  Conversion of gravitational energy into radiation in accretion discs and the
origin of large scale magnetic fields in astrophysical rotators have often been
distinct topics of research. In semi-analytic work on both problems it has been
useful to presume large scale symmetries, necessarily resulting in mean field
theories. MHD turbulence makes the underlying systems locally asymmetric and
nonlinear. Synergy between theory and simulations should aim for the
development of practical mean field models that capture essential physics and
can be used for observational modeling. Mean field dynamo (MFD) theory and
alpha-viscosity accretion theory exemplify such ongoing pursuits. 21st century
MFD theory has more nonlinear predictive power compared to 20th century MFD
theory, whereas accretion theory is still in a 20th century state. In fact,
insights from MFD theory are applicable to accretion theory and the two are
artificially separated pieces of what should be a single theory. I discuss
pieces of progress that provide clues toward a unified theory. A key concept is
that large scale magnetic fields can be sustained via local or global magnetic
helicity fluxes or via relaxation of small scale magnetic fluctuations, without
the kinetic helicity driver of 20th century textbooks. These concepts may help
explain the formation of large scale fields that supply non-local angular
momentum transport via coronae and jets in a unified theory of accretion and
dynamos. In diagnosing the role of helicities and helicity fluxes in disk
simulations, each disk hemisphere should be studied separately to avoid being
misled by cancelation that occurs as a result of reflection asymmetry. The
fraction of helical field energy in disks is expected to be small compared to
the total field in each hemisphere as a result of shear, but can still be
essential for large scale dynamo action.
