Vertex operators for the superstring with manifest $d=6$ $\mathcal{N}=1$ supersymmetry

TL;DR

This paper develops a new vertex operator formalism for the six-dimensional superstring with manifest supersymmetry, linking BRST invariance to super-Yang-Mills equations and enabling amplitude calculations similar to pure spinor methods.

Contribution

It introduces a manifestly supersymmetric vertex operator in six dimensions and connects BRST invariance to super-Yang-Mills equations in superspace.

Findings

Constructed a supersymmetric vertex operator for d=6, N=1 superstring.

Showed BRST invariance implies super-Yang-Mills equations.

Demonstrated amplitude computations analogous to pure spinor formalism.

Abstract

By extending the six-dimensional hybrid formalism for the superstring to include $d=6$ $\mathcal{N}=1$ superspace variables along with unconstrained bosonic ghost fields, we construct a manifestly spacetime supersymmetric vertex operator $U$. We demonstrate that the BRST invariance of $U$ implies the $d=6$ $\mathcal{N}=1$ SYM equations of motion in superspace. Furthermore, we show that spacetime supersymmetric scattering amplitudes can be computed in a manner analogous to that of the non-minimal pure spinor formalism.