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In this paper we analyze the vacuum bosonic current associated with a massive charged scalar field propagating in a $(D+1)$-dimensional anti-de Sitter (AdS) bulk in the presence of an idealized carrying-magnetic-flux cosmic string and also a brane. We assume that the string is perpendicular to the brane which is parallel to the AdS boundary. The brane divides the space in two regions with different properties of vacuum states. We investigate the only non-vanishing azimuthal components of the induced currents in both regions. To develop this analysis we calculate first, for both regions, the positive frequency Wightman functions. These present contributions associated with the presence of a cosmic string only plus the other induced by the brane. In this talk we consider only the contributions induced by the brane., Comment: 9 pages. Work presented in the Fifth International Symposium on the Casimir Effect, Piran (Slovenia)

In this paper, we investigate the vacuum bosonic current density induced by a carrying-magnetic-flux cosmic string in a $(D+1)$-de Sitter spacetime considering the presence of two flat boundaries perpendicular to it. In this setup, the Robin boundary conditions are imposed on the scalar charged quantum field on the boundaries. The particular cases of Dirichlet and Neumann boundary conditions are studied separately. Due to the coupling of the quantum scalar field with the classical gauge field, corresponding to a magnetic flux running along the string's core, a nonzero vacuum expectation value for the current density operator along the azimuthal direction is induced. The two boundaries divide the space in three regions with different properties of the vacuum states. In this way, our main objective is to calculate the induced currents in these three regions. In order to develop this analysis we calculate, for both regions, the positive frequency Wightman functions. Because the vacuum bosonic current in dS space has been investigated before, in this paper we consider only the contributions induced by the boundaries. We show that for each region the azimuthal current densities are odd functions of the magnetic flux along the string. To probe the correctness of our results, we take the particular cases and analyze some asymptotic limits of the parameters of the model. Also some graphs are presented exhibiting the behavior of the current with relevant physical parameter of the system., Comment: 18 pages, 2 figures

Here we analyze the expectation value of the fermionic condensate and the energy-momentum tensor associated with a massive charged fermionic quantum field with a nonzero chemical potential propagating in a magnetic-flux-carrying cosmic string in thermal equilibrium at finite temperature $T$. The expectation values of the fermionic condensate and the energy-momentum tensor are expressed as the sum of vacuum expectation values and the finite temperature contributions coming from the particles and antiparticles excitation. The thermal expectations values of the fermionic condensate and the energy-momentum tensor are even periodic functions of the magnetic flux with period being the quantum flux, and also even functions of the chemical potential. Because the analyses of vacuum expectation of the fermionic condensate and energy-momentum tensor have been developed in literature, here we are mainly interested in the investigation of the thermal corrections. In this way we explicitly study how these observable behaves in the limits of low and high temperatures, and also for points near the string. Besides the analytical discussions, we included some graphs that exhibit the behavior of these observable for different values of the physical parameters of the model., Comment: 25 pages, 3 figures. Discussion about compactification removed, revised version accepted for publication in EPJC

In this paper we investigate the bosonic current induced by a brane and a magnetic flux running along the idealized cosmic string in a $(D+1)$-dimensional anti-de Sitter (AdS) background. We consider the brane is parallel to the AdS boundary and the cosmic string is orthogonal to them. Moreover, we assume that on the brane the charged bosonic field obeys the Robin boundary condition. The brane divides the space into two regions with different properties of the vacuum state. We show that the only nonzero component of the current density is along the azimuthal direction in both regions. In order to develop this analysis we calculate, for both regions, the positive frequency Wightman functions. Both functions present a part associated with the AdS in presence of a cosmic string only, and the other part induced by the brane. In this paper we consider only the contributions induced by the brane. We show that in both regions the azimuthal current densities are odd functions of the magnetic flux along the string. Different analytic and numerical analysis are performed and an application of our results is provided for the Randall-Sundrum braneworld model with a single brane., Comment: 19 pages, 2 figures. Version accepted for publication in EPJC

In this paper we investigate the vacuum expectation values of the field squared and the energy-momentum tensor associated to a charged massive scalar quantum field in a $(1+D)$-dimensional de Sitter spacetime induced by a plate (flat boundary) and a carrying-magnetic-flux cosmic string. In our analysis we admit that the flat boundary is perpendicular to the string, and the scalar field obeys the Robin boundary condition on the plate. In order to do develop this analysis, we obtain the complete set of normalized positive-energy solution of the Klein-Gordon equation compatible with the model setup. Having obtained these bosonic modes, we construct the corresponding Wightman function. The latter is given by the sum of two terms: one associated with the boundary-free spacetime, and the other induced by the flat boundary. Although we have imposed the Robin boundary condition on the field, we apply our formalism considering specifically the Dirichlet and Neumann boundary conditions. The corresponding parts have opposite signs. Because the analysis of bosonic vacuum polarization in boundary-free de Sitter space and in presence of a cosmic string, in some sense, has been developed in the literature, here we are mainly interested in the calculations of the effects induced by the boundary. In this way, closed expressions for the corresponding expectation values are provided, as well as their asymptotic behavior in different limiting regions. We show that the conical topology due to the cosmic string enhances the boundary induced vacuum polarization effects for both field squared and the energy-momentum tensor, compared to the case of a boundary in pure de Sitter spacetime. Moreover, the presence of cosmic string and boundary induce non-zero stress along the direction normal to the boundary. The corresponding vacuum force acting on the boundary is also investigated., Comment: 22 pages, 5 figures. Revised version accepted for publication in Universe

In this paper we investigate the vacuum polarization effects associated to a charged quantum massive scalar field on a $(D+1)$-dimensional anti-de Sitter background induced by a magnetic-flux-carrying cosmic string in the braneworld model context. We consider the brane parallel to the anti-de Sitter boundary and the cosmic string orthogonal to them. Moreover, we assume that the field obeys the Robin boundary condition on the brane. Because the brane divides the space into two regions with different properties of the quantum vacuum, we calculate the vacuum expectation value (VEV) of the field squared and the energy-momentum tensor (EMT) in each region. To develop these analyses, we have constructed the positive frequency Wightman function for both regions. The latter is decomposed in a part associated with the anti-de Sitter bulk in the presence of a cosmic string only, and the other part induced by the brane. The vacuum polarization effects associated with the higher-dimensional anti-de Sitter bulk in the presence of cosmic string have been developed in the literature, and here we are mainly interested in the effects induced by the brane. We show that the VEVs of the field squared and the components of the EMT induced by the cosmic string are finite on the brane. Explicitly, we compare these observables with the corresponding ones induced by the brane only, and show that near the brane the contribution induced by the latter is larger than the one induced by the string; however, for points distant from the brane the situation is reversed. Moreover, some asymptotic expressions for the VEV of the field squared and EMT are provided for specific limiting cases of the physical parameters of the model. Also, an application of our results is given for a cosmic string in the $Z_2$-symmetric Randall-Sundrum braneworld model with a single brane., Comment: 23 pages, 4 figures; Version accepted for publication in EPJC

In this paper we analyze the expectation value of the field squared and the energy-momentum tensor associated with a massive charged scalar quantum field with a nonzero chemical potential propagating in a high-dimensional compactified cosmic string spacetime in thermal equilibrium at finite temperature $T$. Moreover, we assume that the charged quantum field interacts with a very thin magnetic flux running along the core of the idealized cosmic string, and with a magnetic flux enclosed by the compact dimension. These observables are expressed as the vacuum expectation values and the finite temperature contributions coming from the particles and antiparticles excitations. Due to the compactification, the thermal corrections can be decomposed in a part induced by the cosmic string spacetime without compactification, plus a contribution induced by the compactification. This decompositions explicitly follows from the Abel-Plana formula used to proceed the summation over the discrete quantum number associated with the quasiperiodic condition imposed on the quantum field along the compact dimension. The expectations values of the field squared and the energy-momentum tensor are even periodic functions of the magnetic flux with period being the quantum flux, and also even functions of the chemical potential. Our main objectives in this paper concern in the investigation of the thermal corrections only. In this way we explicitly calculate the behavior of these observables in the limits of low and high temperature. We show that the temperature enhance the induced densities. In addition some graphs are also included in order to exhibit these behaviors., Comment: 23 pages, 5 figures; Version accepted for publication in EPJC

For a massive scalar field with a general curvature coupling parameter, we investigate the finite temperature contributions to the Hadamard function and to the charge and current densities in the geometry of a magnetic flux carrying generalized cosmic string embedded in $(D+1)$-dimensional locally AdS spacetime with a compactified spatial dimension. For $D=4$, the geometry on the AdS boundary, in the context of the AdS/CFT duality, corresponds to a cosmic string as a linear defect, compactified along its axis. In contrast to the case of the Minkowski bulk, the upper bound on the chemical potential does not depend on the field mass and is completely determined by the length of compact dimension and by the enclosed magnetic flux. The only nonzero components correspond to the charge density, to the azimuthal current and to the current along the compact dimension. They are periodic functions of magnetic fluxes with the period equal to the flux quantum. The charge density is an odd function and the currents are even functions of the chemical potential. At high temperatures the influence of the gravitational field and topology on the charge density is subdominant and the leading term in the corresponding expansion coincides with that for the charge density in the Minkowski spacetime. The current densities are topology-induced quantities and their behavior at high temperatures is completely different with the linear dependence on the temperature. At small temperatures and for chemical potentials smaller than the critical value, the thermal expectation values are exponentially suppressed for both massive and massless fields., Comment: 30 pages, 7 figures; Version accepted for publication in Physical Review D

We investigate the combined effects of a magnetic flux-carrying cosmic string and a brane on the fermionic condensate (FC) and on the vacuum expectation value (VEV) of the energy-momentum tensor for a massive charged fermionic field in background of 5-dimensional anti-de Sitter (AdS) spacetime. The brane is parallel to the AdS boundary and it divides the space into two regions with distinct properties of the fermionic vacuum. For two types of boundary conditions on the field operator and for the fields realizing two inequivalent representations of the Clifford algebra, the brane-induced contributions in VEVs are explicitly separated. The VEVs are even periodic functions of the magnetic flux, confined in the core, with the period of flux quantum. Near the horizon the FC and the vacuum energy-momentum tensor are dominated by the brane-free contribution, whereas the brane-induced part dominates in the region near the brane. Both the contributions vanish on the AdS boundary. At large distances from the cosmic string, the topological contributions in the VEVs, as functions of the proper distance, exhibit an inverse power-law decrease in the region between the brane and AdS horizon and an exponential decrease in the region between the brane and AdS boundary. We show that the FC and the vacuum energy density can be either positive or negative, depending on the distance from the brane. Applications are discussed in fermionic models invariant under the charge conjugation and parity transformation and also in $Z_{2}$% -symmetric braneworld models. By the limiting transition we derive the expressions of the FC and the vacuum energy-momentum tensor for a cosmic string on 5-dimensional Minkowski bulk in the presence of a boundary perpendicular to the string., Comment: 34 pages, 7 figures. Version accepted for publication in JHEP

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., Comment: 24 pages, 6 figures

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., Comment: 28 pages, 6 figures. Version accepted for publication in Symmetry

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., Comment: JHEP, in press, 29 pages, 11 figures, 1 table, Keywords: Cosmic string, AdS space, Brane, Vacuum polarization

A vector field coming from spontaneous Lorentz violation mechanism, namely Bumblebee model is analysed in a topological framework in a $(1+2)D$ Minkowski space-time. Taking a $(1+2)D$ nonlinear Bumblebee vector matter field dynamics where we include topological like Chern-Simons type terms, a vector version of a soliton state, or vortex was found. The Nielsen-Olesen procedure was used in order to derive a Lorentz-violation vector parameter which characterizes, via Spontaneous Symmetry Breaking mechanism, the non-trivial vacuum. We verify the stability of the model as much as the magnetic vortex, and noticed that the soliton modes with polarized direction generated can be associated with local anisotropy of vacuum energy. The vortex equations of motion and the asymptotic behaviour is presented. We have obtained that the effect of the Lorentz symmetry violation expressed by the a time-like Bumblebee vector field vacuum could be shown as kind of pulse at a fixed point $r_0$ in a limitless universe, or as a barrier at $r_0$ which can represent a boundary in the universe, if the Bumblebee vector field vacuum has space-like characteristic. We also analyse the spectrum via propagators where we note that the topological mass contributes as well to the dynamical mass poles. We obtain that the Chern-Simons type terms, in fact, indicates the "speed" of the field to saturate the asymptotic limit and that the vortex core can not be dimension zero., Comment: 12 pages, 6 figures

In this paper, we consider a massive charged fermionic quantum field and investigate the current densities induced by a magnetic flux running along the core of an idealized cosmic string in the background geometry of a 5-dimensional anti-de Sitter spacetime, assuming that an extra dimension is compactified. Along the compact dimension quasi-periodicity condition is imposed on the field with a general phase. Moreover, we admit the presence of a magnetic flux enclosed by the compactified axis. The latter gives rise to Ahanorov-Bohm-like effect on the vacuum expectation value of the currents. In this setup, only azimuthal and axial current densities take place. The former presents two contributions, with the first one due to the cosmic string in a 5-dimensional AdS spacetime without compact dimension, and the second one being induced by the compactification itself. The latter is an odd function of the magnetic flux along the cosmic string and an even function of the magnetic flux enclosed by the compactified axis with period equal to the quantum flux. As to the induced axial current, it is an even function of the magnetic flux along the string's core and an odd function of the magnetic flux enclosed by the compactification perimeter. For untwisted and twisted field along compact dimension, the axial current vanishes. The massless field case is presented as well as some asymptotic limits for the parameters of the model., Comment: 21 pages, 5 figures, PACS numbers: 03.70.+k 04.62.+v 04.20.Gz 11.27.+d, replaced typo in paragraph after eq. (3.18)

In this paper, we analyze the vacuum expectation values (VEVs) of the field squared and the energy-momentum tensor associated with a charged and massive scalar quantum field in a generalized $(D+1)$-dimensional anti-de Sitter space in the presence of a cosmic string, admitting a magnetic flux running along the string's core. In addition we admit that an extra coordinate is compactified to a circle and presents a magnetic flux running along its center. This compactification is implemented by imposing a quasiperiodic condition on the field with an arbitrary phase. The calculation of the VEVs of the field squared and the energy-moment tensor, are developed by using positive-energy Wightman function. The latter is construct by the mode sum over the complete set of normalized bosonic wavefunctions. Due to the compactification, the Wightman function is presented as the sum of two distinct contributions. The first one corresponding to the idealized cosmic string, and the second is induced by the compactification. The latter goes to zero for an infinite length of the compactification. As a consequence of the general structure of the Wightman function, both VEVs present also this decomposition. Moreover, due to the Aharanov-Bohm type of interaction between the field with the magnetic fluxes, the VEVs depend on the fractional part of the ration between the total flux and the quantum one., Comment: 21 pages, 4 figures. arXiv admin note: text overlap with arXiv:1809.00702 Version accepted for publication in the EPJP

In this paper, we analyse the bosonic current densities induced by a magnetic flux running along the core of an idealized cosmic string in a high-dimensional AdS spacetime, admitting that an extra dimension coordinate is compactified. Additionally we admit the presence of a magnetic flux enclosed by the compactified axis. In order to develop this analysis we calculate the complete set of normalized bosonic wave-functions obeying a quasiperiodicity condition, with arbitrary phase $\beta$, along the compactified extra dimension. In this context, only azimuthal and axial currents densities take place. As to the azimuthal current, two contributions appear. The first one corresponds to the standard azimuthal current in high-dimensional AdS spacetime with a cosmic string without compactification while the second contribution is a new one, induced by the compactification itself. The latter is an even function of the magnetic flux enclosed by the compactified axis and is an odd function of the magnetic flux along its core with period equal to quantum flux, $\Phi_0=2\pi/e$. On the other hand, the nonzero axial current density is an even function of the magnetic flux along the core of the string and an odd function of the magnetic flux enclosed by the compactified axis. We also find that the axial current density vanishes for untwisted and twisted bosonic fields in the absence of the magnetic flux enclosed by the compactified axis. Some asymptotic expressions for the current density are provided for specific limiting cases of the physical parameter of the model., Comment: 21 pages, 4 figures. Version accepted for publication in PRD

We investigate the thermodynamics of a photon gas in an effective field theory model that describes Lorentz violations through dimension-five operators and Horava-Lifshitz theory. We explore the electrodynamics of the model which includes higher order derivatives in the Lagrangian that can modify the dispersion relation for the propagation of the photons. We shall focus on the deformed black body radiation spectrum and modified Stefan-Boltzmann law to address the allowed bounds on the Lorentz-violating parameter., Comment: 8 pages, 6 figures. Version published in PLB

In this paper we investigate statistical entropy of a 3-dimensional rotating acoustic black hole based on generalized uncertainty principle. In our results we obtain an area entropy and a correction term associated with the noncommutative acoustic black hole when $\lambda$ introduced in the generalized uncertainty principle takes a specific value. However, in this method, it is not needed to introduce the ultraviolet cut-off and divergences are eliminated. Moreover, the small mass approximation is not necessary in the original brick-wall model., Comment: 9 pages, no figures; version to appear in PLB. arXiv admin note: substantial text overlap with arXiv:1210.7739

Taking a full 3D nonlinear vector matter field dynamics, a vector version of a soliton state was found. The Nielsen-Olesen procedure was used in order to derive a Lorentz-violation vector parameter which characterizes, via Spontaneous Symmetry Breaking mechanism, the non-trivial vacuum. A stable vortex configuration is obtained, and although the Chern-Simons-type terms do not contribute to the value of the vortex core, the propagator analysis suggests us the possibility of a contribution to the size of the vortex core and to the growth of the field to achieve the asymptotic limit value with the distance., Comment: 9 pages, 1 figure, Revtex4 format

In this paper we study the nonlocal effects of noncommutative spacetime on simple physical systems. Our main point is the assumption that the noncommutative effects are consequences of a background field which generates a local spin structure. So, we reformulate some simple electrostatic models in the presence of a spin-deformation contribution to the geometry of the motion, and we obtain an interesting correlation amongst the deformed area vector, the 3D noncommutative effects and the usual spin vector given in quantum mechanics framework. Remarkably we can observe that a spin-orbit coupling term comes to light on the spatial sector of a potential wrote in terms of noncommutative coordinates what indicates that bound states are particular cases in this procedure. Concerning to confined or bounded particles in this noncommutative domain we verify that the kinetic energy is modified by a deformation factor. Finally, we discuss about perspectives., Comment: 14 pages, 1 figure

We consider a model with a charged vector field along with a Cremmer-Scherk-Kalb-Ramond (CSKR) matter field coupled to a U(1) gauge potential. We obtain a natural Lorentz symmetry violation due to the local U(1) spontaneous symmetry breaking mechanism triggered by the imaginary part of the vector matter. The choice of the unitary gauge leads to the decoupling of the gauge-KR sector from the Higgs-KR sector. The excitation spectrum is carefully analyzed and the physical modes are identified. We propose an identification of the neutral massive spin-1 Higgs-like field with the massive Z' boson of the so-called mirror matter models., Comment: 10 pages, no figures, revtex4, Preprint CBPF-NF-037/03