Electromagnetic field correlators and the Casimir effect for planar boundaries in AdS spacetime with application in braneworlds

TL;DR

This paper calculates electromagnetic field correlators and Casimir forces between parallel plates in AdS spacetime, exploring boundary conditions, vacuum energies, and applications to braneworld models, revealing attractive interaction forces and boundary-dependent self-actions.

Contribution

It provides a detailed analysis of electromagnetic correlators, Casimir forces, and vacuum energies in AdS with planar boundaries, extending to braneworld applications.

Findings

Interaction Casimir forces are attractive for both boundary conditions.

At large separations, forces decay exponentially with distance.

Self-action forces depend on boundary conditions and can be attractive or repulsive.

Abstract

We evaluate the correlators for the vector potential and for the field strength tensor of the electromagnetic field in the geometry of two parallel planar plates in AdS spacetime. Two types of boundary conditions are considered on the plates. The first one is a generalization of perfect conductor boundary condition and the second one corresponds to the confining boundary conditions. By using the expressions for the correlators, the vacuum expectation values (VEVs) of the photon condensate and of the electric and magnetic fields squared are investigated. As another important local characteristic of the vacuum state we consider the VEV of the energy-momentum tensor. The Casimir forces acting on the plates are decomposed into the self-action and interaction parts. It is shown that the interaction forces are attractive for both types of boundary conditions. At separations between the plates larger than the curvature radius of the background geometry they decay exponentially as functions of the proper distance. The self-action force per unit surface of a single plate does not depend on its location and depending on the boundary condition and on the number of spatial dimensions can be either attractive or repulsive with respect to the AdS boundary. By using the generalized zeta function technique we also evaluate the total Casimir energy. Applications are given in $Z_{2}$-symmetric braneworld models of the Randall-Sundrum type for vector fields with even and odd parities.