The S-matrix algebra of the AdS2 X S2 superstring

TL;DR

This paper uncovers the Yangian algebra governing the integrability of the AdS2 X S2 superstring, analyzing its S-matrix, symmetries, and classical r-matrix, and explores a free fermion model in a zero-coupling limit.

Contribution

It provides the first detailed construction of the Yangian algebra and secret symmetries for the AdS2 X S2 superstring, including alternative algebra presentations and the classical r-matrix analysis.

Findings

Confirmed the symmetry of the exact S-matrix in the massive sector

Identified the secret symmetry in the algebraic structure

Derived a free fermion model from the zero-coupling limit

Abstract

In this paper we find the Yangian algebra responsible for the integrability of the AdS2 X S2 X T^6 superstring in the planar limit. We demonstrate the symmetry of the corresponding exact S-matrix in the massive sector, including the presence of the secret symmetry. We give two alternative presentations of the Hopf algebra, along with related discussions on the issue of evaluation representations. We study the classical r-matrix, and re-discover the need for a secret symmetry also in this context. Finally, taking the simplifying zero-coupling limit of the S-matrix as a generating R-matrix for the Algebraic Bethe Ansatz, we obtain an effective model of free fermions on a periodic spin-chain. This limit should provide hints to the one-loop anomalous dimension of the mysterious superconformal quantum mechanics dual to the superstring theory in this geometry.