We present a 1.4 GHz Karl G. Jansky Very Large Array (VLA) study of a sample of early-type galaxies (ETGs) from the volume- and magnitude-limited ATLAS-3D survey. The radio morphologies of these ETGs at a resolution of 5 are diverse and include sources that are compact on sub-kpc scales, resolved structures similar to those seen in star-forming spiral galaxies, and kpc-scale radio jets/lobes associated with active nuclei. We compare the 1.4 GHz, molecular gas, and infrared (IR) properties of these ETGs. The most CO-rich ATLAS-3D ETGs have radio luminosities consistent with extrapolations from H_2-mass-derived star formation rates from studies of late-type galaxies. These ETGs also follow the radio-IR correlation. However, ETGs with lower molecular gas masses tend to have less radio emission relative to their CO and IR emission compared to spirals. The fraction of galaxies in our sample with high IR-radio ratios is much higher than in previous studies, and cannot be explained by a systematic underestimation of the radio luminosity due to the presence extended, low-surface-brightness emission that was resolved-out in our VLA observations. In addition, we find that the high IR-radio ratios tend to occur at low IR luminosities, but are not associated with low dynamical mass or metallicity. Thus, we have identified a population of ETGs that have a genuine shortfall of radio emission relative to both their IR and molecular gas emission. A number of mechanisms may conspire to cause this radio deficiency, including a bottom-heavy stellar initial mass function, weak magnetic fields, a higher prevalence of environmental effects compared to spirals and enhanced cosmic ray losses.
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