Vacuum Polarization Effects in Higher Dimensional Global Monopole Spacetime

In this paper we analyse the vacuum polarization effects associated with a massless scalar field in higher-dimensional global monopole spacetime. Specifically we calculate the renormalized vacuum expectation value of the field square, $<\Phi^2(x)>_{Ren}$, induced by a global monopole. Two different spacetimes will be considered: $i)$ In the first, the global monopole lives in whole universe, and $ii)$ in the second, the global monopole lives in a $n=3$ dimensional sub-manifold of the higher-dimensional (bulk) spacetime in the "braneworld" scenario. In order to develop these analysis we calculate the general Euclidean scalar Green function for both spacetimes. Also a general curvature coupling parameter between the field and the geometry is admitted. We explicitly show that $<\Phi^2(x)>_{Ren}$ depends crucially on the dimension of the spacetime and on the specific geometry adopted to describe the world. We also investigate the general structure of the renormalized vacuum expectation value of the energy-momentum tensor, $<T_{\mu\nu}(x)>_{Ren.}$.