On purely transmitting defects in affine Toda field theory

TL;DR

This paper analyzes purely transmitting defects in affine Toda field theories, especially the a_2 model, deriving a quantum transmission matrix and exploring classical-quantum disparities and new phenomena like unstable bound states.

Contribution

It provides a complete classical and quantum characterization of purely transmitting defects in affine Toda theories, including a new quantum transmission matrix for the a_2 model.

Findings

Quantum transmission matrix derived for a_2 model

Discovery of unstable bound states in quantum regime

Differences observed between classical and quantum descriptions

Abstract

Affine Toda field theories with a purely transmitting integrable defect are considered and the model based on a_2 is analysed in detail. After providing a complete characterization of the problem in a classical framework, a suitable quantum transmission matrix, able to describe the interaction between an integrable defect and solitons, is found. Two independent paths are taken to reach the result. One is an investigation of the triangle equations using the S-matrix for the imaginary coupling bulk affine Toda field theories proposed by Hollowood, and the other uses a functional integral approach together with a bootstrap procedure. Evidence to support the results is collected in various ways: for instance, through the calculation of the transmission factors for the lightest breathers. While previous discoveries within the sine-Gordon model motivated this study, there are several new phenomena displayed in the a_2 model including intriguing disparities between the classical and the quantum pictures. For example, in the quantum framework, for a specific range of the coupling constant that excludes a neighbourhood of the classical limit, there is an unstable bound state.