The Yangian of sl(n|m) and the universal R-matrix

Abstract

In this paper we study Yangians of sl(n|m) superalgebras. We derive the universal R-matrix and evaluate it on the fundamental representation obtaining the standard Yang R-matrix with unitary dressing factors. For m=0, we directly recover up to a CDD factor the well-known S-matrices for relativistic integrable models with su(N) symmetry. Hence, the universal R-matrix found provides an abstract plug-in formula, which leads to results obeying fundamental physical constraints: crossing symmetry, unitrarity and the Yang-Baxter equation. This implies that the Yangian double unifies all desired symmetries into one algebraic structure. In particular, our analysis is valid in the case of sl(n|n), where one has to extend the algebra by an additional generator leading to the algebra gl(n|n). We find two-parameter families of scalar factors in this case and provide a detailed study for gl(1|1).

arXiv comment24 pages, 2 figures

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• Conformal algebra: R-matrix and star-triangle relation
• Oscillator Construction of su(n|m) Q-Operators
• Nonlocal Symmetries and Factorized Scattering
• Review of AdS/CFT Integrability, Chapter VI.2: Yangian Algebra
• Universal R-matrix of quantum affine gl(1,1)
• Flag Integrable Models and Generalized Graded Algebras
• Multi-parametric R-matrix for the sl(2|1) Yangian