From scattering amplitudes to the dilatation generator in SYM

Abstract

The complete spin chain representation of the planar SYM dilatation generator has long been known at one loop, where it involves leading nearest-neighbor 2 → 2 interactions. In this work, we use superconformal symmetry to derive the unique solution for the leading L → 2 interactions of the planar dilatation generator for arbitrarily large L. We then propose that these interactions are given by a scattering operator that has SYM tree-level scattering amplitudes as matrix elements. We provide compelling evidence for this proposal, including explicit checks for L = 2, 3 and a proof of consistency with superconformal symmetry.