Boundary scattering, symmetric spaces and the principal chiral model on the half-line

TL;DR

This paper explores integrable boundary conditions and rational solutions for the principal chiral model on a half-line, revealing connections with symmetric spaces and proposing boundary S-matrices based on these structures.

Contribution

It introduces a novel classification of integrable boundary conditions linked to symmetric spaces and constructs boundary S-matrices parametrized by these spaces.

Findings

Boundary conditions restricted to cosets of H in G

Rational solutions of the boundary Yang-Baxter equation parametrized by G/H

Proposed boundary S-matrices corresponding to boundary conditions

Abstract

We investigate integrable boundary conditions (BCs) for the principal chiral model on the half-line, and rational solutions of the boundary Yang-Baxter equation (BYBE). In each case we find a connection with (type I, Riemannian, globally) symmetric spaces G/H: there is a class of integrable BCs in which the boundary field is restricted to lie in a coset of H; these BCs are parametrized by G/H x G/H; there are rational solutions of the BYBE in the defining representations of all classical G parametrized by G/H; and using these we propose boundary S-matrices for the principal chiral model, parametrized by G/H x G/H, which correspond to our boundary conditions.