  Observational constraints on dust properties in protoplanetary disks are key
to better understanding disks' evolution. We continue our exploration of the
protoplanetary disk around AB Aur by characterizing its dust properties. We
present ALMA observations at 2.2 mm and VLA observations at 6.8 mm. Together
with previous ALMA and NOEMA observations at 0.87 and 1.1 mm, these
observations are used to compute global spectral index profiles as well as
spectral index maps. On the interpretation side, we present the results of a
simple isothermal slab model to help constrain dust properties along the ring
of continuum emission. We also present results of dust radiative transfer
calculations based on a disc-planet hydrodynamical simulation to explain how
the azimuthal contrast ratio of the ring emission varies with millimeter
wavelength. The spectral energy distribution and the radial profiles of the
spectral index indicate that the radiation from the compact source towards the
center is not dominated by dust thermal emission, but most likely by free-free
emission originating in the radio jet: it constitutes 93% of the emission at
6.8 mm, and 37% at 0.87 mm. The protoplanetary disk has a typical spectral
index of 2.3. We estimate a dust disk mass of 8$\rm \times 10^{-5}$ M$\rm
_{\odot}$ which, assuming a mean gas-to-dust ratio of 40, gives a total disk
mass of 3.2$\rm \times 10^{-3}$ M$\rm _{\odot}$. The azimuthal contrast ratio
of the ring outside the millimeter cavity is smaller at 2.2 mm than at 1.1 mm,
in agreement with previous findings. The VLA image shows several knots of
$5\sigma$ emission all along the ring, which are consistent with the ring
emission being nearly axisymmetric at that wavelength. The decrease in the
azimuthal contrast ratio of the ring emission from 0.87 to 6.8 mm can be
explained by a dust-losing decaying vortex at the outer edge of a planet gap.
