Ward identities and the vanishing theorem for loop amplitudes of the closed N=2 string

TL;DR

This paper derives Ward identities from the ground ring in the N=2 string's BRST cohomology, providing a new proof of the vanishing theorem for loop amplitudes with more than three external legs.

Contribution

It introduces a novel approach using the ground ring to establish Ward identities, leading to a rederivation of the vanishing theorem for N=2 string loop amplitudes.

Findings

Ward identities are derived from the ground ring in the N=2 string.

The identities reprove the vanishing of loop amplitudes with more than three external legs.

The approach applies at arbitrary genus.

Abstract

The existence of a ground ring of ghost number zero operators in the chiral BRST cohomology of the N=2 string is used to derive an infinite set of Ward identities for the closed-string scattering amplitudes at arbitrary genus. These identities are sufficient to rederive the well known vanishing theorem for loop amplitudes with more than three external legs.