Multi-parametric R-matrix for the sl(2|1) Yangian

TL;DR

This paper derives a multi-parametric R-matrix for the sl(2|1) Yangian using Drinfeld's realization, analyzing its properties and similarities to integrable models in AdS/CFT.

Contribution

It provides a new explicit construction of the R-matrix for the sl(2|1) Yangian, including antiparticle, crossing, and unitarity conditions, with detailed analytic structure analysis.

Findings

Explicit multi-parametric R-matrix derived

Antiparticle representation and crossing conditions obtained

Analytic structure of the R-matrix analyzed

Abstract

We study the Yangian of the 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 AdS/CFT correspondence, although they present obvious crucial differences.