Multigluon amplitudes, ${\cal N}=4$ constraints and the WZW model

TL;DR

This paper demonstrates how a WZW action on extended superspace can solve certain ${ m N}=4$ Yang-Mills constraints and generate MHV and non-MHV amplitudes, linking superspace constraints with amplitude calculations.

Contribution

It introduces a WZW model on extended superspace that provides solutions to ${ m N}=4$ Yang-Mills constraints and expresses all tree-level amplitudes.

Findings

Solutions to superspace constraints lead to MHV amplitudes.

Non-MHV amplitudes are also expressed via the WZW action.

The approach connects superspace constraints with amplitude computations.

Abstract

Classical ${\cal N}=4$ Yang-Mills theory is defined by the superspace constraints. We obtain a solution of a subset of these constraints and show that it leads to the maximally helicity violating (MHV) amplitudes. The action which leads to the solvable part of the constraints is a Wess-Zumino-Witten (WZW) action on a suitably extended superspace. The non-MHV tree amplitudes can also be expressed in terms of this action.