Fermionic vacuum polarization by a cosmic string in anti-de Sitter spacetime

Abstract

In this paper, we investigate the fermionic condensate (FC) and the vacuum expectation value (VEV) of the energy–momentum tensor, associated with a massive fermionic field, induced by the presence of a cosmic string in the anti-de Sitter (AdS) spacetime. In order to develop this analysis we construct the complete set of normalized eigenfunctions in the corresponding spacetime. We consider a special case of boundary conditions on the AdS boundary, when the MIT bag boundary condition is imposed on the field operator at a finite distance from the boundary, which is then taken to zero. The FC and the VEV of the energy–momentum tensor are decomposed into the pure AdS and string-induced parts. Because the analysis of one-loop quantum effects in the AdS spacetime has been developed in the literature, here we are mainly interested to investigate the influence of the cosmic string on the VEVs. The string-induced part in the VEV of the energy–momentum tensor is diagonal and the axial and radial stresses are equal to the energy density. For points near the string, the effects of the curvature are subdominant and to leading order, the VEVs coincide with the corresponding VEVs for the cosmic string in the Minkowski bulk. At large proper distances from the string, the decay of the VEVs show a power-law dependence of the distance for both massless and massive fields. This is in contrast to the case of the Minkowski bulk where, for a massive field, the string-induced parts decay exponentially.