Related papers: SU(2) Chern-Simons Theory Coupled to Competing Sca…
Chern-Simons gauge theories in 2+1 dimensions with multiple gauge fields exhibit novel properties that are analysed here in some detail. A striking feature is the possibility of a non-propagating Chern-Simons field acquiring a massless…
The Chern-Simons theories on a noncommutative plane, which is shown to be describing the quantum Hall liquid, is considered. We introduce matter fields fundamentally coupled to the noncommutative Chern-Simons field. Exploiting BPS equations…
We formulate models of complex scalar fields in the space-time that has a two-dimensional sphere as extra dimensions. The Dirac-Wu-Yang monopole is set in two-sphere S^2 as a background gauge field. The nontrivial topology of the monopole…
We perform a systematic study of generic accidental Higgs-family and CP symmetries that could occur in the two-Higgs-doublet-model potential, based on a Majorana scalar-field formalism which realizes a subgroup of GL(8,C). We derive the…
We compute the structure of flux $h/(2e)$ vortices in a d-wave superconductor which emerges from a higher temperature pseudogap metal. Such a transition is described by a continuum theory of the Higgs condensation of 2 flavors of charge $e$…
It is well known that the presence of multiple constraints of non-Abelian relativisitic Chern--Simons--Higgs vortex equations makes it difficult to develop an existence theory when the underlying Cartan matrix $K$ of the equations is that…
Extending work of Caffarelli-Yang and Tarantello, we present a variational existence proof for two-vortex solutions of the periodic Chern-Simons Higgs model and analyze the asymptotic behavior of these solutions as the parameter coupling…
The core of the vortex in a general superconducting order parameter in graphene is argued to be ordered, with the possible order parameters forming the algebra U(1) X Cl(3), where Cl(3) is the three dimensional Clifford algebra. A…
We consider SU(N) Chern-Simons theory coupled to a scalar field in the fundamental representation at strictly zero temperature and finite chemical potential for the global U(1)_B particle number or flavour symmetry. In the semiclassical…
We study a non-Abelian Chern-Simons system in $\mathbb{R}^2$, including the simple Lie algebras $A_2$ and $B_2$. In a previous work, we proved the existence of radial non-topological solutions with prescribed asymptotic behaviors via the…
We construct an artificial U(1) gauge field in the cold atom system to form a monopole along with vortices. It is supposed that the cold atoms are confined on a spherical surface, and two sets of identical laser beams in the opposite…
A magnetic field applied to type-II superconductors introduces quantized vortices that locally quench superconductivity, providing a unique opportunity to investigate electronic orders that may compete with superconductivity. This is…
In these lectures I review classical aspects of the self-dual Chern-Simons systems which describe charged scalar fields in $2+1$ dimensions coupled to a gauge field whose dynamics is provided by a pure Chern-Simons Lagrangian. These…
We propose an extension to the standard model incorporating a dark sector with a non-Abelian SU(2) gauge symmetry. The model yields stable dark matter candidates, protected by a residual $Z_3$ symmetry arising after the spontaneous symmetry…
The quantisation of the reduced first-order dynamics of the nonrelativistic model for Chern-Simons vortices introduced by Manton is studied on a sphere of given radius. We perform geometric quantisation on the moduli space of static…
Non-linear sigma models with scalar fields taking values on $\mathbb{C}\mathbb{P}^n$ complex manifolds are addressed. In the simplest $n=1$ case, where the target manifold is the $\mathbb{S}^2$ sphere, we describe the scalar fields by means…
In this paper, we construct two component dark matter model and revisit fine-tuning, unitarity and vacuum stability problem in this framework. Through Higgs-portal interactions, the additional scalar and vector singlet field can interact…
The study of topological defects occurring in vector and tensor fields is an intriguing subject and little explored in the literature. In this article, we analyze the topological defects arising from the spontaneous violation of Lorentz…
We study the quantum mechanics of a system of topologically interacting particles in 2+1 dimensions, which is described by coupling the particles to a Chern-Simons gauge field of an inhomogeneous group. Analysis of the phase space shows…
In this paper we study fractional as well as semi-local Chern-Simons vortices in G = U(1) x SO(2M) and G = U(1) x USp(2M) theories. The master equations are solved numerically using appropriate Ansatze for the moduli matrix field. In the…