  We show that a large-scale, weak magnetic field threading a turbulent
accretion disk tends to be advected inward, contrary to previous suggestions
that it will be stopped by outward diffusion. The efficient inward transport is
a consequence of the diffuse, magnetically-dominated surface layers of the
disk, where the turbulence is suppressed and the conductivity is very high.
This structure arises naturally in three-dimensional simulations of
magnetorotationally unstable disks, and we demonstrate here that it can easily
support inward advection and compression of a weak field. The advected field is
anchored in the surface layer but penetrates the main body of the disk, where
it can generate strong turbulence and produce values of alpha (i.e., the
turbulent stress) large enough to match observational constraints; typical
values of the vertical magnetic field merely need to reach a few percent of
equipartition for this to occur. Overall, these results have important
implications for models of jet formation which require strong, large-scale
magnetic fields to exist over a region of the inner accretion disk.
