Quantum group symmetry in sine-Gordon and affine Toda field theories on the half-line

TL;DR

This paper explores how quantum group symmetries persist in sine-Gordon and affine Toda field theories with boundaries, developing a framework for solving reflection equations using coideal subalgebras.

Contribution

It introduces a general method for deriving solutions to the reflection equation via intertwining properties of coideal subalgebras in quantized affine algebras.

Findings

Quantum affine algebra symmetry remains in the quantum sine-Gordon and affine Toda models with boundaries.

A new framework for solving reflection equations using coideal subalgebras is developed.

The approach provides explicit solutions for boundary scattering problems.

Abstract

We consider the sine-Gordon and affine Toda field theories on the half-line with classically integrable boundary conditions, and show that in the quantum theory a remnant survives of the bulk quantized affine algebra symmetry generated by non-local charges. The paper also develops a general framework for obtaining solutions of the reflection equation by solving an intertwining property for representations of certain coideal subalgebras of quantized affine algebras.