  Supergiant Fast X-ray Transients (SFXTs) are a new class of HMXBs discovered
thanks to the monitoring of the Galactic plane performed with the INTEGRAL
satellite in the last 5 years. These sources display short outbursts
(significantly shorter than typical Be/X-ray binaries) with a peak luminosity
of a few 1E36 erg/s. The quiescent level, measured only in a few sources, is
around 1E32 erg/s. We are performing a monitoring campaign with Swift of four
SFXTs (IGRJ16479-4514, XTEJ1739-302, IGRJ17544-2619 and
AXJ1841.0-0536/IGRJ18410-0535). We report on the first four months of Swift
observations, started on 2007 October 26. We detect a low level X-ray activity
in all four SFXTs which demonstrates that these transient sources accrete
matter even outside their outbursts. This fainter X-ray activity is composed of
many flares with a large flux variability, on timescales of thousands of
seconds. The lightcurve variability is also evident on larger timescales of
days, weeks and months, with a dynamic range of more than one order of
magnitude in all four SFXTs. The X-ray spectra are typically hard, with an
average 2-10 keV luminosity during this monitoring of about 1E33-1E34 erg/s. We
detected pulsations from the pulsar AXJ1841.0-0536, with a period of
4.7008+/-0.0004 s. This monitoring demonstrates that these transients spend
most of the time accreting matter, although at a much lower level (~100-1000
times lower than during the bright outbusts), and that the true quiescence,
characterized by a soft spectrum and a luminosity of a few 1E32 erg/s, observed
in the past only in a couple of members of this class, is probably a very rare
state.
