Induced vacuum current and magnetic flux in quantum scalar matter in the background of a vortex defect with the Neumann boundary condition

A topological defect in the form of the Abrikosov-Nielsen-Olesen vortex in a space of arbitrary dimension is considered as a gauge-flux-carrying tube that is impenetrable for quantum matter. Charged scalar matter field is quantized in the vortex background with the perfectly rigid (Neumann) boundary condition imposed at the side surface of the vortex. We show that a current circulating around the vortex is induced in the vacuum, if the Compton wavelength of the matter field exceeds the transverse size of the vortex considerably. The vacuum current is periodic in the value of the gauge flux of the vortex, providing a quantum-field-theoretical manifestation of the Aharonov-Bohm effect. The vacuum current leads to the appearance of an induced vacuum magnetic flux that for some values of the tube thickness exceeds the vacuum magnetic flux induced by a singular vortex filament. The results were compared to the results obtained earlier in the case of the perfectly reflecting (Dirichlet) boundary condition imposed at the side surface of the vortex. It is shown that the absolute value of the induced vacuum current and the induced vacuum magnetic flux in the case of the Neumann boundary condition is greater than in the case of the Dirichlet boundary condition.