The r-matrix of the Alday-Arutyunov-Frolov model

TL;DR

This paper studies the classical integrability of the Alday-Arutyunov-Frolov model, deriving its r-matrix structure by simplifying the Lax connection and applying a generalized Maillet regularization for non-ultralocal models.

Contribution

It simplifies the Lax connection to a 2x2 form and extends Maillet's regularization to derive the r- and s-matrices for the model.

Findings

Derived the r- and s-matrices for the model

Reduced the Lax connection to a 2x2 form

Connected classical regularization with quantum operator regularization

Abstract

We investigate the classical integrability of the Alday-Arutyunov-Frolov model, and show that the Lax connection can be reduced to a simpler 2 x 2 representation. Based on this result, we calculate the algebra between the L-operators and find that it has a highly non-ultralocal form. We then employ and make a suitable generalization of the regularization technique proposed by Maillet for a simpler class of non-ultralocal models, and find the corresponding r- and s-matrices. We also make a connection between the operator-regularization method proposed earlier for the quantum case, and the Maillet's symmetric limit regularization prescription used for non-ultralocal algebras in the classical theory.