Vacuum fermionic currents in braneworld models on AdS bulk with a cosmic string

Abstract

We investigate the effects of a brane and magnetic-flux-carrying cosmic string on the vacuum expectation value (VEV) of the current density for a charged fermionic field in the background geometry of (4+1)-dimensional anti-de Sitter (AdS) spacetime. The brane is parallel to the AdS boundary and the cosmic string is orthogonal to the brane. Two types of boundary conditions are considered on the brane that include the MIT bag boundary condition and the boundary conditions in Z2-symmetric braneworld models. The brane divides the space into two regions with different properties of the vacuum state. The only nonzero component of the current density is along the azimuthal direction and in both the regions the corresponding VEV is decomposed into the brane- free and brane-induced contributions. The latter vanishes on the string and near the string the total current is dominated by the brane-free part. At large distances from the string and in the region between the brane and AdS horizon the decay of the brane-induced current density, as a function of the proper distance, is power-law for both massless and massive fields. For a massive field this behavior is essentially different from that in the Minkowski bulk. In the region between the brane and AdS boundary the large-distance decay of the current density is exponential. Depending on the boundary condition on the brane, the brane-induced contribution is dominant or subdominant in the total current density at large distances from the string. By using the results for fields realizing two inequivalent irreducible representations of the Clifford algebra, the vacuum current density is investigated in C - and P -symmetric fermionic models. Applications are given for a cosmic string in the Randall-Sundrum-type braneworld model with a single brane.

Topological effects in fermion condensate induced by cosmic string and compactification on AdS bulk

“…The VEVs of the field squared and of the energy-momentum tensor in that geometry were discussed in [45]. The vacuum fermionic current induced by a magnetic flux running along the cosmic string on AdS bulk in the presence of a brane parallel to the AdS boundary was studied as well [46]. This paper is organized as follows.…”

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

“…As representatives of those properties the FC and the VEV of the energy-momentum tensor are considered. For the evaluation of the corresponding expectation values the direct summation over the complete set of the fermionic modes from [12] has been used. They are specified by the set of quantum numbers (λ, j, p, k z , η).…”

“…The VEVs of physical observables bilinear in the field operator can be expressed in terms of the mode sum over the complete set of solutions of the field equation. For the system under consideration, those solutions were obtained in [12]. They are specified by the set of quantum numbers σ = (λ, j, p, k z , η), where 0 ≤ λ, p < ∞, j = ±1/2, ±3/2, .…”

“…We investigate those contributions for the fermionic condensate (FC) and for the expectation value of the energy-momentum tensor for fields realizing two inequivalent irreducible representations of the Clifford algebra. The corresponding VEV of the current density for a charged fermionic field has been considered in [12]. Another type of conditions imposed on the operator of a quantum field appears in models with compact spatial dimensions.…”

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

“…We investigate those contributions for the fermionic condensate (FC) and for the expectation value of the energy-momentum tensor for fields realizing two inequivalent irreducible representations of the Clifford algebra. The corresponding VEV of the current density for a charged fermionic field has been considered in [34]. Another type of conditions imposed on the operator of a quantum field appears in models with compact spatial dimensions.…”