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

We discuss a classical integrability in the type IIB string theory on the AdS$_5\times$ S$^5$ background. By using the Roiban--Siegel formulation of the superstring on the AdS$_5\times $S$^5$, we carefully treat the Wess\endash 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\endash Polchinski\endash 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.

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Published 1 January 2005