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We have used previously published observations of the CO emission from theAntennae (NGC 4038/39) to study the detailed properties of the super giantmolecular complexes with the goal of understanding the formation of youngmassive star clusters. Over a mass range from 5E6 to 9E8 solar masses, themolecular complexes follow a power-law mass function with a slope of -1.4 +/-0.1, which is very similar to the slope seen at lower masses in molecularclouds and cloud cores in the Galaxy. Compared to the spiral galaxy M51, whichhas a similar surface density and total mass of molecular gas, the Antennaecontain clouds that are an order of magnitude more massive. Many of theyoungest star clusters lie in the gas-rich overlap region, where extinctions ashigh as Av~100 imply that the clusters must lie in front of the gas. Combiningdata on the young clusters, thermal and nonthermal radio sources, and themolecular gas suggests that young massive clusters could have formed at aconstant rate in the Antennae over the last 160 Myr and that sufficient gasexists to sustain this cluster formation rate well into the future. However,this conclusion requires that a very high fraction of the massive clusters thatform initially in the Antennae do not survive as long as 100 Myr. Finally, wecompare our data with two models for massive star cluster formation andconclude that the model where young massive star clusters form from dense coreswithin the observed super giant molecular complexes is most consistent with ourcurrent understanding of this merging system. (abbreviated)Comment: 40 pages, four figures; accepted for publication in Ap

The Mass Function of Supergiant Molecular Complexes and Implications for Forming Young Massive Star Clusters in the Antennae (NGC 4038/4039)