The RTT-Realization for the Deformed gl(2|2) Yangian

Abstract

In this paper we work out the RTT-realization for the Yangian algebra of the Hubbard model and AdS/CFT correspondence. We find that this Yangian algebra is of a non-standard type in which the levels of the Yangian mix. The crucial feature that allows this is a braiding factor that deforms the coproduct and generates the central extensions of the underlying sl(2|2) Lie algebra. In our RTT-realization we have also been able to incorporate the so-called secret symmetry and we were able to extend it to higher Yangian levels. Finally, we discuss the center of the Yangian and the automorphisms related to crossing symmetry.

42 pages, v2: minor corrections and improvements

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• The S-matrix algebra of the AdS2 X S2 superstring
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• Separation of variables bases for integrable $g{l}_{\mathcal{M}|\mathcal{N}}$ and Hubbard models
• Popcorn Drude weights from quantum symmetry
• Integrable deformations of AdS/CFT
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• $q$-Poincaré invariance of the $Ad{S}_3/CF{T}_2$ $R$-matrix
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• An algebraic approach to the Hubbard model
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• Classical Lie Bialgebras for AdS/CFT Integrability by Contraction and Reduction
• Bound State Scattering Simplified
• Complex D($2,1;\zeta$) and spin chain solutions from Chern-Simons theory
• Flag Integrable Models and Generalized Graded Algebras