Fractional and semi-local non-Abelian Chern–Simons vortices

Abstract

In this paper we study fractional as well as semi-local Chern-Simons vortices in G = U (1) × SO(2M ) and G = U (1) × U Sp(2M ) theories. The master equations are solved numerically using appropriate Ansätze for the moduli matrix field. In the fractional case the vortices are solved in the transverse plane due to the broken axial symmetry of the configurations (i.e. they are non-rotational invariant). It is shown that unless the fractional vortex-centers are all coincident (i.e. local case) the ring-like flux structure, characteristic of Chern-Simons vortices, will become bell-like fluxes -just as those of the standard Yang-Mills vortices. The asymptotic profile functions are calculated in all cases and the effective size is identified.

On Non-Topological Solutions for Planar Liouville Systems of Toda-Type

“…Motivated by the delicate issue of "'quark confinement"', Gudnason in [33,34] introduced a non-abelian Chern-Simons model formulated within a N = 2 Supersymmetric (SUSY) Field Theory, with a general gauge group of the type: G = U (1) × G ′ allowing solutions with orientational modes. For the model in [33,34], the author identifies the BPS-sector of the theory and the corresponding self-dual equations. In particular, when G ′ = SO (2) or G ′ = U S p (2), Gudnason in [33,34] introduced some meaningful physical ansatz on the structure of the vortex solutions, by which (as in [40]) the corresponding self-dual equations reduced to the following set of Master's equations:…”

“…In this context, a successful way to detect vortices is to identify the BPS-sector of the theory, since in such regime vortex configurations simply correspond to (static) solutions of the so called self-dual equations of Bogomolnyi type, and saturate the minimal energy allowed by the system. For this reason, it has been useful to invoke "duality" and formulate the theory within the general framework of N = 2 Supersymmetric (SUSY) Field Theory, in this direction see for example: [27,28,31,33,34,55,60] for more details . We observe that, when the Chern-Simons Lagrangian is taken into account then the theory can attain self-duality only with the help of a six-order scalar potential field, see [26,67,71], in place of the more familiar quadratic (double-well) potential of the Maxwell-Higgs model, see [40].…”

“…The main purpose of this paper is to analyse the solvability of (not necessarily integrable) planar "'singular"' Liouville systems, as they occur in various Chern-Simons vortex problems, see e.g. [33,34,55], or in other physical context decribed for example in [44,45,46,47], and which include the Toda system as a particular case.…”

“…

Motivated by the study of non-abelian Chern Simons vortices of non-topological type in Gauge Field Theory, see e.g. [33,34], [26], we analyse the solvability of the following (normalised) Liouville-type system in presence of singular sources:2π R 2 e u1 and β 2 = 1 2π R 2 e u2 , with τ > 0 and N > 0. We identify necessary and sufficient conditions on the parameter τ and the "flux" pair: (β 1 , β 2 ), which ensure the radial solvability of (1) τ .

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Small Data Global Existence and Decay for Relativistic Chern–Simons Equations

“…The supersymmetric Chern-Simons model was discussed in [16,17,37]. Topological solutions were constructed by Yang [51].…”