Induced current in high-dimensional AdS spacetime in the presence of a cosmic string and a compactified extra dimension

In this paper, we analyze the bosonic current densities induced by a magnetic flux running along the core of an idealized cosmic string in a high-dimensional anti-de Sitter spacetime, admitting that an extra dimension coordinate is compactified. Additionally, we admit the presence of a magnetic flux enclosed by the compactified axis. 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 extra dimension. In this context, only azimuthal and axial currents densities take place. As to the azimuthal current, two contributions appear. The first one corresponds to the standard azimuthal current in high-dimensional anti-de Sitter spacetime with a cosmic string 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 compactified axis and is an odd function of the magnetic flux along its core with period equal to quantum flux, ${\mathrm{\Phi }}_0=2\pi /e$. 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 the compactified axis. 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 compactified axis. Some asymptotic expressions for the current density are provided for specific limiting cases of the physical parameter of the model.

Figure 1

The azimuthal current density without compactification for $D=4$ in Eq. (3.17) is plotted, in units of $e{a}^{-5}$, in terms of $ϵ$, for $r/w=1$; $ma=1$; $\xi =0$; and $q=1$, 1.5, 2.5.

Figure 2

The azimuthal current density without compactification for $D=4$ in Eq. (3.17) is plotted, in units of $e{a}^{-5}$, in terms of the proper distance, $r/w$, for $ϵ=0.25$; $\xi =0$; and $q=1$, 1.5, 2.5. The plot on the left is for $ma=1$, while the plot on the right is for $ma=5$.

Figure 3

The azimuthal current density induced by compactification for $D=4$ is plotted, in units of $e{a}^{-5}$, in terms of $\tilde{\beta }$ for $ma=1$; $\xi =0$; $ϵ=0.25$, and $q=1$, 1.5, 2.5.

Figure 4

The axial current density is plotted for $D=4$, in units of $e{a}^{-4}$, as a function of $\tilde{\beta }$ for $ma=1$; $\xi =0$; $L/a=1$; and $q=1$, 1.5, 2.5. In the left plot, we consider $ϵ=0$, while in the right plot, we take $ϵ=0.25$.