We present first results from the SXDF-ALMA 1.5 arcmin^2 deep survey at 1.1 mm using Atacama Large Millimeter Array (ALMA). The map reaches a 1sigma depth of 55 uJy/beam and covers 12 Halpha-selected star-forming galaxies at z = 2.19 or z=2.53. We have detected continuum emission from three of our Halpha-selected sample, including one compact star-forming galaxy with high stellar surface density, NB2315-07. They are all red in the rest-frame optical and have stellar masses of log (M*/Msun)>10.9 whereas the other blue, main-sequence galaxies with log(M*/Msun)=10.0-10.8 are exceedingly faint, <290 uJy (2sigma upper limit). We also find the 1.1 mm-brightest galaxy, NB2315-02, to be associated with a compact (R_e=0.7+-0.1 kpc), dusty star-forming component. Given high gas fraction (44^{+20}_{-8}% or 37^{+25}_{-3}%) and high star formation rate surface density (126^{+27}_{-30} Msun yr^{-1}kpc^{-2}), the concentrated starburst can within less than 50^{+12}_{-11} Myr build up a stellar surface density matching that of massive compact galaxies at z~2, provided at least 19+-3% of the total gas is converted into stars in the galaxy centre. On the other hand, NB2315-07, which already has such a high stellar surface density core, shows a gas fraction (23+-8%) and is located in the lower envelope of the star formation main-sequence. This compact less star-forming galaxy is likely to be in an intermediate phase between compact dusty star-forming and quiescent galaxies.
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