From Scattering Amplitudes to the Dilatation Generator in N=4 SYM

TL;DR

This paper derives the leading interactions of the planar N=4 SYM dilatation generator for any chain length using superconformal symmetry and proposes they are given by the scattering operator related to tree-level scattering amplitudes.

Contribution

It introduces a novel connection between the dilatation generator's interactions and N=4 SYM scattering amplitudes, extending understanding to arbitrary chain lengths.

Findings

Derived the unique L -> 2 interactions for any chain length using symmetry.

Proposed that these interactions are given by the scattering operator with tree-level amplitudes.

Provided explicit checks and consistency proofs supporting the proposal.

Abstract

The complete spin chain representation of the planar N=4 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 the scattering operator that has N=4 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.