Coideal Quantum Affine Algebra and Boundary Scattering of the Deformed Hubbard Chain

Marius de Leeuw, Takuya Matsumoto, Vidas Regelskis

Abstract

We consider boundary scattering for a semi-infinite one-dimensional deformed Hubbard chain with boundary conditions of the same type as for the $Y=0$ giant graviton in the AdS/CFT correspondence. We show that the recently constructed quantum affine algebra of the deformed Hubbard chain has a coideal subalgebra which is consistent with the reflection (boundary Yang-Baxter) equation. We derive the corresponding reflection matrix and furthermore show that the aforementioned algebra in the rational limit specializes to the (generalized) twisted Yangian of the $Y=0$ giant graviton.

Keywords: Quantum affine algebra, Coideal subalgebra, Deformed Hubbard chain, Boundary scattering.