  We investigate the spacetime of a spinning cosmic string in conformal
invariant gravity, where the interior consists of a gauged scalar field. We
find exact solutions of the exterior of a stationary spinning cosmic string,
where we write the metric as $ g_{\mu\nu}=\omega^2\tilde g_{\mu\nu}$, with
$\omega$ a dilaton field which contains all the scale dependences. The
"unphysical" metric $\tilde g_{\mu\nu}$ is related to the $(2+1)$-dimensional
Kerr spacetime. The equation for the angular momentum $J$ decouples, for the
vacuum situation as well as for global strings, from the other field equations
and delivers a kind of spin-mass relation. For the most realistic solution, $J$
falls off as $\sim\frac{1}{r}$ and $\partial_r J \rightarrow 0$ close to the
core. The spacetime is Ricci flat. The formation of closed timelike curves can
be pushed to space infinity for suitable values of the parameters and the
violation of the weak energy condition can be avoided. For the interior, a
numerical solution is found. This solution can easily be matched at the
boundary on the exterior exact solution by special choice of the parameters of
the string. It turns out, as expected from the "holographic" principle, that
the exact solution of the exterior is equivalent with the warped
five-dimensional brane world model, with only a cosmological constant in the
bulk. This example shows the power of conformal invariance to bridge the gap
between general relativity and quantum field theory.
