Quantum complex sine-Gordon dressed boundaries

TL;DR

This paper studies the quantum reflection properties of the complex sine-Gordon model with dressed boundaries, proposing a quantum reflection matrix and analyzing its classical and quantum features.

Contribution

It introduces a conjectured quantum reflection matrix for the dressed boundary in the complex sine-Gordon model, extending classical results to the quantum regime.

Findings

Proposed a quantum reflection matrix consistent with bootstrap equations.

Verified the classical limit matches known results.

Analyzed poles related to Coleman-Thun diagrams.

Abstract

In this paper we investigate the quantum reflection factor for the CSG dressed boundary, previously constructed by dressing the Dirichlet boundary with the integrable CSG defect. We analyse classical bound states and use semi-classical methods to investigate the quantum boundary spectrum. We conjecture a fully quantum reflection matrix for a particle reflecting from an unexcited boundary. By using the reflection and boundary bootstrap equations, the reflection matrix for a charge Q=+n soliton reflecting from the mth excited boundary is constructed. Evidence supporting our conjecture is given by checking that the bootstrap closes and that the reflection matrices agrees with known results in the classical limit. A partial analysis of the poles in the reflection matrices which arise from Coleman-Thun diagrams is given.