Vortices in (Abelian) Chern–Simons gauge theory (original) (raw)

Chern-Simons term and charged vortices in abelian and nonabelian gauge theories

Arxiv preprint hep-th/9505043, 1995

In this article we review some of the recent advances regarding the charged vortex solutions in abelian and nonabelian gauge theories with Chern-Simons (CS) term in two space dimensions. Since these nontrivial results are essentially because of the CS term, hence, we first discuss in some detail the various properties of the CS term in two space dimensions. In particular, it is pointed out that this parity (P) and time reversal (T) violating but gauge invariant term when added to the Maxwell Lagrangian gives a massive gauge quanta and yet the theory is still gauge invariant. Further, the vacuum of such a theory shows the magneto-electric effect. Besides, we show that the CS term can also be generated by spontaneous symmetry breaking as well as by radiative corrections. A detailed discussion about Coleman-Hill theorem is also given which aserts that the parity-odd piece of the vacuum polarization tensor at zero momentum transfer is unaffected by two and multi-loop effects. Topological quantization of the coefficient of the CS term in nonabelian gauge theories is also elaborated in some detail. One of the dramatic effect of the CS term is that the vortices of the abelian (as well as nonabelian) Higgs model now acquire finite quantized charge and angular momentum. The various properties of these vortices are discussed at length with special emphasis on some of the recent developments including the discovery of the self-dual charged vortex solutions.

Lectures on (abelian) Chern-Simons vortices

Various aspects including the construction and the symmetries of Abelian Chern-Simons vortices are reviewed. Extended version of the Lectures delivered at NIKHEF (Amsterdam), July 2006. ArXiv: 0704.3220 1 arXiv:0704.3220v2 [hep-th] 9 May 2007 1 4

Comment on vortices in Chern-Simons and Maxwell electrodynamics with Higgs fields

Physics Letters B, 1994

We compare the vortex-like solutions of two different theories in (2 + 1) dimensions. In the first a nonrelativistic field self-interacts through a Chern-Simons gauge connection. It is P and T violating. The second is the standard Maxwell scalar electrodynamics. We show that for specific values of some parameters the same vortex-configurations provide solutions for both theories.

Topological quantization of self-dual Chern-Simons vortices on Riemann Surfaces

2005

The self-duality equations of Chern-Simons Higgs theory in a background curved spacetime are studied by making use of the U(1) gauge potential decomposition theory and phi\phiphi-mapping method. The special form of the gauge potential decomposition is obtained directly from the first of the self-duality equations. Using this decomposition, a rigorous proof of magnetic flux quantization in background curved spacetime is given and the unit magnetic flux in curved spacetime is also found . Furthermore, the precise self-dual vortex equation with topological term is obtained, in which the topological term has always been ignored.

Chern–Simons vortices in the Gudnason model

Journal of Functional Analysis, 2014

We present a series of existence theorems for multiple vortex solutions in the Gudnason model of the N = 2 supersymmetric field theory where non-Abelian gauge fields are governed by the pure Chern-Simons dynamics at dual levels and realized as the solutions of a system of elliptic equations with exponential nonlinearity over two-dimensional domains. In the full plane situation, our method utilizes a minimization approach, and in the doubly periodic situation, we employ an-inequality constrained minimization approach. In the latter case, we also obtain sufficient conditions under which we show that there exist at least two gauge-distinct solutions for any prescribed distribution of vortices. In other words, there are distinct solutions with identical vortex distribution, energy, and electric and magnetic charges.

A topological field theory for non-abelian vortices

Physics Letters B, 1990

We construct a two-dimensional topological field theory for non-abelian Higgs vortices. We discuss relevant features of the resulting BRST quantized theory and also discuss topological invariants.