  We study the detectability of the emission associated with the AGN dusty
structure at sub-mm wavelengths using ALMA, in a theoretical and observational
way. Theoretically, we use the Clumpy models from Nenkova et al. together with
the mid-infrared to X-ray and the radio fundamental plane scaling relations. We
find that it is more likely to detect bigger and denser dusty tori at the
highest ALMA frequency (666 GHz/450 micron). We also find that with 1h at 353
GHz/850 micron and 10h at 666 GHz/450 micron we can detect, with a high
detection limit, a 1 mJy torus (characteristic of bright AGN). This means, an
object for which the unresolved SED at 12 micron has a flux ~1mJy.
Observationally, we use four prototypical AGN: NGC\,1052 (low-luminosity AGN),
NGC\,1068 (Type-2), NGC\,3516 (Type 1.5), and IZw1 (QSO), with radio,
sub-millimeter, and mid-IR data available. All the mid-infrared spectra are
best fit with the smooth model reported by Fritz et al. A power law and a
single, or a composition of, synchrotron component/s reproduce the cm radio
wavelengths. We combined and extrapolated both fits to compare the
extrapolation of both torus and jet contributors at sub-mm wavelengths with
data at these wavelengths. Our observational results are consistent with our
theoretical results. The most promising candidate to detect the torus is the
QSO IZw1 (therefore, highly accreting sources in general), although it cannot
be resolved due to the distance of this source. We suggest that to explore the
detection of a torus at sub-mm wavelengths, it is necessary to perform an SED
analysis including radio data, with particular attention to the angular
resolution.
