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

TY - JOUR

T1 - Multi-parametric R-matrix for the sl(2|1) Yangian

AU - Torrielli, Alessandro

AU - Babichenko, Andrei

PY - 2012/8/1

Y1 - 2012/8/1

N2 - 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 derive the Rmatrix, the antiparticle representation, the crossing and 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.

AB - 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 derive the Rmatrix, the antiparticle representation, the crossing and 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.

U2 - 10.1063/1.4740022

DO - 10.1063/1.4740022

M3 - Article

SN - 0022-2488

VL - 53

SP - 1

EP - 26

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

IS - 8

M1 - 082302

ER -