Induced vacuum bosonic current by magnetic flux in a higher dimensional compactified cosmic string spacetime

In this paper, we analyze the bosonic current densities induced by a magnetic flux running along an idealized cosmic string in a high-dimensional spacetime, admitting that the coordinate along the string's axis is compactified. Additionally we admit the presence of a magnetic flux enclosed by the compactification axis. In order to develop this analysis we calculate the complete set of normalized bosonic wave functions obeying a quasiperiodicity condition, with arbitrary phase beta, along the compactified dimension. In this context, only azimuthal and axial currents densities take place. As to the azimuthal current, two contributions appear. The first contribution corresponds to the standard azimuthal current in a cosmic string spacetime without compactification, while the second contribution is a new one, induced by the compactification itself. The latter is an even function of the magnetic flux enclosed by the string axis and is an odd function of the magnetic flux along its core with period equal to quantum flux, Phi(0) = 2 pi/e. On the other hand, the nonzero axial current density is an even function of the magnetic flux along the core of the string and an odd function of the magnetic flux enclosed by it. We also find that the axial current density vanishes for untwisted and twisted bosonic fields in the absence of the magnetic flux enclosed by the string axis. Some asymptotic expressions for the current density are provided for specific limiting cases of the physical parameter of the model.