Twisting the N=2 String

Abstract

The most general homogeneous monodromy conditions in $N=2$ string theory are classified in terms of the conjugacy classes of the global symmetry group $U(1,1)\otimes {\mathbf{Z}}_2$. For classes which generate a discrete subgroup $\G$, the corresponding target space backgrounds ${\bf C}^{1,1}/\G$ include half spaces, complex orbifolds and tori. We propose a generalization of the intercept formula to matrix-valued twists, but find massless physical states only for $\Gamma =1$ (untwisted) and $\Gamma ={\mathbf{Z}}_2$ (à la Mathur and Mukhi), as well as for $\Gamma$ being a parabolic element of $U(1,1)$. In particular, the sixteen ${\mathbf{Z}}_2$-twisted sectors of the $N=2$ string are investigated, and the corresponding ground states are identified via bosonization and BRST cohomology. We find enough room for an extended multiplet of `spacetime' supersymmetry, with the number of supersymmetries being dependent on global `spacetime' topology. However, world-sheet locality for the chiral vertex operators does not permit interactions among all massless `spacetime' fermions.

42 pages, LaTeX, no figures, 120 kb, ITP-UH-24/93, DESY 93-191 (abstract and introduction clarified, minor corrections added)

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• BRST Quantisation of the N=2 String in a Real Spacetime Structure
• A Heterotic N=2 String with Space-Time Supersymmetry
• N=2 Strings on Orbifolds
• $A_{\infty }$ Action of Open $\mathcal{N}=2$ Superstring Field Theory