Generating MHV super-vertices in light-cone gauge

TL;DR

This paper constructs the $ ext{N}=1$ SYM Lagrangian in light-cone gauge using chiral superfields, deriving MHV super-vertices with a formula akin to $ ext{N}=4$ super-amplitudes, and discusses connections to Nair's formula.

Contribution

It introduces a novel formulation of the $ ext{N}=1$ SYM Lagrangian using chiral superfields and derives MHV super-vertices similar to $ ext{N}=4$ SYM.

Findings

Derived $ ext{N}=1$ MHV super-vertices formula

Connected light-cone Lagrangian to $ ext{N}=4$ super-amplitudes

Outlined a method to derive Nair's formula from light-cone Lagrangian

Abstract

We constructe the $\mathcal{N}=1$ SYM lagrangian in light-cone gauge using chiral superfields instead of the standard vector superfield approach and derive the MHV lagrangian. The canonical transformations of the gauge field and gaugino fields are summarised by the transformation condition of chiral superfields. We show that $\mathcal{N}=1$ MHV super-vertices can be described by a formula similar to that of the $\mathcal{N}=4$ MHV super-amplitude. In the discussions we briefly remark on how to derive Nair's formula for $\mathcal{N}=4$ SYM theory directly from light-cone lagrangian.