Fermionic vacuum polarization around a cosmic string in compactified AdS spacetime

Abstract

We investigate topological effects of a cosmic string and compactification of a spatial dimension on the vacuum expectation value (VEV) of the energy-momentum tensor for a fermionic field in (4+1)-dimensional locally AdS spacetime. The contribution induced by the compactification is explicitly extracted by using the Abel-Plana summation formula. The mean energy-momentum tensor is diagonal and the vacuum stresses along the direction perpendicular to the AdS boundary and along the cosmic string are equal to the energy density. All the components are even periodic functions of the magnetic fluxes inside the string core and enclosed by compact dimension, with the period equal to the flux quantum. The vacuum energy density can be either positive or negative, depending on the values of the parameters and the distance from the string. The topological contributions in the VEV of the energy-momentum tensor vanish on the AdS boundary. Near the string the effects of compactification and gravitational field are weak and the leading term in the asymptotic expansion coincides with the corresponding VEV in (4+1)-dimensional Minkowski spacetime. At large distances, the decay of the cosmic string induced contribution in the vacuum energy-momentum tensor, as a function of the proper distance from the string, follows a power law. For a cosmic string in the Minkowski bulk and for massive fields the corresponding fall off is exponential. Within the framework of the AdS/CFT correspondence, the geometry for conformal field theory on the AdS boundary corresponds to the standard cosmic string in (3+1)-dimensional Minkowski spacetime compactified along its axis.

24 pages, 6 figures

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Cited by in corpus (5)

• Cosmic string and brane induced effects on the fermionic vacuum in AdS spacetime
• Vacuum densities and the Casimir forces for branes orthogonal to the AdS boundary
• Induced current by a cosmic string and a brane in high-dimensional AdS spacetime
• Finite temperature charge and current densities around a cosmic string in AdS spacetime with compact dimension
• Electromagnetic vacuum stresses and energy fluxes induced by a cosmic string in de Sitter spacetime