Magnetic flux in the vacuum of quantum bosonic matter in the cosmic string background

The relativistic spin-0 matter field is quantized in the background of a straight cosmic string with nonvanishing transverse size. The most general boundary condition ensuring the impenetrability of the matter field into the interior of the cosmic string is shown to be the Robin condition with a boundary parameter varying arbitrarily from point to point of the boundary. The role of the bound states in the spectrum of solutions to the Fock-Klein-Gordon equation is elucidated. We derive, in the general case, an analytic expression for the total magnetic flux, which is induced in the vacuum in the cosmic string background. Further numerical analysis and the requirement of physical plausibility are shown to restrict ambiguity, which is due to the boundary condition. The dependence of the induced vacuum magnetic flux on the string flux and tension, as well as on the transverse size of the string, is analyzed.