  We use high-resolution continuum images obtained at 870microns with the
Atacama Large Millimeter Array (ALMA) to probe the surface density of
star-formation in z~2 galaxies and study the different physical properties
between galaxies within and above the star-formation main sequence of galaxies.
This sample of eight star-forming galaxies at z~2 selected among the most
massive Herschel galaxies in the GOODS-South field is supplemented with eleven
galaxies from the public data of the 1.3 mm survey of the Hubble Ultra-Deep
Field. ALMA reveals systematically dense concentrations of dusty star-formation
close to the center of the stellar component of the galaxies. We identify two
different starburst regimes: (i) the classical population of starbursts located
above the SFR-M* main sequence, with enhanced gas fractions and short depletion
times and (ii) a sub-population of galaxies located within the scatter of the
main sequence that experience compact star formation with depletion timescales
typical of starbursts of ~150 Myr. In both starburst populations, the far
infrared and UV are distributed in distinct regions and dust-corrected star
formation rates estimated using UV-optical-NIR data alone underestimate the
total star formation rate. Starbursts hidden in the main sequence show instead
the lowest gas fractions of our sample and could represent the last stage of
star-formation before they become passive. Being Herschel-selected, these main
sequence galaxies are located in the high-mass end of the main sequence, hence
we do not know whether these "starbursts hidden in the main sequence" also
exist below 10^11 Msun. Active galactic nuclei are found to be ubiquitous in
these compact starbursts, suggesting that the triggering mechanism also feeds
the central black hole or that the active nucleus triggers star formation.
