Hopf algebra structure of the AdS/CFTS-matrix

Abstract

We formulate the Hopf algebra underlying the $\mathfrak{s}\mathfrak{u}(2|2)$ world sheet $S$-matrix of the ${\mathrm{AdS}}_{5}\ifmmode\times\else\texttimes\fi{}{S}^{5}$ string in the AdS/CFT correspondence. For this we extend the previous construction in the $\mathfrak{s}\mathfrak{u}(1|2)$ 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.