Classical Integrability and Super Yangian of Superstring on AdS_5 x S^5

TL;DR

This work establishes classical integrability for the type IIB superstring on $AdS_5\times S^5$ by employing the Roiban-Siegel formulation to carefully handle the Wess-Zumino term and fermionic constraints. It explicitly constructs an infinite tower of κ-invariant non-local charges, derives the $\;GL(4|4)\;$ super Yangian, and proves the Serre relations, all within a framework supported by a Lax pair and a transfer matrix. The classical $r$-matrix obtained from the transfer-matrix Poisson brackets satisfies the classical Yang-Baxter equation, signaling robust integrability and suggesting a path toward quantum integrability and a deeper link to the AdS/CFT correspondence. The paper also clarifies technical aspects such as regularization of non-ultra local terms and the role of the super-stability group in the non-symmetric coset setting, with future directions including semiclassical quantization and connections to spin-chain dynamics in N=4 SYM.

Abstract

We discuss a classical integrability in the type IIB string theory on the AdS_5 x S^5 background. By using the Roiban-Siegel formulation of the superstring on the AdS_5 x 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.