We present 7 mm Very Large Array continuum images of the starburst galaxy M82. On arcsecond scales, two-thirds of the 7 mm continuum consists of free-free emission from H?II regions. In the subarcsecond resolution map, we identify 14 compact sources, including 9 bright H?II regions with N lyc > 1051 s–1. Four of the H?II regions have rising spectra, implying emission measures >108 cm–6 pc. Except for one compact source with peculiar features, all other compact radio sources are found in dust lanes and do not have optical or near-infrared continuum counterparts. Four regions of extended, high brightness (EM >107 cm-6 pc) radio emission are found in our high-resolution map, including some as large as ~2'', or 30 pc, representing either associations of small H?II regions, or sheet-like structures of denser gas. The good correlation between 7 mm emission and Spitzer IRAC 8 μm continuum-removed polycyclic aromatic hydrocarbon (PAH) feature suggests that PAH emission may track the recently formed OB stars. We find an excellent correlation between molecular gas and star formation, particularly dense gas traced by HCN, down to the ~45 pc scale in M82. We also find star formation efficiencies (SFEs) of 1%-10% on the same scale, based on CO maps. The highest SFE are found in regions with the highest dense gas fractions.
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