Multi-parametric R-matrix for the $\mathfrak {sl}(2|1)$sl(2|1) Yangian

Abstract

We study the Yangian of the \documentclass[12pt]{minimal}\begin{document}$\mathfrak {sl}(2|1)$\end{document}sl(2|1) Lie superalgebra in a multi-parametric four-dimensional representation. We use Drinfeld's second realization to independently rederive the R-matrix, and to obtain the antiparticle representation, the crossing and the unitarity condition. We consistently apply the Yangian antipode and its inverse to the individual particles involved in the scattering. We explicitly find a scalar factor solving the crossing and unitarity conditions, and study the analytic structure of the resulting dressed R-matrix. The formulas we obtain bear some similarities with those familiar from the study of integrable structures in the Anti de Sitter (AdS) / Conformal Field Theory (CFT) correspondence, although they present obvious crucial differences.