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

TL;DR

This paper develops a Hopf algebra framework for the full su(2|2) S-matrix in AdS/CFT, extending previous work and revealing new algebraic structures related to length-changing effects.

Contribution

It extends the Hopf algebra construction from the su(1|2) subsector to the full su(2|2) algebra, detailing the coproduct, antipode, and central braiding.

Findings

Explicitly determined the antiparticle representation.

Identified the role of length-changing effects in the coproduct.

Introduced an unusual central braiding in the algebra structure.

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.