Twisted Bethe equations from a twisted S-matrix

All-loop asymptotic Bethe equations for a 3-parameter deformation of AdS₅/CFT₄ have been proposed by Beisert and Roiban. We propose a Drinfeld-Reshetikhin twist of the AdS₅/CFT₄ S-matrix, together with c-number diagonal twists of the boundary conditions, from which we derive these Bethe equations. Although the undeformed S-matrix factorizes into a product of two su(2|2) factors, the deformed S-matrix cannot be so factored. Diagonalization of the corresponding transfer matrix requires a generalization of the conventional algebraic Bethe ansatz approach, which we first illustrate for the simpler case of the twisted su(2) principal chiral model. We also demonstrate that the transfer matrix is spectrally equivalent to a transfer matrix which is constructed using instead untwisted S-matrices and boundary conditions with operatorial twists.