Fermionic Casimir densities in anti-de Sitter spacetime

TL;DR

This paper investigates the fermionic Casimir effect in anti-de Sitter spacetime with two boundaries, analyzing vacuum expectation values, boundary effects, and forces, with implications for braneworld models.

Contribution

It provides a detailed analysis of fermionic Casimir densities in AdS space with boundaries, including boundary-induced effects and their decay properties, extending to Randall-Sundrum braneworlds.

Findings

Boundary-induced fermionic condensate is negative.

Vacuum energy density is exponentially suppressed at large distances.

Interaction forces between boundaries are attractive and decay exponentially.

Abstract

The fermionic condensate and vacuum expectation value of the energy-momentum tensor, for a massive fermionic field on the background of anti-de Sitter spacetime, in the geometry of two parallel boundaries with bag boundary conditions, are investigated. Vacuum expectation values, expressed as series involving the eigenvalues of the radial quantum number, are neatly decomposed into boundary-free, single-boundary-induced, and second-boundary-induced parts, with the help of the generalized Abel-Plana summation formula. In this way, the renormalization procedure is very conveniently reduced to the one corresponding to boundary-free AdS spacetime. The boundary-induced contributions to the fermionic condensate and to the vacuum expectation value of the energy density are proven to be everywhere negative. The vacuum expectation values are exponentially suppressed at distances from the boundaries much larger than the curvature radius of the AdS space. Near the boundaries, effects related with the curvature of the background spacetime are shown to be subdominant and, to leading order, all known results for boundaries in the Minkowski bulk are recovered. Zeta function techniques are successfully used for the evaluation of the total vacuum energy in the region between the boundaries. It is proven that the resulting interaction forces between them are attractive and that, for large separations, they also decay exponentially. Finally, our results are extended and explicitly translated to fermionic Casimir densities in braneworld scenarios of Randall-Sundrum type.