A note on dual superconformal symmetry of the N=4 super Yang-Mills S-matrix

TL;DR

This paper proves that the tree-level S-matrix in N=4 super Yang-Mills theory exhibits dual superconformal symmetry using a supersymmetric recursion relation, and explores the implications for loop amplitudes.

Contribution

It introduces a supersymmetric recursion relation and demonstrates the dual superconformal covariance of the tree-level S-matrix in N=4 super Yang-Mills.

Findings

Tree-level S-matrix is covariant under dual superconformal transformations.

One-loop amplitude coefficients transform covariantly under the symmetry.

Tree and loop amplitudes share similar transformation properties.

Abstract

We present a supersymmetric recursion relation for tree-level scattering amplitudes in N=4 super Yang-Mills. Using this recursion relation, we prove that the tree-level S-matrix of the maximally supersymmetric theory is covariant under dual superconformal transformations. We further analyse the consequences that the transformation properties of the trees under this symmetry have on those of the loops. In particular, we show that the coefficients of the expansion of generic one-loop amplitudes in a basis of pseudo-conformally invariant scalar box functions transform covariantly under dual superconformal symmetry, and in exactly the same way as the corresponding tree-level amplitudes.