Structure of the string R-matrix

TL;DR

This paper rederives Beisert's quantum R-matrix by enforcing Yangian symmetry, revealing a difference form dependence on spectral parameters and providing a clearer, tensorial structure that highlights new algebraic relations.

Contribution

It presents a reformulation of the quantum R-matrix with explicit dependence on representation labels and spectral parameters, emphasizing the difference form and tensorial structure.

Findings

Spectral parameters depend only on their difference u_1 - u_2

The R-matrix entries exhibit a cleaner, more structured form

New relations among R-matrix entries are identified

Abstract

By requiring invariance directly under the Yangian symmetry, we rederive Beisert's quantum R-matrix, in a form that carries explicit dependence on the representation labels, the braiding factors, and the spectral parameters u_i. In this way, we demonstrate that there exist a rewriting of its entries, such that the dependence on the spectral parameters is purely of difference form. Namely, the latter enter only in the combination u_1-u_2, as indicated by the shift automorphism of the Yangian. When recasted in this fashion, the entries exhibit a cleaner structure, which allows to spot new interesting relations among them. This permits to package them into a practical tensorial expression, where the non-diagonal entries are taken care by explicit combinations of symmetry algebra generators.