Classical integrability and super Yangian of superstring on $\mathrm{AdS}_5\times \mathrm{S}^5$

Abstract

We discuss a classical integrability in the type IIB string theory on the $\mathrm{AdS}_5\times \mathrm{S}^5$ background. By using the Roiban-Siegel formulation of the superstring on the $\mathrm{AdS}_5\times \mathrm{S}^5$, we carefully treat the Wess-Zumino term and the constraint conditions intrinsic to the supersymmetric case and construct explicitly non-local charges for a hidden infinite-dimensional symmetry. The existence of the symmetry is shown by Bena-Polchinski-Roiban. Then the super Yangian algebra is calculated. We also show the Serre relation ensuring the structure of the Hopf algebra. In addition, the classical integrability is discussed by constructing the Lax pair and the transfer matrix.