  Luminous and ultra-luminous infrared galaxies ((U)LIRGs) are rare today but
are increasingly abundant at high redshifts. They are believed to be dusty
starbursts, and hence should have high rates of supernovae (multiple events per
year). Due to their extremely dusty environment, however, such supernovae could
only be detected in restframe infrared and longer wavelengths, where our
current facilities lack the capability of finding them individually beyond the
local universe. We propose a new technique for higher redshifts, which is to
search for the presence of supernovae through the variability of the integrated
rest-frame infrared light of the entire hosts. We present a pilot study to
assess the feasibility of this technique. We exploit a unique region, the "IRAC
Dark Field" (IDF), that the Spitzer Space Telescope has observed for more than
14 years in 3--5 micron. The IDF also has deep far-infrared data (200--550
micron) from the Herschel Space Observatory that allow us to select
high-redshift (U)LIRGs. We obtain a sample of (U)LIRGs that have secure optical
counterparts, and examine their light curves in 3--5 micron. While the
variabilities could also be caused by AGNs, we show that such contaminations
can be identified. We present two cases where the distinct features in their
light curves are consistent with multiple supernovae overlapping in time.
Searching for supernovae this way will be relevant to the James Webb Space
Telescope (JWST) to probe high-redshift (U)LIRGs into their nuclear regions
where JWST will be limited by its resolution.
