Fermionic currents in topologically nontrivial braneworlds

Abstract

We investigate the influence of a brane on the vacuum expectation value (VEV) of the current density for a charged fermionic field in background of locally AdS spacetime with an arbitrary number of toroidally compact dimensions and in the presence of a constant gauge field. Along compact dimensions the field operator obeys quasiperiodicity conditions with arbitrary phases and on the brane it is constrained by the bag boundary condition. The brane is parallel to the AdS boundary and it divides the space into two regions with different properties for the fermionic vacuum. In both these regions, the VEVs for the charge density and the components of the current density along uncompact dimensions vanish. The components along compact dimensions are decomposed into the brane-free and brane-induced contributions. The behavior of the latter in various asymptotic regions of the parameters is investigated. It particular, it is shown that the brane-induced contribution is mainly located near the brane and vanishes on the AdS boundary and on the horizon. An important feature is the finiteness of the current density on the brane. Applications are given to Z 2 -symmetric braneworlds of the Randall-Sundrum type with compact dimensions for two classes of boundary conditions on the fermionic field. For the second one we show that the contribution of the brane to the current does not vanish when the location of the brane tends to the AdS boundary. In odd spacetime dimensions, the fermionic fields realizing two inequivalent irreducible representations of the Clifford algebra and having equal phases in the periodicity conditions give the same contribution to the vacuum current density. Combining the contributions from these fields, the current density in odd-dimensional C-,Pand T -symmetric models is obtained. In the special case of three-dimensional spacetime, the corresponding results are applied for the investigation of the edge effects on the ground state current density induced in curved graphene tubes by an enclosed magnetic flux.

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

“…Note that for an observer located on the brane y = 0 the line element (7.1) is reduced to the standard line element for a cosmic string in (3+1)-dimensional Minkowski spacetime. The boundary condition for the field ψ(x) on the brane is obtained on the basis of the Z 2 -symmetry (see discussion in [51,72]).…”

“…In braneworld models these boundary conditions are dictated by the Z 2 -symmetry under the reflection with respect to the brane. Note that the vacuum current densities on locally AdS bulk with a part of spatial dimensions compactified to a torus and in the presence of branes have been investigated in [47][48][49] and [50][51][52] for charged scalar and fermionic fields, respectively.…”

Fermionic vacuum currents in topologically nontrivial braneworlds: Two-brane geometry

“…With the curved spacetime gamma matrices γ µ = (z/a)δ µ b γ (b) , the complete set of solutions of the field equation (2.2) (with A µ = 0 in the gauge under consideration) can be found in a way similar to that given in [29]. Introducing the one-column matrices w (σ) , σ = 1, .…”

“…The first term in the right-hand side of (4.8) is given by 10) and it corresponds to the current density in the region z 1 z < ∞ for the geometry of a single brane located at z = z 1 . The single brane part (4.10) has been investigated in [29]. It is decomposed as…”

Fermionic Condensate on Finite Radius Cones

“…A more complicated geometry of hemisphere capped tubes is considered in [9]. The ground state charge and current densities of a fermionic field on curved graphene tubes with locally anti-de Sitter geometry were discussed in [10,11].…”