Worldsheet Scattering in AdS_5 x S^5

TL;DR

This paper computes the leading order S-matrix for the AdS_5 x S^5 superstring sigma-model, revealing a Hopf algebra structure and connections to the dual gauge theory's spin chain at strong coupling.

Contribution

It demonstrates the realization of supersymmetry via a Hopf algebra structure in the worldsheet scattering matrix, linking string theory and gauge theory integrability.

Findings

S-matrix satisfies a modified classical Yang-Baxter equation

Supercharges act nonlocally, forming a Hopf algebra

Results connect string scattering to gauge theory spin chain at strong coupling

Abstract

We calculate the S-matrix in the gauge-fixed sigma-model on AdS_5 x S^5 to the leading order in perturbation theory, and analyze how supersymmetry is realized on the scattering states. A mild nonlocality of the supercharges implies that their action on multi-particle states does not follow the Leibniz rule, which is replaced by a nontrivial coproduct. The plane wave symmetry algebra is thus naturally enhanced to a Hopf algebra. The scattering matrix elements obey the classical Yang-Baxter equation modified by the existence of the coproduct. This structure mirrors that of the large 't Hooft coupling expansion of the S-matrix for the spin chain in the dual super-Yang-Mills theory.