The su(2|2) Dynamic S-Matrix

TL;DR

Beisert derives and analyzes the two-particle S-matrix for the planar su(2|3) dynamic spin chain associated with N=4 SYM. The S-matrix is completely fixed by residual su(2|2) symmetry up to an overall phase and satisfies the Yang-Baxter equation; a nested Bethe ansatz then yields the asymptotic Bethe equations for periodic states. This work directly validates the Beisert conjecture for the full asymptotic spectrum, modulo the undetermined abelian phase and finite-wrap corrections. It also outlines the dressing phase structure and a path to generalise the framework to psu(2,2|4) with direct implications for AdS/CFT integrability.

Abstract

We derive and investigate the S-matrix for the su(2|3) dynamic spin chain and for planar N=4 super Yang-Mills. Due to the large amount of residual symmetry in the excitation picture, the S-matrix turns out to be fully constrained up to an overall phase. We carry on by diagonalising it and obtain Bethe equations for periodic states. This proves an earlier proposal for the asymptotic Bethe equations for the su(2|3) dynamic spin chain and for N=4 SYM.