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arXiv · 0806.1299

Structure of the string R-matrix

Alessandro Torrielli
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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.

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Alessandro Torrielli. 2008-06-18. Structure of the string R-matrix. https://doi.org/10.1088/1751-8113%2F42%2F5%2F055204

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