ALMA Submillimeter Continuum Imaging of the Host Galaxies of GRB021004
  and GRB080607
  We report 345 GHz continuum observations of the host galaxies of gamma-ray
bursts (GRBs) 021004 and 080607 at z>2 using the Atacama Large
Millimeter/Submillimeter Array (ALMA) in Cycle 0. Of the two bursts, GRB021004
is one of the few GRBs that originates in a Lyman limit host, while GRB080607
is classified as a "dark burst" and its host galaxy is a candidate of dusty
star forming galaxy at z~3. With an order of magnitude improvement in the
sensitivities of the new imaging searches, we detect the host galaxy of
GRB080607 with a flux of S_{345} = 0.31+/-0.09 mJy and a corresponding infrared
luminosity of L_{IR}=(2.4-4.5)x10^{11} L_sun. However, the host galaxy of
GRB021004 remains undetected and the ALMA observations allow us to place a
3-sigma upper limit of L_{IR}<3.1x10^{11} L_sun for the host galaxy. The
continuum imaging observations show that the two galaxies are not ultraluminous
infrared galaxies but are at the faintest end of the dusty galaxy population
that gives rise to the submillimeter extragalactic background light. The
derived star formation rates of the two GRB host galaxies are less than 100
M_sun yr^{-1}, which are broadly consistent with optical measurements. The
result suggests that the large extinction (A_V~3) in the afterglow of GRB080607
is confined along its particularly dusty sightline, and not representative of
the global properties of the host galaxy.
