Nantais et al. used the Hubble Space Telescope to localize probable globular clusters (GCs) in M81, a spiral galaxy at a distance of 3.63 Mpc. Theory predicts that GCs can host intermediate-mass black holes (IMBHs) with masses M_BH sim 100 - 100,000 M_sun. Finding IMBHs in GCs could validate a formation channel for seed BHs in the early universe, bolster gravitational-wave predictions for space missions, and test scaling relations between stellar systems and the central BHs they host. We used the NRAO Karl G. Jansky Very Large Array (VLA) to search for the radiative signatures of IMBH accretion from 206 probable GCs in a mosaic of M81. The observing wavelength was 5.5 cm and the spatial resolution was 1.5 arcsec (26.4 pc). None of the individual GCs are detected, nor are weighted-mean image stacks of the 206 GCs and the 49 massive GCs with stellar masses M_star gtrsim 200,000 M_sun. We apply a semi-empirical model to predict the mass of an IMBH that, if undergoing accretion in the long-lived hard X-ray state, is consistent with a given radio luminosity. The 3$sigma$ radio-luminosity upper limits correspond to mean IMBH masses of M_BH(all) < 42,000 M_sun for the all-cluster stack and M_BH(massive) < 51,000 M_sun for the massive-cluster stack. We also apply the empirical fundamental-plane relation to two X-ray-detected clusters, finding that their individual IMBH masses at 95% confidence are M_BH < 99,000 M_sun and M_BH < 15,000 M_sun. Finally, no analog of HLX-1, a strong IMBH candidate in an extragalactic star cluster, occurs in any individual GC in M81. This underscores the uniqueness or rarity of the HLX-1 phenomenon.
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