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.

Cosmic string and brane induced effects on the fermionic vacuum in AdS spacetime

“…The second contribution to the VEVs presents the part that is induced by the cosmic string in the brane-free geometry. Those contribution for the FC and the energy-momentum tensor have been investigated in [52] and [53], respectively. Our main interest in the present paper is concentrated on the contributions in the FC and the energy-momentum tensor induced by the presence of the brane.…”

“…The analysis of the FC and of the mean energy-momentum tensor on the pure AdS spacetime considering the presence of branes has been developed in [57]. As to the investigation of those VEVs on the AdS background in the presence of a magnetic flux-carrying cosmic string, it was considered in [52,53]. Here in this paper, we want to investigate the influence of the gravitational field, the nontrivial spatial topology and the presence of the brane on the local properties of the FC and the VEV of the energy-momentum tensor.…”

“…An additional topological influence of a cosmic string on the vacuum currents has been considered in [49][50][51]. The FC and the VEV of the energy-momentum tensor for a charged massive fermionic field were investigated in [52,53]. The influence of the brane on those characteristics of the fermionic vacuum in the geometry of a cosmic string on a locally AdS bulk is the main concern in the present paper.…”