  It is shown that the existence of static, cylindrically symmetric wormholes
does not require violation of the weak or null energy conditions near the
throat, and cylindrically symmetric wormhole geometries can appear with less
exotic sources than wormholes whose throats have a spherical topology. Examples
of exact wormhole solutions are given with scalar, spinor and electromagnetic
fields as sources, and these fields are not necessarily phantom. In particular,
there are wormhole solutions for a massless, minimally coupled scalar field in
the presence of a negative cosmological constant, and for an azimuthal Maxwell
electromagnetic field. All these solutions are not asymptotically flat. A no-go
theorem is proved, according to which a flat (or string) asymptotic behavior on
both sides of a cylindrical wormhole throat is impossible if the energy density
of matter is everywhere nonnegative.
