  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.
