Global conformal anomaly in N=2 string

TL;DR

This paper identifies a global anomaly in N=2 string theory's one-loop graphs that affects helicity amplitudes, and explores supersymmetric extensions and duality relations in the theory.

Contribution

It reveals a global anomaly in N=2 string theory's one-loop graphs and formulates a supersymmetric completion considering target space-time spin-statistics.

Findings

Existence of a global anomaly in one-loop N=2 string graphs.

Supersymmetric extension of the N=2 string spectrum with an external spin factor.

Demonstration of duality relations between open and closed string amplitudes.

Abstract

We show the existence of a global anomaly in the one-loop graphs of N=2 string theory, defined by sewing tree amplitudes, unless spacetime supersymmetry is imposed. The anomaly is responsible for the non-vanishing maximally helicity violating amplitudes. The supersymmetric completion of the N=2 string spectrum is formulated by extending the previous cohomological analysis with an external spin factor; the target space-time spin-statistics of these individual fields in a selfdual background are compatible with previous cohomological analysis as fields of arbitrary spin may be bosonized into one another. We further analyze duality relations between the open and closed string amplitudes and demonstrate this in the supersymmetric extension of the target space-time theory through the insertion of zero-momentum operators.