Fermion zero modes in the vortex background of a Chern-Simons-Higgs theory with a hidden sector (original) (raw)
Related papers
An analysis of the two-vortex case in the Chern-Simons Higgs model
Peking University series in mathematics, 2017
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 gauge field with the scalar field tends to 0. * dg-ga/9710006
Physical Review D
While the phase structure of the U (1) × U (1)-symmetric Higgs theory is still under debate, a version of this theory with an additional Chern-Simons term was recently shown to undergo a second-order phase transition [V. Shyta, J. van den Brink, and F. S. Nogueira, Phys. Rev. Lett. 127, 045701 (2021)]. This theory is dual to a topological field theory of massless fermions featuring two gauge fields. Here we elaborate on several aspects of this duality, focusing on the critical current correlators and on the nature of the critical point as reflected by the bosonization duality. The current correlators associated to the U (1) × U (1) symmetry and the topological current are shown to coincide up to a universal prefactor, which we find to be the same for both U (1) and U (1) × U (1) topological Higgs theories. The established duality offers in addition another way to substantiate the claim about the existence of a critical point in the bosonic Chern-Simons U (1) × U (1) Higgs model: a Schwinger-Dyson analysis of the fermionic dual model shows that no dynamical mass generation occurs. The same cannot be said for the theory without the Chern-Simons term in the action.
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.
Peculiar charged vortices in Higgs models with pure Chern-Simons term
Physics Letters B, 1990
We show that abelian as well as nonabelian Higgs models in (2+ 1) dimensions with the pure Chern-Simons term possess peculiar charged vortex solutions of finite energy. For all of them the magnetic field vanishes not only at infinity but also at the origin. Such objects can also be shown to exist in an abelian Higgs model without the Chern-Simons term but with non-minimal coupling.
Vortices in Higgs models with and without Chern-Simons terms
Physics Letters B, 1989
We note that neutrl vortices in a fermionic background acquire the same local charge and spin quantum numbers as charged vortices in a Chern-Simons theory, provided the Chern-Simons mass is obtained by integrating out the fermions. We also point out that in an SU(2) theory involving (globally) charged fermions, (globally) neutral fermions appear as pairs of Z2 solitons and comment on their relevance to condensed matter systems.
Vortex condensation in the Chern-Simons Higgs model: An existence theorem
Communications in Mathematical Physics, 1995
It is shown that there is a critical value of the Chern-Simons coupling parameter so that, below the value, there exists self-dual doubly periodic vortex solutions, and, above the value, the vortices are absent. Solutions of such a nature indicate the existence of dyon condensates carrying quantized electric and magnetic charges.
Nontopological condensates for the self-dual Chern-Simons-Higgs Model
Communications on Pure and Applied Mathematics, 2014
For the abelian self-dual Chern-Simons-Higgs model we address existence issues of periodic vortex configurations -the so-called condensates-of non-topological type as k → 0, where k > 0 is the Chern-Simons parameter. We provide a positive answer to the long-standing problem on the existence of non-topological condensates with magnetic field concentrated at some of the vortex points (as a sum of Dirac measures) as k → 0, a question which is of definite physical interest.
Electrically and magnetically charged vortices in the Chern–Simons–Higgs theory
2009
In this paper, we prove the existence of finite-energy electrically and magnetically charged vortex solutions in the full Chern-Simons-Higgs theory for which both the Maxwell term and Chern-Simons term are present in the Lagrangian density. We consider both Abelian and non-Abelian cases. The solutions are smooth and satisfy natural boundary conditions. Existence is established via a constrained minimization procedure applied on indefinite action functionals. This work settles a long-standing open problem concerning the existence of dually charged vortices in the classical gauge field Higgs model minimally extended to contain a Chern-Simons term.
Advances in High Energy Physics, 2016
We have studied the existence of self-dual solitonic solutions in a generalization of the Abelian Chern-Simons-Higgs model. Such a generalization introduces two different nonnegative functions,ω1(|ϕ|)andω(|ϕ|), which split the kinetic term of the Higgs field,|Dμϕ|2→ω1(|ϕ|)|D0ϕ|2-ω(|ϕ|)|Dkϕ|2, breaking explicitly the Lorentz covariance. We have shown that a clean implementation of the Bogomolnyi procedure only can be implemented whetherω(|ϕ|)∝β|ϕ|2β-2withβ≥1. The self-dual or Bogomolnyi equations produce an infinity number of soliton solutions by choosing conveniently the generalizing functionω1(|ϕ|)which must be able to provide a finite magnetic field. Also, we have shown that by properly choosing the generalizing functions it is possible to reproduce the Bogomolnyi equations of the Abelian Maxwell-Higgs and Chern-Simons-Higgs models. Finally, some new self-dual|ϕ|6-vortex solutions have been analyzed from both theoretical and numerical point of view.