Induced current in high-dimensional AdS bulk in the presence of a cosmic string and brane

In this paper, we analyze the vacuum bosonic current associated with a massive charged scalar field propagating in a [Formula: see text]-dimensional anti-de Sitter (AdS) bulk in the presence of an idealized carrying-magnetic-flux cosmic string and also a brane. We assume that the string is perpendicular to the brane, which is parallel to the AdS boundary. The brane divides the space in two regions with different properties of vacuum states. We investigate the only nonvanishing azimuthal components of the induced currents in both regions. To develop this analysis, we calculate first, for both regions, the positive frequency Wightman functions. These present contributions associated with the presence of a cosmic string only plus the other induced by the brane. In this paper, we consider only the contributions induced by the brane.