The Yangian of sl(n|m) and its quantum R-matrices

Adam Rej*, Fabian Spill

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


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).

Original languageEnglish
Article number012
JournalJournal of High Energy Physics
Issue number5
Publication statusPublished - 2011


  • AdS-CFT correspondence
  • Extended supersymmetry
  • Integrable field theories
  • Sigma models

ASJC Scopus subject areas

  • Nuclear and High Energy Physics


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