Wightman function and vacuum densities for a Z_2-symmetric thick brane in AdS spacetime

TL;DR

This paper calculates the quantum vacuum effects, including the Wightman function and energy-momentum tensor, for a Z2-symmetric thick brane in AdS spacetime, revealing how these effects depend on the brane's properties and the scalar field coupling.

Contribution

It provides a comprehensive analysis of vacuum expectation values for a thick brane in AdS, including a specific model with Minkowski interior, extending previous thin-brane studies.

Findings

Vacuum expectation values are split into free AdS and brane-induced parts.

For conformally coupled massless scalars, the brane-induced energy-momentum tensor vanishes.

Interior vacuum forces tend to decrease the brane thickness.

Abstract

Positive frequency Wightman function, vacuum expectation values of the field square and the energy-momentum tensor induced by a Z_{2}-symmetric brane with finite thickness located on (D+1)- dimensional AdS background are evaluated for a massive scalar field with general curvature coupling parameter. For the general case of static plane symmetric interior structure the expectation values in the region outside the brane are presented as the sum of free AdS and brane induced parts. For a conformally coupled massless scalar the brane induced part in the vacuum energy-momentum tensor vanishes. In the limit of strong gravitational fields the brane induced parts are exponentially suppressed for points not too close to the brane boundary. As an application of general results a special model is considered in which the geometry inside the brane is a slice of the Minkowski spacetime orbifolded along the direction perpendicular to the brane. For this model the Wightman function, vacuum expectation values of the field square and the energy-momentum tensor inside the brane are evaluated as well and their behavior is discussed in various asymptotic regions of the parameters. It is shown that for both minimally and conformally coupled scalar fields the interior vacuum forces acting on the brane boundaries tend to decrease the brane thickness.