Generalisations of the Coleman-Thun mechanism and boundary reflection factors

TL;DR

This paper thoroughly analyzes the pole structure of boundary reflection factors in the boundary scaling Lee-Yang model, revealing new mechanisms for pole generation and clarifying boundary condition ambiguities.

Contribution

It introduces new mechanisms for simple pole generation in boundary reflection factors and discusses ambiguities in boundary condition identification.

Findings

Uncovered new mechanisms for simple pole generation.

Identified ambiguities in boundary reflection factors.

Proposed a way to resolve some boundary condition ambiguities.

Abstract

We make a complete pole analysis of the reflection factors of the boundary scaling Lee-Yang model. In the process we uncover a number of previously unremarked mechanisms for the generation of simple poles in boundary reflection factors, which have implications for attempts to close the boundary bootstrap in more general models. We also explain how different boundary conditions can sometimes share the same fundamental reflection factor, by relating the phenomenon to potential ambiguities in the interpretation of certain poles. In the case discussed, this ambiguity can be lifted by specifying the sign of a bulk-boundary coupling. While the recipe we employ for the association of poles with general on-shell diagrams is empirically correct, we stress that a justification on the basis of more fundamental principles remains a challenge for future work.