Vortices and Superfields on a Graph

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.

27 pages. RevTeX4. Revised version accepted for publication in PRD

References in corpus (19)

• Electroweak symmetry breaking from dimensional deconstruction
• (De)Constructing Dimensions
• The Stueckelberg Field
• Gauge Invariant Effective Lagrangian for Kaluza-Klein Modes
• Aspects of the Stueckelberg Extension
• A Three Site Higgsless Model
• Supersymmetry and Bogomol'nyi equations in the Abelian Higgs Model
• Higgsless Electroweak Symmetry Breaking from Theory Space
• Vortices in Theories with Flat Directions
• Electroweak Corrections and Unitarity in Linear Moose Models
• Cosmic Strings from Supersymmetric Flat Directions
• Nonvanishing quantum corrections to the mass and central charge of the N=2 vortex and BPS saturation
• Quantum corrections to mass and central charge of supersymmetric solitons
• Fermion zero modes in N=2 supervortices
• Chaotic D-Term Inflation
• Divergences in QED on a Graph
• The Supersymmetric Stueckelberg Mass and Overcoming the Fayet-Iliopoulos Mechanism for Breaking Symmetry
• On axially symmetrical solitons in Abelian-Higgs models
• On vortices and rings in extended Abelian models

Cited by in corpus (7)

• A Newtonian Analysis of Multi-scalar Boson Stars with Large Self-couplings
• Supersymmetric Gauge Theory on the Graph
• The Volume of the Quiver Vortex Moduli Space
• Kazakov-Migdal model on the Graph and Ihara Zeta Function
• Simple Models in Supersymmetric Quantum Mechanics on a Graph
• Fermion spectrum and localization on kinks in a deconstructed dimension
• Boson Stars under Deconstruction