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Register a new userVacuum fermionic currents in braneworld models on AdS bulk with a cosmic string
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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.
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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.
We study the fermionic condensate (FC) and the vacuum expectation value (VEV) of the energy-momentum tensor for a massive spinor field in the de Sitter (dS) spacetime including an ideal cosmic string. In addition, spatial dimension along the string is compactified to a circle of length $L$. The fermionic field is assumed to obey quasi-periodic condition along the $z$-axis. There are also magnetic fluxes running along the cosmic string and enclosed by the compact dimension. Both, the FC and the VEV of the energy-momentum tensor, are decomposed into two parts: one induced by the cosmic string in dS spacetime considering the absence of the compactification, and another one induced by the compactification. In particular, we show that the FC vanishes for a massless fermionic field.
In the present paper, we study the vacuum bosonic currents in the geometry of a compactified cosmic string in the background of the de Sitter spacetime. The currents are induced by magnetic fluxes, one running along the cosmic string and another one enclosed by the compact dimension. To develop the analysis, we obtain the complete set of normalized bosonic wave-functions obeying a quasiperiodicity condition. In this context, we calculate the azimuthal and axial current densities and we show that these quantities are explicitly decomposed into two contributions: one originating from the geometry of a straight uncompactified cosmic string and the other induced by the compactification. We also compare the results with the literature in the case of a massive fermionic field in the same geometry.
We review the results of investigations for brane-induced effects on the local properties of quantum vacuum in background of AdS spacetime. Two geometries are considered: a brane parallel to the AdS boundary and a brane intersecting the AdS boundary. For both these cases the contribution in the vacuum expectation value (VEV) of the energy-momentum tensor is separated explicitly and its behavior in various asymptotic regions of the parameters is studied. It is shown that the influence of the gravitational field on the local properties of the quantum vacuum is essential at distance from the brane larger than the AdS curvature radius. In the geometry with a brane parallel to the AdS boundary the VEV of the energy-momentum tensor is considered for scalar field with the Robin boundary condition, for Dirac field with the bag boundary condition and for the electromagnetic field. In the latter case two types of boundary conditions are discussed. The first one is a generalization of the perfect conductor boundary condition and the second one corresponds to the confining boundary condition used in QCD for gluons. For the geometry of a brane intersecting the AdS boundary, the case of a scalar field is considered. The corresponding energy-momentum tensor, apart from the diagonal components, has nonzero off-diagonal component. As a consequence of the latter, in addition to the normal component, the Casimir force acquires a component parallel to the brane.
We investigate the fermion condensate (FC) for a massive spinor field on background of the 5-dimensional locally anti-de Sitter (AdS) spacetime with a compact dimension and in the presence of a cosmic string carrying a magnetic flux. The FC is decomposed into two 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 parameters, the total FC can be either positive or negative. As a limiting case, the expression for the FC on locally Minkowski spacetime is derived. It vanishes for a massless fermion field and the nonzero FC on the AdS bulk in the massless case is an effect induced by gravitation. This shows that the gravitational field may essentially influence the parameters 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 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.
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