Boundary remnant of Yangian symmetry and the structure of rational reflection matrices

TL;DR

This paper investigates the boundary remnants of Yangian symmetry in the classical principal chiral model, deriving rational reflection matrices and their solutions, including for non-trivial boundary states, through algebraic and fusion methods.

Contribution

It identifies conserved Yangian charges under boundary conditions and constructs rational reflection matrices, extending understanding of integrable boundary conditions in quantum models.

Findings

Derived conserved Yangian charges for boundary conditions.

Constructed rational reflection matrices for SU(N).

Validated solutions via fusion methods.

Abstract

For the classical principal chiral model with boundary, we give the subset of the Yangian charges which remains conserved under certain integrable boundary conditions, and extract them from the monodromy matrix. Quantized versions of these charges are used to deduce the structure of rational solutions of the reflection equation, analogous to the 'tensor product graph' for solutions of the Yang-Baxter equation. We give a variety of such solutions, including some for reflection from non-trivial boundary states, for the SU(N) case, and confirm these by constructing them by fusion from the basic solutions.