| Vortices and Superfields on a Graph | | | Nahomi Kan, Koichiro Kobayashi and Kiyoshi Shiraishi | | | Yamaguchi Junior College and Yamaguchi University | | |
Physical Review D80 045005 [0901.1168] | | |
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. | | |
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