Exacting 𝒩 = 4 superconformal symmetry

Abstract

Tree level scattering amplitudes in N = 4 super Yang-Mills theory are al- most, but not exactly invariant under the free action of the N = 4 superconformal algebra. What causes the non-invariance is the holomorphic anomaly at poles where external par- ticles become collinear. In this paper we propose a deformation of the free superconformal representation by contributions which change the number of external legs. This modified classical representation not only makes tree amplitudes fully invariant, but it also leads to additional constraints from symmetry alone mediating between hitherto unrelated ampli- tudes. Moreover, in a constructive approach it appears to fully constrain all tree amplitudes when combined with dual superconformal alias Yangian symmetry.