  One model for the origin of typical galactic star clusters such as the Orion
Nebula Cluster (ONC) is that they form via the rapid, efficient collapse of a
bound gas clump within a larger, gravitationally-unbound giant molecular cloud.
However, simulations in support of this scenario have thus far have not
included the radiation feedback produced by the stars; radiative simulations
have been limited to significantly smaller or lower density regions. Here we
use the ORION adaptive mesh refinement code to conduct the first ever
radiation-hydrodynamic simulations of the global collapse scenario for the
formation of an ONC-like cluster. We show that radiative feedback has a
dramatic effect on the evolution: once the first ~10-20% of the gas mass is
incorporated into stars, their radiative feedback raises the gas temperature
high enough to suppress any further fragmentation. However, gas continues to
accrete onto existing stars, and, as a result, the stellar mass distribution
becomes increasingly top-heavy, eventually rendering it incompatible with the
observed IMF. Systematic variation in the location of the IMF peak as star
formation proceeds is incompatible with the observed invariance of the IMF
between star clusters, unless some unknown mechanism synchronizes the IMFs in
different clusters by ensuring that star formation is always truncated when the
IMF peak reaches a particular value. We therefore conclude that the global
collapse scenario, at least in its simplest form, is not compatible with the
observed stellar IMF. We speculate that processes that slow down star
formation, and thus reduce the accretion luminosity, may be able to resolve the
problem.
