The Classical r-matrix of AdS/CFT and its Lie Bialgebra Structure

Abstract

In this paper we investigate the algebraic structure of AdS/CFT in the strong-coupling limit. We propose an expression for the classical r-matrix with (deformed) u(2|2) symmetry, which leads to a quasi-triangular Lie bialgebra as the underlying symmetry algebra. On the fundamental representation our r-matrix coincides with the classical limit of the quantum R-matrix.

31 pages, v2: added comment on classical double structure in 4.5. new section 5 on relation to other algebras (from old appendix and new results). fixed typos and mathematical inaccuracies, added references, v3: improved mathematical presentation, to appear in CMP