  We report the first direct imaging of protoplanetary disks in the
star-forming region of Carina, the most distant, massive cluster in which disks
have been imaged. Using the Atacama Large Millimeter/sub-millimeter Array
(ALMA), disks are observed around two young stellar objects (YSOs) that are
embedded inside evaporating gaseous globules and exhibit jet activity. The
disks have an average size of 120 AU and total masses of 30 and 50 M_Jup. Given
the measured masses, the minimum timescale required for planet formation (~1-2
Myr) and the average age of the Carina population (~1-4 Myr), it is plausible
that young planets are present or their formation is currently ongoing in these
disks. The non-detection of millimeter emission above the 4sigma threshold (~7
M_Jup) in the core of the massive cluster Trumpler~14, an area containing
previously identified proplyd candidates, suggest evidence for rapid
photo-evaporative disk destruction in the cluster's harsh radiation field. This
would prevent the formation of giant gas planets in disks located in the cores
of Carina's dense sub-clusters, whereas the majority of YSO disks in the wider
Carina region remain unaffected by external photo-evaporation.
