Self - Dual Charged Vortices of Finite Energy per Unit Length in 3 + 1 Dimensions

We obtain both topological as well as nontopological self-dual charged vortex solutions of finite energy per unit length in a generalized abelian Higgs model in 3 + 1 dimensions. In this model the Bogomol’nyi bound on the energy per unit length is obtained as a linear combination of the magnetic flux and the electric charge per unit length. PACS NO. 11.15. -q, 11.10.Lm, 03.65.Ge Typeset using REVTEX 1 It is well known that the Ginzburg-Landau model of superconductivity [1] and also its relativistic generalization, i.e., the abelian Higgs model admits topologically stable vortex solutions of finite energy per unit length in 3 + 1 dimensions [2]. These vortices have received considerable attention in the literature because of their possible relevance in the context of cosmic strings as well as superconductivity. These vortices are electrically neutral. Infact in 1975 Julia and Zee [3] showed that unlike the case of dyons in SO(3) Georgi-Glashow model, the abelian Higgs model does not admit charged generalization. Sometime ago, one of us (AK) with Paul showed [4] that in 2 + 1 dimensions this Julia-Zee objection can be overcomed and one can have charged vortices ( solitons to be more precise ) of finite energy in the abelian Higgs model with Chern-Simons (CS) term. However, to the best of our knowledge, as far as 3 + 1 dimensions are concerned, no one has been able to overcome the Julia-Zee objection and obtain charged vortex solutions of finite energy per unit length. The purpose of this letter is to show that the Julia-Zee objection can be overcomed in 3 + 1 dimensions and one can have charged vortices of finite energy per unit length. We consider a generalized abelian Higgs model with a dielectric function and a neutral scalar field and show that such a model admits self-dual toplogical as well as nontopological charged vortex solutions of finite energy per unit length. Remarkably enough, the Bogomol’nyi equations [5] of our model can be shown to be essentially identical to the corresponding equations of the pure CS Higgs vortices [6]. However, unlike in that case, the Bogomol’nyi bound on the energy per unit length is obtained as a linear combination of the magnetic flux and the electric charge per unit length. As a result, unlike in the CS case, the nontopological self-dual charged vortices turn out to be unstable against decay to the elmentary excitations. Finally using the cylindrical ansatz, we show that the angular momentum and the magnetic moment of the vortices can also be computed