  We show that the "dark condensates" that arise when excitons form a
Bose-Einstein condensate in a material with an indirect bandgap are not
completely dark to optical emission. Rather, such states are "leaky
condensates" in which optical emission is facilitated by many-body
interactions. We analyze the properties of these leaky condensates in the
context of twisted bilayers of transition metal dichalcogenides, which host
strongly interacting excitons and an indirect bandgap. We show that this
interaction-driven "leaky" emission dominates photoluminescence at low
temperatures, with distinctive qualitative features. Finally, we propose that
in these materials, unique intervalley physics can lead to crystal
symmetry-breaking excitonic ordering, with implications for optical processes.
