BPS domain wall solutions in self-dual Chern-Simons-Higgs systems (original) (raw)
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.
Nontopological solitons in Chern-Simons systems
Physical Review D, 1991
We show that in the relativistic Abelian case nontopological Chem-Simons solitons are stable against the emission of elementary particles, when a particular small correction is added to the potential corresponding to the self-dual system. We also analyze other potentials and introduce a necessary condition for the existence of nontopological solitons in Chem-Simons systems. A great deal of attention has been recently drawn to three-dimensional relativistic systems in which the gauge field dynamics is solely governed by the Chem-Simons term [1-10]. In particular, from Refs. [1-3] one learns that when the potential in a relativistic Abelian system has a very specific form, the corresponding field configurations satisfy first-order self-dual equations. Furthermore, this specific form of the potential corresponds to a first-order transition point in which the symmetric and asymmetric vacua are degenerate, and the self-dual Chem-Simons sol
Self-dual soliton solutions in a Chern–Simons-CP(1) model with a nonstandard kinetic term
Modern Physics Letters A, 2014
A generalization of the Chern-Simons-CP(1) model is considered by introducing a nonstandard kinetic term. For a particular case, of this nonstandard kinetic term, we show that the model support self-dual Bogomolnyi equations. The BPS energy has a bound proportional to the sum of the magnetic flux and the CP(1) topological charge. The self-dual equations are solved analytically and verified numerically.
A generalized self-dual Chern-Simons Higgs theory
Letters in Mathematical Physics, 1991
In the recently discovered Chern-Slmons model, the reduction to a Bogomol'nyi bound or self-duality depends crucially on the specific form of the Higgs potential energy function, which is characterized by a ~b 6 type self-interaction. The purpose of this paper is to show that a much wider class of Higgs self-interaction may be allowed to achieve self-duality provided that the kinetic energy term of the Higgs scalar is suitably modified. The existence of topological multivortex solutions is also established. Furthermore, it 1s remarked that the Melssner effect may occur in the model.
SELF-DUAL SOLITONS IN N=2 SUPERSYMMETRIC SEMILOCAL CHERN–SIMONS THEORY
Modern Physics Letters A, 1998
We embed the semilocal Chern-Simons-Higgs theory into an N = 2 supersymmetric system. We construct the corresponding conserved supercharges and derive the Bogomol'nyi equations of the model from supersymmetry considerations. We show that these equations hold provided certain conditions on the coupling constants as well as on the Higgs potential of the system, which are a consequence of the huge symmetry of the theory, are satisfied. They admit string-like solutions which break one half of the supersymmetries -BPS Chern-Simons semilocal cosmic strings-whose magnetic flux is concentrated at the center of the vortex. We study such solutions and show that their stability is provided by supersymmetry through the existence of a lower bound for the energy, even though the manifold of the Higgs vacuum does not contain non-contractible loops.
Self-dual SU(3) Chern-Simons Higgs systems
Physical Review D, 1994
We explore self-dual Chern-Simons Higgs systems with the local SU(3) and global U(1) symmetries where the matter field lies in the adjoint representation.
Self-dual Chern-Simons solitons in noncommutative space
Journal of High Energy Physics, 2001
We construct exact soliton solutions to the Chern-Simons-Higgs system in noncommutative space, for non-relativistic and relativistic models. In both cases we find regular vortex-like solutions to the BPS equations which approach the ordinary selfdual non-topological and topological solitons when the noncommutative parameter theta\thetatheta goes to zero.
Self-Dual Chern–Simons Solitons and Quantum Potential
Journal of Nonlinear Mathematical Physics, 2001
ABSTRACT An influence of the quantum potential on the Chern–Simons solitons leads to quan-tization of the statistical parameter κ = me 2 /g, and the quantum potential strenght s = 1 − m 2 . A new type of exponentially localized Chern–Simons solitons for the Bloch electrons near the hyperbolic energy band boundary are found.
Physical Review D, 2000
We discuss topologically stable solitons in two-dimensional theories with the extended supersymmetry assuming that the spatial coordinate is compact. This problem arises in the consideration of the domain walls in the popular theories with compactified extra dimensions. Contrary to naive expectations, it is shown that the solitons on the cylinder can be BPS saturated. In the case of one chiral superfield, a complete theory of the BPS saturated solitons is worked out. We describe the classical solutions of the BPS equations. Depending on the choice of the Kähler metric, the number of such solutions can be arbitrarily large. Although the property of the BPS saturation is preserved order by order in perturbation theory, nonperturbative effects eliminate the majority of the classical BPS states upon passing to the quantum level. The number of the quantum BPS states is found. It is shown that the N = 2 field theory includes an auxiliary N = 1 quantum mechanics, Witten's index of which counts the number of the BPS particles. † Permanent address
New soliton solutions of anti-self-dual Yang-Mills equations
2020
We study exact soliton solutions of anti-self-dual Yang-Mills equations for G=GL(2)G =GL(2)G=GL(2) in four-dimensional spaces with the Euclidean, Minkowski and Ultrahyperbolic signatures and construct special kinds of one-soliton solutions whose action density Tr$F_{\mu\nu}F^{\mu\nu}$ can be real-valued. These solitons are shown to be new type of domain walls in four dimension by explicit calculation of the real-valued action density. Our results are successful applications of the Darboux transformation developed by Nimmo, Gilson and Ohta. More surprisingly, integration of these action densities over the four-dimensional spaces are not infinity but zero. Furthermore, whether gauge group G=U(2)G= U(2)G=U(2) can be realized on our solition solutions or not is also discussed on each real space.