Related papers: Topological Features in a Two-Dimensional Higgs Mo…
The investigation of topological properties of the gauge field in a two-dimensional Higgs model can help in understanding anomalous fermion number violation.
I review, at a general non-technical level, the main properties of models in extra dimensions where the Higgs field is identified with some internal component of a gauge field.
We present a description of two dimensional Yang-Mills gauge theory on the plane and on compact surfaces, examining the topological, geometric and probabilistic aspects.
We introduce topological gauge fields as nontrivial field configurations enforced by topological currents. These fields crucially determine the form of statistical gauge fields that couple to matter and transmute their statistics. We…
We describe topological gauge theories for which duality properties are encoded by construction. We study them for compact manifolds of dimensions four, eight and two. The fields and their duals are treated symmetrically, within the context…
The 2-dimensional U(1) gauge-Higgs model with a topological term is a simple example of a lattice field theory where the complex action problem comes from the topological term. We show that the model can be exactly rewritten in terms of…
The real-time dynamics of topological defects and turbulent configurations of gauge fields for electric and magnetic confinement are studied numerically within a 2+1D Abelian Higgs model. It is shown that confinement is appearing in such…
We discuss the study of topological characteristics of random fields that are used for numerical simulation of oil and gas reservoirs and numerical algorithms (see arXiv:1302.3669), for computing such characteristics, for which we…
In this paper we give an overview of different Morse-theoretic methods used to study the topology of moduli spaces of Higgs bundles.
Lattice simulations of five-dimensional gauge theories on an orbifold revealed that there is spontaneous symmetry breaking. Some of the extra-dimensional components of the gauge field play the role of a Higgs field and some of the…
In this review we summarize the ongoing effort to study extra-dimensional gauge theories with lattice simulations. In these models the Higgs field is identified with extra-dimensional components of the gauge field. The Higgs potential is…
In this article, we review gauge-Higgs unification models based on gauge theories defined on six-dimensional spacetime with $S^2/Z_2$ topology in the extra spatial dimensions. On the extra $S^2/Z_2$ space, non-trivial boundary conditions…
A complete model of cosmological evolution of a classical scalar field with the Higgs potential is studied and simulated on a computer without assumption that the Hubble constant is nonnegative. The corresponding dynamical system is…
We continue our analysis of the general N-Higgs-doublet model and focus of the Higgs potential description in the space of gauge orbits. We develop a geometric technique that allows us to study the global minimum of the potential without…
To appear in Encyclopedia of Mathematical Physics, published by Elsevier in early 2006. Comments/corrections welcome. The article surveys topological aspects in gauge theories.
Gauge coupling unification is studied within the framework where there are extra Higgs doublets and $E_6$ exotic fields. Supersymmetric models and nonsupersymmetric models are investigated, and a catalog of models with gauge coupling…
Using Perelman's approach for geometrical flows in terms of an entropy functional, the Higgs mechanism is studied dynamically along flows defined in the space of parameters and in fields space. The model corresponds to two-dimensional…
We study the emergence of gauge couplings in the surface states of topological insulators. We show that gauge fields arise when a three dimensional strong topological insulator is coated with an easy-plane ferromagnet with magnetization…
We study some topological properties of attractors.
We demonstrate applications of topological characteristics of oil and gas reservoirs considered as three-dimensional bodies to geological modeling.