Vacuum current and polarization induced by magnetic flux in a higher-dimensional cosmic string in the presence of a flat boundary

In this present paper, we investigate the vacuum bosonic current and polarization induced by a magnetic flux running along a higher-dimensional cosmic string in the presence of a flat boundary orthogonal to the string. In our analysis, we assume that the quantum field obeys Dirichlet or Neunmann conditions on the flat boundary. To develop this analysis we calculate the corresponding positive frequency Wightman function. As consequence of the boundary condition, the Wightamn function is expressed in term of two contributions: The first one corresponds to the Wightman function in cosmic string spacetime in the absence of boundary, while the second one is induced by the presence of the boundary. Due to the fact that the analysis of induced bosonic current and polarization effects in the pure cosmic string spacetime have been developed by many authors, the main objective of this paper is to study the effects induced by the boundary. Regarding to the induced current, we show that, depending on the condition adopted, the boundary-induced azimuthal current can cancel or intensifies the total induced azimuthal current on the boundary; moreover, the boundary-induced azimuthal current is a periodic odd function of the magnetic flux. As to the vacuum expectation values of the field squared and the energy-momentum tensor, the boundary-induced contributions are even functions of magnetic flux. In particular, we consider some special cases of the boundary-induced part of the energy density and evaluate the normal vacuum force on the boundary.