We study the relationship between dense gas and star formation in the Antennae galaxies by comparing ALMA observations of dense gas tracers (HCN, HCO$^+$, and HNC $mathrm{J}=1-0$) to the total infrared luminosity ($mathrm{L_{TIR}}$) calculated using data from the textit{Herschel} Space Observatory and the textit{Spitzer} Space Telescope. We compare the luminosities of our SFR and gas tracers using aperture photometry and employing two methods for defining apertures. We taper the ALMA dataset to match the resolution of our $mathrm{L_{TIR}}$ maps and present new detections of dense gas emission from complexes in the overlap and western arm regions. Using OVRO CO $mathrm{J}=1-0$ data, we compare with the total molecular gas content, $mathrm{M(H_2)_{tot}}$, and calculate star formation efficiencies and dense gas mass fractions for these different regions. We derive HCN, HCO$^+$ and HNC upper limits for apertures where emission was not significantly detected, as we expect emission from dense gas should be present in most star-forming regions. The Antennae extends the linear $mathrm{L_{TIR}-L_{HCN}}$ relationship found in previous studies. The $mathrm{L_{TIR}-L_{HCN}}$ ratio varies by up to a factor of $sim$10 across different regions of the Antennae implying variations in the star formation efficiency of dense gas, with the nuclei, NGC 4038 and NGC 4039, showing the lowest SFE$_mathrm{dense}$ (0.44 and 0.70 $times10^{-8}$ yr$^{-1}$). The nuclei also exhibit the highest dense gas fractions ($sim 9.1%$ and $sim7.9%$).
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