Topological Effects in a Fermionic Condensate Induced by a Cosmic String and Compactification on the AdS Bulk

Abstract

In this paper, we analyzed the fermionic condensate (FC) associated with a massive fermionic field on a five-dimensional anti-de Sitter (AdS) spacetime in the presence of a cosmic string taking into account a magnetic flux running along its core. In addition, a compactified dimension was considered. Due to this compactification, the FC is expressed in terms of two distinct contributions: the first one corresponds to the geometry without compactification, and the second one is induced by the compactification. Depending on the values of the physical parameters, the total FC can be positive or negative. As a limiting case, the expression for the FC on locally Minkowski spacetime was derived. It vanishes for a massless fermionic field, and the nonzero FC on the AdS background space in the massless case is an effect induced by gravitation. This shows that the gravitational field may essentially influence the parameter space for phase transitions. For a massive field, the FC diverges on the string as the inverse cube of the proper distance from the string. In the case of a massless field, depending on the magnetic flux along the string and planar angle deficit, the limiting value of the FC on the string can be either finite or infinite. At large distances, the decay of the FC as a function of the distance from the string is a power law for both cases of massive and massless fields. For a cosmic string on the Minkowski bulk and for a massive field, the decay is exponential. The topological part in the FC vanishes on the AdS boundary. We show that the FCs coincide for the fields realizing two inequivalent irreducible representations of the Clifford algebra. In the special case of the zero planar angle deficit, the results presented in this paper describe Aharonov–Bohm-type effects induced by magnetic fluxes in curved spacetime.

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

“…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.…”

“…is the contribution of the cosmic string in the brane-free geometry (see [52]). The integral over p in this expression is expressed in terms of the associated Legendre function of the second kind and the final expression for ψψ cs can be found in [52]. As seen from (3.12), one has ψψ cs | s=−1 = − ψψ cs | s=+1 .…”

“…The expression for the FC induced by the cosmic string in the boundary-free (4+1)-dimensional Minkowski spacetime can be found in [52]. For a massless field the latter vanishes.…”

“…In the case of a massless field on the AdS bulk the contribution in the FC induced by a cosmic string in the absence of the boundary is given by [52]…”

“…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.…”