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.

The two-point functions of the vector potential and of the field tensor for the electromagnetic field in background of anti-de Sitter (AdS) spacetime are evaluated. First we consider the twopoint functions in the boundary-free geometry and then generalize the results in the presence of a reflecting boundary parallel to the AdS horizon. By using the expressions for the two-point functions of the field tensor, we investigate the vacuum expectation values of the electric field squared and of the energy-momentum tensor. Simple asymptotic expressions are provided near the AdS boundary and horizon.

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The vacuum expectation value of the energy-momentum tensor is investigated for a charged scalar field in dS space-time with toroidally compact spatial dimensions in the presence of a classical constant gauge field. Due to the nontrivial topology, the latter gives rise to an Aharonov-Bohm-like effect on the vacuum characteristics. The vacuum energy density and stresses are even periodic functions of the magnetic flux enclosed by the compact dimensions. For small values of the comoving lengths of the compact dimensions as compared with the dS curvature radius, the effects of gravity on the topological contributions are small, and the expectation values are expressed in terms of the corresponding quantities in the Minkowski bulk by the standard conformal relation. For large values of the comoving lengths, depending on the field mass, two regimes are realized with monotonic and oscillatory damping of the expectation values. We show that the sign of the the vacuum energy density can be controlled by tuning the magnetic flux enclosed by the compact dimensions.