Twisted Bethe equations from a twisted S-matrix

TL;DR

This paper derives all-loop asymptotic Bethe equations for a 3-parameter deformation of AdS5/CFT4 by proposing a Drinfeld twist of the S-matrix, extending the algebraic Bethe ansatz to the twisted case.

Contribution

It introduces a novel Drinfeld twist of the AdS5/CFT4 S-matrix and generalizes the algebraic Bethe ansatz to handle non-factorizable deformed S-matrices.

Findings

Derived twisted Bethe equations from the twisted S-matrix.

Showed the necessity of a generalized algebraic Bethe ansatz.

Presented an alternative derivation using untwisted S-matrices with operatorial twists.

Abstract

All-loop asymptotic Bethe equations for a 3-parameter deformation of AdS5/CFT4 have been proposed by Beisert and Roiban. We propose a Drinfeld 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 same twisted Bethe equations can alternatively be derived using instead untwisted S-matrices and boundary conditions with operatorial twists.