We use the CARMA millimeter interferometer to map the Antennae Galaxies (NGC4038/39), tracing the bulk of the molecular gas via the 12CO(1-0) line and denser molecular gas via the high density transitions HCN(1-0), HCO+(1-0), CS(2-1), and HNC(1-0). We detect bright emission from all tracers in both the two nuclei and three locales in the overlap region between the two nuclei. These three overlap region peaks correspond to previously identified supergiant molecular clouds. We combine the CARMA data with Herschel infrared (IR) data to compare observational indicators of the star formation efficiency (SFR/H2~IR/CO), dense gas fraction (HCN/CO), and dense gas star formation efficiency (IR/HCN). Regions within the Antennae show ratios consistent with those seen for entire galaxies, but these ratios vary by up to a factor of 6 within the galaxy. The five detected regions vary strongly in both their integrated intensities and these ratios. The northern nucleus is the brightest region in mm-wave line emission, while the overlap region is the brightest part of the system in the IR. We combine the CARMA and Herschel data with ALMA CO data to report line ratio patterns for each bright point. CO shows a declining spectral line energy distribution, consistent with previous studies. HCO+(1-0) emission is stronger than HCN(1-0) emission, perhaps indicating either more gas at moderate densities or higher optical depth than is commonly seen in more advanced mergers.
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