Twisting the N=2 String

TL;DR

This paper classifies monodromy conditions in N=2 string theory, explores their implications for target space backgrounds, and investigates twisted sectors and supersymmetry, revealing limitations on interactions among massless fermions.

Contribution

It generalizes the monodromy classification in N=2 strings, analyzes twisted sectors, and examines supersymmetry and locality constraints in these models.

Findings

Classified monodromy conditions via conjugacy classes of U(1,1)

Identified physical states in specific twisted sectors

Found restrictions on interactions among massless fermions

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 $U(1,1)\otimes{\bf Z}_2$. 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 $\Gamma{=}{\bf 1}$ (untwisted) and $\Gamma{=}{\bf Z}_2$ (\`a la Mathur and Mukhi), as well as for $\Gamma$ being a parabolic element of $U(1,1)$. In particular, the sixteen ${\bf Z}_2$-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.