N=2 Quantum String Scattering

TL;DR

This paper computes genus-one scattering amplitudes in a 2+2 dimensional N=(2,2) superstring, revealing their vanishing and connections to self-dual field theories and supergravity.

Contribution

It introduces a new calculation of genus-one amplitudes in N=2 string theory using spinor helicity and explicitly shows their vanishing, linking to supergravity divergences.

Findings

Genus-one amplitudes vanish in this N=2 string model.

The amplitudes correspond to self-dual gravity in a 2D setting.

No one-loop divergences are present in related supergravity theories.

Abstract

We calculate the genus-one three- and four-point amplitudes in the 2+2 dimensional closed N=(2,2) worldsheet supersymmetric string within the RNS formulation. Vertex operators are redefined with the incorporation of spinor helicity techniques, and the quantum scattering is shown to be manifestly gauge and Lorentz invariant after normalizing the string states. The continuous spin structure summation over the monodromies of the worldsheet fermions is carried out explicitly, and the field-theory limit is extracted. The amplitude in this limit is shown to be the maximally helicity violating amplitude in pure gravity evaluated in a two-dimensional setting, which vanishes, unlike the four-dimensional result. The vanishing of the genus-one N=2 closed string amplitude is related to the absence of one-loop divergences in dimensionally regulated IIB supergravity. Comparisons and contrasts between self-dual field theory and the N=2 string theory are made at the quantum level; they have different S-matrices. Finally, we point to further relations with self-dual field theory and two-dimensional models.