Twisting the N=2 string

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)direct-product openZ2. For classes which generate a discrete subgroup Γ, the corresponding target space backgrounds openC1,1/Γ 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 Γ=open1 (untwisted) and Γ=openZ2 (in the manner of Mathur and Mukhi), as well as for Γ being a parabolic element of U(1,1). In particular, the 16 openZ2-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