Weakly coupled N=4 Super Yang-Mills and N=6 Chern-Simons theories from u(2|2) Yangian symmetry

Abstract

In this paper we derive the universal R-matrix for the Yangian Y(u(2|2)), which is an abstract algebraic object leading to rational solutions of the Yang-Baxter equation on representations. We find that on the fundamental representation the universal R-matrix reduces to the standard rational R-matrix R = R_0(1 + P/u), where the scalar prefactor is surprisingly simple compared to prefactors one finds e.g. for sl(n) R-matrices. This leads precisely to the S-matrix giving the Bethe Ansatz of one-loop N = 4 Super Yang-Mills theory and two-loop N = 6 Chern-Simons theory.

16 pages

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Cited by in corpus (9)

• Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory
• The classical R-matrix of AdS/CFT and its Lie dialgebra structure
• Yangians, S-matrices and AdS/CFT
• Secret Symmetries of Type IIB Superstring Theory on AdS3 x S3 x M4
• The Classical Trigonometric r-Matrix for the Quantum-Deformed Hubbard Chain
• Universal blocks of the AdS/CFT Scattering Matrix
• Serre Relation and Higher Grade Generators of the AdS/CFT Yangian Symmetry
• The Morphology of N=6 Chern-Simons Theory
• The Yangian of sl(n|m) and the universal R-matrix