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Fast-rotating pulsars and magnetars have been suggested as the centralengines of super-luminous supernovae (SLSNe) and fast radio bursts, and thisscenario naturally predicts non-thermal synchrotron emission from their nascentpulsar wind nebulae (PWNe). We report results of high-frequency radioobservations with ALMA and NOEMA for three SLSNe (SN 2015bn, SN 2016ard, and SN2017egm), and present a detailed theoretical model to calculate non-thermalemission from PWNe with an age of about 1-3 yr. We find that the ALMA datadisfavors a PWN model motivated by the Crab nebula for SN 2015bn and SN2017egm, and argue that this tension can be resolved if the nebularmagnetization is very high or very low. Such models can be tested by futureMeV-GeV gamma-ray telescopes such as AMEGO.

ALMA and NOEMA constraints on synchrotron nebular emission from embryonic superluminous supernova remnants and radio-gamma-ray connection