Structure of the string R-matrix

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 ui. In this way, we demonstrate that there exists rewriting of its entries, such that the dependence on the spectral parameters is purely of a difference form. Namely, the latter enter only in the combination u1 − u2, as indicated by the shift automorphism of the Yangian. When recasted in this fashion, the entries exhibit a cleaner structure, which allows us to spot new interesting relations among them. This permits us to package them into a practical tensorial expression, where the nondiagonal entries are taken care of by explicit combinations of symmetry algebra generators.