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Affine Classical Lie Bialgebras for AdS/CFT Integrability (2401.10327v1)

Published 18 Jan 2024 in hep-th, math-ph, math.MP, and math.QA

Abstract: In this article we continue the classical analysis of the symmetry algebra underlying the integrability of the spectrum in the AdS_5/CFT_4 and in the Hubbard model. We extend the construction of the quasi-triangular Lie bialgebra gl(2|2) by contraction and reduction studied in the earlier work to the case of the affine algebra sl(2)1 times d(2,1;alpha)1. The reduced affine derivation naturally measures the deviation of the classical r-matrix from the difference form. Moreover, it implements a Lorentz boost symmetry, originally suggested to be related to a q-deformed 2D Poincare algebra. We also discuss the classical double construction for the bialgebra of interest and comment on the representation of the affine structure.

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  1. Niklas Beisert
  2. Egor Im

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