SMA observations on faint Submillimeter Galaxies with S$_{850}$ < 2 mJy:
  Ultra Dusty Low-Luminosity Galaxies at High Redshift
  We obtained SMA observations of eight faint (intrinsic 850 $\mu$m fluxes $<$
2 mJy) submillimeter galaxies (SMGs) discovered in SCUBA images of the massive
lensing cluster fields A370, A2390, and A1689 and detected five. In total, we
obtain 5 SMA detections, all of which have de-lensed fluxes $<$1 mJy with
estimated total infrared luminosities 10$^{10}-10^{12}$ $L_\odot$, comparable
to luminous infrared galaxies (LIRGs) and normal star-forming galaxies. Based
on the latest number counts, these galaxies contribute $\sim$70% of the 850
$\mu$m extragalactic background light and represent the dominant star-forming
galaxy population in the dusty universe. However, only 40$^{+30}_{-16}$% of our
faint SMGs would be detected in deep optical or near-infrared surveys, which
suggests many of these sources are at high redshifts ($z \gtrsim 3$) or
extremely dusty, and they are not included in current star formation history
estimates.
