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

TL;DR

This paper studies boundary scattering in a deformed Hubbard chain, revealing a coideal quantum affine algebra structure that leads to a reflection matrix consistent with boundary Yang-Baxter equations, connecting to giant graviton symmetries.

Contribution

It demonstrates the existence of a coideal subalgebra within the quantum affine algebra of the deformed Hubbard chain and derives the associated reflection matrix.

Findings

The quantum affine algebra admits a coideal subalgebra compatible with boundary conditions.

The derived reflection matrix satisfies the boundary Yang-Baxter equation.

In the rational limit, the algebra reduces to a twisted Yangian related to giant graviton symmetries.

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.