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.

Kazakov-Migdal model on the graph and Ihara zeta function

“…The Ihara zeta function associated with a finite graph is an analog of the Riemann zeta function, which plays very important role in the number theory. The Ihara zeta function and its related theorems are very beautiful and meaningful and have been applied mainly to mathematics, but have not been applied much in high energy physics, except for applications to quiver gauge theory [8][9][10] and discretized (supersymmetric) gauge theory [11][12][13][14][15][16][17].…”

Kazakov-Migdal model on the Graph and Ihara Zeta Function

“…The logarithm of the Ihara zeta function has the following series expansion log ζ DT (q) = 4q 3 + 2q 4 + 4q 6 + 4q 7 + q 8 + 16q 9 3 + 12q 10 + 4q 11 + 26q 12…”

“…The Ihara zeta function associated with a finite graph is an analog of the Riemann zeta function, which plays very important role in the number theory. The Ihara zeta function and its related theorems are very beautiful and meaningful and have been applied mainly to mathematics, but have not been applied much in high energy physics, except for applications to quiver gauge theory [8][9][10] and discretized (supersymmetric) gauge theory [11][12][13][14][15][16][17].…”

Newtonian analysis of multiscalar boson stars with large self-couplings

“…The model we propose contains N scalar fields interacting with oneself and with 'adjacent' scalar fields on a graph. A similar type of many U(1) interacting fields has been motivated by the graph-oriented model with supersymmetry [21].…”