Electromagnetic Wightman functions and vacuum densities for a brane intersecting the AdS boundary

TL;DR

This paper analyzes how a brane intersecting the AdS boundary influences electromagnetic vacuum properties, deriving explicit expressions for vacuum expectation values under different boundary conditions.

Contribution

It provides explicit formulas for Wightman functions and vacuum densities in AdS with a brane, considering PEC and PMC boundary conditions, extending prior models.

Findings

Brane-induced contributions to vacuum densities have opposite signs for PEC and PMC conditions.

Vacuum energy density is positive for PMC boundary condition.

The vacuum energy-momentum tensor exhibits a nonzero off-diagonal component.

Abstract

We investigate the combined effects of a brane intersecting the AdS boundary and background gravitational field on the local characteristics of the electromagnetic vacuum. Two types of boundary conditions on the brane are considered, which are higher-dimensional generalizations of the perfect electric (PEC) and perfect magnetic (PMC) boundary conditions in Maxwell's electrodynamics. The brane-induced contributions to the Wightman functions of the vector potential and field tensor are explicitly extracted. Simple expressions in terms of elementary functions are provided. The behavior of the vacuum expectation values (VEVs) is mimicked by a scalar field with a negative effective mass squared determined by the radius of the AdS spacetime. The expectation values of the electric and magnetic fields squares and of the energy-momentum tensor are investigated as local characteristics of the vacuum state. The brane-induced contributions to these VEVs have opposite signs for the PEC and PMC conditions. For the PMC condition, this contribution is negative for the electric field squared and positive for the magnetic field squared. The VEV of the energy-momentum tensor has a nonzero off-diagonal component. The brane-induced vacuum energy density is positive for PMC condition, whereas the normal and parallel stresses change sign as functions of the distance from the brane. Unlike the problem involving a planar boundary in the Minkowski bulk, the vacuum energy-momentum tensor does not vanish in (3+1)-dimensional AdS spacetime.