Vortices and Superfields on a Graph

TL;DR

This paper generalizes dimensional deconstruction using graph theory, introducing supersymmetry and vortex solutions in U(1) gauge models based on arbitrary graphs.

Contribution

It extends the moose diagram framework to general graphs with oriented edges, incorporating supersymmetry and exploring vortex solutions in multi-U(1) models.

Findings

Identifies vortex solutions in specific graph-based models.

Demonstrates supersymmetric extension with superfields.

Shows symmetry breaking from [U(1)]^p to U(1).

Abstract

We extend the dimensional deconstruction by utilizing the knowledge of graph theory. In the dimensional deconstruction, one uses the moose diagram to exhibit the structure of the `theory space'. We generalize the moose diagram to a general graph with oriented edges. In the present paper, we consider only the U(1) gauge symmetry. We also introduce supersymmetry into our model by use of superfields. We suppose that vector superfields reside at the vertices and chiral superfields at the edges of a given graph. Then we can consider multi-vector, multi-Higgs models. In our model, $[U(1)]^p$ (where $p$ is the number of vertices) is broken to a single U(1). Therefore for specific graphs, we get vortex-like classical solutions in our model. We show some examples of the graphs admitting the vortex solutions of simple structure as the Bogomolnyi solution.