Affine Classical Lie Bialgebras for AdS/CFT Integrability

TL;DR

This paper extends the classical Lie bialgebra analysis of integrable models in AdS/CFT, focusing on affine algebras and their symmetries, revealing new structures and symmetries relevant to the integrability spectrum.

Contribution

It constructs and analyzes the affine Lie bialgebra structure for models related to AdS/CFT integrability, extending previous work to more complex affine algebras and exploring their symmetries.

Findings

Extended the construction of the quasi-triangular Lie bialgebra to affine algebras

Identified the role of the affine derivation in measuring deviations from difference form

Discussed the classical double construction and affine structure representations

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.