A manifestly MHV Lagrangian for N=4 Yang-Mills

TL;DR

This paper derives a manifestly MHV Lagrangian for N=4 supersymmetric Yang-Mills theory in light-cone superspace, simplifying the description of scattering amplitudes and revealing new structural insights.

Contribution

It introduces a canonical superfield redefinition that yields a non-polynomial, manifestly MHV Lagrangian for N=4 SYM, facilitating amplitude calculations.

Findings

Reproduces correct gluon MHV vertices from the superspace Lagrangian

Provides a new superfield formulation with simplified MHV vertices

Ensures the superfields describe the correct degrees of freedom

Abstract

We derive a manifestly MHV Lagrangian for the N=4 supersymmetric Yang-Mills theory in light-cone superspace. This is achieved by constructing a canonical redefinition which maps the N=4 superfield and its conjugate to a new pair of superfields. In terms of these new superfields the N=4 Lagrangian takes a (non-polynomial) manifestly MHV form, containing vertices involving two superfields of negative helicity and an arbitrary number of superfields of positive helicity. We also discuss constraints satisfied by the new superfields, which ensure that they describe the correct degrees of freedom in the N=4 supermultiplet. We test our derivation by showing that an expansion of our superspace Lagrangian in component fields reproduces the correct gluon MHV vertices.