  Spiral arms, rings and large scale asymmetries are structures observed in
high resolution observations of protoplanetary disks, and it appears that some
of the disks showing spiral arms in scattered light also show asymmetries in
millimeter-sized dust. HD~135344B is one of these disks. Planets are invoked as
the origin of these structures, but no planet has been observed so far. We
investigate the nature of the asymmetric structure in the HD~135344B disk in
order to understand the origin of the spirals and of the asymmetry seen in this
disk. Ultimately, we aim at understanding whether or not one or more planets
are needed to explain such structures. We present new ALMA sub-0.1" resolution
observations in Band 3 and 4. The high spatial resolution allows us to
characterize the mm-dust morphology of the disk. The low optical depth of
continuum emission probes the bulk of the dust in vortex. Moreover, we combine
the new observations with archival data to perform a multi-wavelength analysis
and to obtain information about the dust distribution and properties inside the
asymmetry. We resolve the asymmetric disk into a symmetric ring + asymmetric
crescent, and observe that: (1) the spectral index strongly decreases at the
center of the vortex, consistent with the presence of large grains; (2) for the
first time, an azimuthal shift of the peak of the vortex with wavelength is
observed; (3) the azimuthal width of the vortex decreases at longer
wavelengths, as expected for dust traps. These features allow to confirm the
nature of the asymmetry as a vortex. Finally a lower limit to the total mass of
the vortex is $0.3 M_{\rm Jupiter}$. Considering the uncertainties involved in
this estimate, it is possible that the actual mass of the vortex is higher and
possibly within the required values ($\sim 4\,\rm M_{\rm Jupiter}$) to launch
spiral arms similar to those observed in scattered light.
