  In this paper we survey the theory of wind accretion in high mass X-ray
binaries hosting a magnetic neutron star and a supergiant companion.
  We concentrate on the different types of interaction between the inflowing
wind matter and the neutron star magnetosphere that are relevant when accretion
of matter onto the neutron star surface is largely inhibited; these include the
inhibition through the centrifugal and magnetic barriers. Expanding on earlier
work, we calculate the expected luminosity for each regime and derive the
conditions under which transition from one regime to another can take place. We
show that very large luminosity swings (~10^4 or more on time scales as short
as hours) can result from transitions across different regimes.
  The activity displayed by supergiant fast X-ray transients, a recently
discovered class of high mass X-ray binaries in our galaxy, has often been
interpreted in terms of direct accretion onto a neutron star immersed in an
extremely clumpy stellar wind. We show here that the transitions across the
magnetic and/or centrifugal barriers can explain the variability properties of
these sources as a results of relatively modest variations in the stellar wind
velocity and/or density. According to this interpretation we expect that
supergiant fast X-ray transients which display very large luminosity swings and
host a slowly spinning neutron star are characterized by magnetar-like fields,
irrespective of whether the magnetic or the centrifugal barrier applies.
  Supergiant fast X-ray transients might thus provide a new opportunity to
detect and study magnetars in binary systems.
