Integrable Defects at Junctions within a Network

TL;DR

This paper investigates the properties of integrable, purely transmitting defects at network junctions, revealing restrictive conditions and differences between conformal and massive models, mainly in classical field theory contexts.

Contribution

It introduces a detailed analysis of integrable defects at network junctions, highlighting their restrictive sewing conditions and differences across model types.

Findings

Number of domains at a junction must be even for integrability.

Distinct behaviors observed between conformal and massive models.

Classical field theory models demonstrate these properties clearly.

Abstract

The purpose of this article is to explore the properties of integrable, purely transmitting, defects placed at the junctions of several one-dimensional domains within a network. The defect sewing conditions turn out to be quite restrictive - for example, requiring the number of domains meeting at a junction to be even - and there is a clear distinction between the behaviour of conformal and massive integrable models. The ideas are mainly developed within classical field theory and illustrated using a variety of field theory models defined on the branches of the network, including both linear and nonlinear examples.