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.
Highlights
At least in the relativistic case, presenting the argument the other way round, the presence of defects that preserve a suitably modified energy and momentum seems to require the fields on either side of the defect to be integrable
The sineGordon model can be adapted in a manner suitable for a network by allowing the basic wave speeds to be different within its separated segments [24]
For the sine-Gordon model, a junction can only have two branches, or be a junction that acts as a meeting point of defects, each with two branches
Summary
At least in the relativistic case, presenting the argument the other way round, the presence of defects that preserve a suitably modified energy and momentum seems to require the fields on either side of the defect to be integrable. Such defects break space translation invariance (since they have a specific location) but are purely transmitting. The sineGordon model can be adapted in a manner suitable for a network by allowing the basic wave speeds to be different within its separated segments [24] Characteristic of these particular junction conditions is continuity of the fields as they match at a junction. The two cases introduced above will be dealt with separately
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