Vacuum Polarization Effects on Flat Branes due to a Global Monopole

Abstract

In this paper we analyse the vacuum polarization effects associated with a massless scalar field in the higher-dimensional spacetime. Specifically we calculate the renormalized vacuum expectation value of the square of the field, $<\Phi^2(x)>_{Ren}$, induced by a global monopole in the "braneworld" scenario. In this context the global monopole lives in a $n=3$ dimensional sub-manifold of the higher-dimensional (bulk) spacetime, and our Universe is represented by a transverse flat $(p-1)-$ dimensional brane. In order to develop this analysis we calculate the general Green function admitting that the scalar field propagates in the bulk. Also a general curvature coupling parameter between the field and the geometry is assumed. We explicitly show that the vacuum polarization effects depend crucially on the values attributed to $p$. We also investigate the general structure of the renormalized vacuum expectation value of the energy-momentum tensor, $<T_{\mu\nu}(x)>_{Ren.}$, for $p=3$.