Related papers: Vortices and Superfields on a Graph
We present a simple scheme for constructing models that achieve successful gauge mediation of supersymmetry breaking. In addition to our previous work [1] that proposed drastically simplified models using metastable vacua of supersymmetry…
We introduce the Density Formula for (topological) drawings of graphs in the plane or on the sphere, which relates the number of edges, vertices, crossings, and sizes of cells in the drawing. We demonstrate its capability by providing…
We discuss the possible applications supersymmetric theories might find in the field of elementary particle physics. The supersymmetric generalization of the $SU(3)\times SU(2)\times U(1)$ standard model is discussed in detail. Special…
We discuss supersymmetric $SU(2)$ gauge theory with a single matter field in the $I=3/2$ representation. This theory has a moduli space of exactly degenerate vacua. Classically it is the complex plane with an orbifold singularity at the…
The study of the graph diameter of polytopes is a classical open problem in polyhedral geometry and the theory of linear optimization. In this paper we continue the investigation initiated in [4] by introducing a vast hierarchy of…
In type-II superconductors, the dynamics of superconducting vortices determine their transport properties. In the Ginzburg-Landau theory, vortices correspond to topological defects in the complex order parameter. Extracting their precise…
Hypergraphs generalize classical graphs by allowing a single edge to connect multiple vertices, providing a natural language for modeling higher-order interactions. Superhypergraphs extend this paradigm further by accommodating nested,…
We propose a $\mathbb{U}(1) \times \mathbb{Z}_2$ effective gauge theory for vortices in a $p_x+ip_y$ superfluid in two dimensions. The combined gauge transformation binds $\mathbb{U}(1)$ and $\mathbb{Z}_2$ defects so that the total…
Based on the U(1) gauge potential decomposition theory and $\phi$-mapping theory, the topological inner structure of the self-duality (Bogomol'nyi-type) equations are studied. The special form of the gauge potential decomposition is…
We present a detailed study of a single vortex in a holographic symmetry breaking phase. At low energies the system flows to an nontrivial conformal fixed point. Novel vortex physics arises from the interaction of these gapless degrees of…
Vortex solutions are topologically stable field configurations that can play an important role in condensed matter, field theory, and cosmology. We investigate vortex configuration in a 2+1 dimensional Abelian Higgs theory supplemented by…
We develop random graph models where graphs are generated by connecting not only pairs of vertices by edges but also larger subsets of vertices by copies of small atomic subgraphs of arbitrary topology. This allows the for the generation of…
We present explicit descriptions of the decompositions of vertices of a hypercube graph with respect to its distinguished symmetric cycle.
We present a geometrical approach for studying dimers. We introduce a connection for dimer problems on bipartite and non-bipartite graphs. In the bipartite case the connection is flat but has non-trivial ${\bf Z}_2$ holonomy round certain…
A novel U(1) topological gauge field theory for topological defects in liquid crystals is constructed by considering the U(1) gauge field is invariant under the director inversion. Via the U(1) gauge potential decomposition theory and the…
We consider deletion problems in graphs and supermodular functions where the goal is to reduce density. In Graph Density Deletion (GraphDD), we are given a graph $G=(V,E)$ with non-negative vertex costs and a non-negative parameter $\rho…
In many real world datasets arising from social networks, there are hidden higher order relations among data points which cannot be captured using graph modeling. It is natural to use a more general notion of hypergraphs to model such…
Let $G=(V,E)$ be a finite, connected graph. We consider a greedy selection of vertices: given a list of vertices $x_1, \dots, x_k$, take $x_{k+1}$ to be any vertex maximizing the sum of distances to the existing vertices and iterate: we…
Mixed anomalies, higher form symmetries, two-group symmetries and non-invertible symmetries have proved to be useful in providing non-trivial constraints on the dynamics of quantum field theories. We study mixed anomalies involving discrete…
We construct exact vortex solutions in 3+1 dimensions to a theory which is an extension, due to Gies, of the Skyrme-Faddeev model, and that is believed to describe some aspects of the low energy limit of the pure SU(2) Yang-Mills theory.…