MHV Lagrangian for N=4 Super Yang-Mills

TL;DR

This paper formulates a new MHV Lagrangian for N=4 Super Yang-Mills using specific field redefinitions in light cone superspace, simplifying the analysis of scattering amplitudes and their loop-level properties.

Contribution

It introduces a canonical transformation-based MHV Lagrangian in superspace that aligns with the CSW expansion and facilitates loop-level analysis.

Findings

Reproduces known 4-point MHV amplitude

Simplifies superspace loop analysis

Clarifies relation to CSW off-shell continuation

Abstract

Here we formulate two field redefinitions for N=4 Super Yang-Mills in light cone superspace that generates only MHV vertices in the new Lagrangian. After careful consideration of the S-matrix equivalence theorem, we see that only the canonical transformation gives the MHV Lagrangian that would correspond to the CSW expansion. Being in superspace, it is easier to analyse the equivalence theorem at loop level. We calculate the on shell amplitude for 4pt $(\bar{\Lambda}\bar{{\rm A}}\Lambda {\rm A})$ MHV in the new lagrangian and show that it reproduces the previously known form. We also briefly discuss the relationship with the off-shell continuation prescription of CSW.