Solving topological defects via fusion

TL;DR

This paper develops a method to analyze topological defects in integrable models by fusing them with boundaries, enabling explicit solutions and calculations of defect properties in sinh-Gordon and Lee-Yang models.

Contribution

It introduces a fusion-based approach to derive explicit defect solutions and transmission factors in integrable quantum field theories.

Findings

Transmission factors verified via perturbation theory in sinh-Gordon model.

Defect energies matched with thermodynamic Bethe ansatz calculations.

Spectrum of defect bound-states determined for Lee-Yang model.

Abstract

Integrable defects in two-dimensional integrable models are purely transmitting thus topological. By fusing them to integrable boundaries new integrable boundary conditions can be generated, and, from the comparison of the two solved boundary theories, explicit solutions of defect models can be extracted. This idea is used to determine the transmission factors and defect energies of topological defects in sinh-Gordon and Lee-Yang models. The transmission factors are checked in Lagrangian perturbation theory in the sinh-Gordon case, while the defect energies are checked against defect thermodynamic Bethe ansatz equations derived to describe the ground-state energy of diagonal defect systems on a cylinder. Defect bootstrap equations are also analyzed and are closed by determining the spectrum of defect bound-states in the Lee-Yang model.