Note on dual superconformal symmetry of theN=4super Yang-MillsSmatrix

Abstract

We present a supersymmetric recursion relation for tree-level scattering amplitudes in $\mathcal{N}=4$ 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 analyze 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 pseudoconformally invariant scalar box functions transform covariantly under dual superconformal symmetry, and in exactly the same way as the corresponding tree-level amplitudes.