Quantum vacuum effects in braneworlds on AdS bulk

TL;DR

This paper reviews how quantum vacuum properties are affected by branes in AdS spacetime, analyzing different geometries and boundary conditions, and highlighting the gravitational influence on vacuum energy-momentum tensor behavior.

Contribution

It provides a detailed analysis of vacuum expectation values and Casimir forces for various fields and boundary conditions in braneworlds within AdS backgrounds, considering different brane geometries.

Findings

Gravitational field significantly affects quantum vacuum properties beyond the AdS curvature radius.

Explicit separation of vacuum energy-momentum tensor contributions for different geometries.

Identification of non-zero off-diagonal components leading to parallel Casimir forces.

Abstract

We review the results of investigations for brane-induced effects on the local properties of quantum vacuum in background of AdS spacetime. Two geometries are considered: a brane parallel to the AdS boundary and a brane intersecting the AdS boundary. For both these cases the contribution in the vacuum expectation value (VEV) of the energy-momentum tensor is separated explicitly and its behavior in various asymptotic regions of the parameters is studied. It is shown that the influence of the gravitational field on the local properties of the quantum vacuum is essential at distance from the brane larger than the AdS curvature radius. In the geometry with a brane parallel to the AdS boundary the VEV of the energy-momentum tensor is considered for scalar field with the Robin boundary condition, for Dirac field with the bag boundary condition and for the electromagnetic field. In the latter case two types of boundary conditions are discussed. The first one is a generalization of the perfect conductor boundary condition and the second one corresponds to the confining boundary condition used in QCD for gluons. For the geometry of a brane intersecting the AdS boundary, the case of a scalar field is considered. The corresponding energy-momentum tensor, apart from the diagonal components, has nonzero off-diagonal component. As a consequence of the latter, in addition to the normal component, the Casimir force acquires a component parallel to the brane.