Vacuum Polarization Effects on Flat Branes due to a Global Monopole

TL;DR

This paper studies how a global monopole in higher-dimensional spacetime influences vacuum polarization effects of a scalar field on a flat brane, revealing dependence on the brane's dimensionality and calculating related quantum expectation values.

Contribution

It provides a detailed calculation of vacuum polarization effects and the energy-momentum tensor in a braneworld with a global monopole, including the Green function and curvature coupling effects.

Findings

Vacuum polarization effects depend critically on the brane's dimensionality.

Explicit expressions for the renormalized vacuum expectation value of the scalar field squared.

Analysis of the energy-momentum tensor structure for specific brane dimensions.

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 $p=3$.