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

In this paper we analyze 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. In order to develop this analysis we calculate the corresponding Wightman function. As consequence of the boundary, the Wightamn function is expressed in term of two contributions: The first one corresponds to the boundary-free cosmic string Wightman function, while the second one is induced by the boundary. The boundary-induced contributions have opposite signs for Dirichlet and Newman scalars. Because the analysis of vacuum current and polarization effects in the boundary-free cosmic string spacetime have been developed in the literature, here we are mainly interested in the calculations of 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.