On the Hopf algebra structure of the AdS/CFT S-matrix

TL;DR

The paper extends the Hopf-algebra framework for the AdS/CFT S-matrix from the su(1|2) subsector to the full su(2|2) symmetry, showing how length-changing (dynamic) generators induce a nontrivial central braiding in the coproduct. It systematically constructs the deformed coproduct, antipode, and counit, and derives a consistent charge-conjugation operation that yields the antiparticle representation directly from the algebra. The results validate the Hopf-algebra axioms in this deformed setting and point toward a universal R-matrix as the next step to encode crossing and fix the overall scalar factor. This algebraic perspective provides a potentially powerful, representation-independent handle on the AdS/CFT S-matrix structure and its underlying symmetries.

Abstract

We formulate the Hopf algebra underlying the su(2|2) worldsheet S-matrix of the AdS_5 x S^5 string in the AdS/CFT correspondence. For this we extend the previous construction in the su(1|2) subsector due to Janik to the full algebra by specifying the action of the coproduct and the antipode on the remaining generators. The nontriviality of the coproduct is determined by length-changing effects and results in an unusual central braiding. As an application we explicitly determine the antiparticle representation by means of the established antipode.