All tree-level amplitudes in N=4 SYM

TL;DR

This paper provides a comprehensive, explicit formula for all tree-level scattering amplitudes in N=4 supersymmetric Yang-Mills theory, utilizing supersymmetric recursion relations and manifest symmetries.

Contribution

It introduces a compact, supersymmetric formula for all tree amplitudes in N=4 SYM, enabling extraction of component amplitudes for any external particle configuration.

Findings

Formula respects both superconformal and dual superconformal symmetry.

Allows calculation of any tree-level amplitude in N=4 SYM.

Applicable to arbitrary external particles and helicity arrangements.

Abstract

We give an explicit formula for all tree amplitudes in N=4 SYM, derived by solving the recently presented supersymmetric tree-level recursion relations. The result is given in a compact, manifestly supersymmetric form and we show how to extract from it all possible component amplitudes for an arbitrary number of external particles and any arrangement of external particles and helicities. We focus particularly on extracting gluon amplitudes which are valid for any gauge theory. The formula for all tree-level amplitudes is given in terms of nested sums of dual superconformal invariants and it therefore manifestly respects both conventional and dual superconformal symmetry.