The S-Matrix of AdS/CFT and Yangian Symmetry

TL;DR

This work analyzes the S-matrix of planar AdS/CFT from an algebraic perspective, showing that it enjoys a Yangian symmetry based on the centrally extended $\mathfrak{su}(2|2)$ algebra. It develops the Hopf-algebra and braided coproduct structure of $U(\mathfrak{h})$ and its Yangian $Y(\mathfrak{h})$, identifies a consistent fundamental evaluation representation, and demonstrates S-matrix invariance under both Lie and Yangian generators. The results connect AdS/CFT integrability to the Hubbard model via Shastry’s R-matrix and highlight a non-difference-form S-matrix arising from braiding, with implications for the dressing phase and potential universal R-matrix constructions. The analysis opens questions on representation lifting, reducibility points, and the full Yangian extension, offering a framework for rigorous treatment of the AdS/CFT integrable structure at finite coupling.

Abstract

We review the algebraic construction of the S-matrix of AdS/CFT. We also present its symmetry algebra which turns out to be a Yangian of the centrally extended su(2|2) superalgebra.