyzes superstring vacua based on H_4 x M conformal field theories, revealing new sectors with fractional charges and extending supersymmetry beyond typical backgrounds, with implications for DLCQ string theory.

Contribution

It explicitly constructs superstring vacua with enhanced supersymmetry using H_4 x M models and classifies their physical states, including novel sectors with fractional charges.

Findings

Constructed superstring vacua with 8 supercharges.

Classified physical states into two sectors based on U(1)_R-charges.

Proved supersymmetric cancellation in N=2 SCFTs of c=12.

Abstract

We study the superstring vacua constructed from the conformal field theories of the type H_4 x M, where H_4 denotes the super Nappi-Witten model (super WZW model on the 4-dimensional Heisenberg group H_4) 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 H_4 x CY_3. We explicitly construct as physical vertices the space-time SUSY algebra that is a natural extension of H_4 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.