Counterparts of Candidate Dusty Starbursts at z>6
  We present an analysis of the optical-to-near-IR counterparts of a sample of
candidate dusty starbursts at $z>6$. These objects were pre-selected based on
the rising trend of their far-infrared-to-sub-millimeter spectral energy
distributions and the fact that they are radio-weak. Their precise positions
are available through millimeter and/or radio interferometry, which enable us
to search for their counterparts in the deep optical-to-near-IR images. The
sample include five $z>6$ candidates. Three of them have their counterparts
identified, one is still invisible in the deepest images, and one is a known
galaxy at $z=5.667$ that is completely blocked by a foreground galaxy. The
three with counterparts identified are analyzed using population synthesis
model, and their photometric redshifts range from 6.2 to 8.9. Assuming that
they are not gravitationally lensed, their total IR luminosities are
$10^{13.6-14.0} L_\odot$ and the inferred star formation rates are 4.0--10
$\times 10^3$ $M_\odot$ yr$^{-1}$. The very existence of these dusty starbursts
means that the universe must be forming stars intensely very early in time in
at least some galaxies, otherwise there would be no enough dust to produce the
descendants observed at these redshifts. The inferred stellar masses of their
host galaxies, which are at $> 10^{11} M_\odot$ (if not affected by
gravitational lensing), present a difficulty in explanation unless we are
willing to accept that their progenitors kept forming stars at a rate of
$>10^3$ $M_\odot$ yr$^{-1}$ or were formed through intense instantaneous
bursts. Spectroscopic confirmation of such these objects will be imperative.
