It has been widely argued that Type-I super-luminous supernovae (SLSNe-I) are driven by powerful central engines with a long-lasting energy injection after the core-collapse of massive progenitors. One of the popular hypotheses is that the hidden engines are fast-rotating pulsars with a magnetic field of $Bsim{10}^{13}-{10}^{15}$ G. Murase, Kashiyama & Meszaros (2016) showed that quasi-steady radio/submm emission from non-thermal electron-positron pairs in nascent pulsar wind nebulae can be used as a counterpart of such pulsar-driven supernovae (SNe). In this work, focusing on the nascent SLSN-I remnants, we examine constraints that can be placed by radio emission. We show that the Atacama Large Millimeter/submillimetre Array (ALMA) can detect the radio nebula from SNe at $D_{rm L} sim 1 rm Gpc$ in a few years after the explosion, while the Jansky Very Large Array (VLA) can also detect the counterpart in a few decades. The proposed radio followup observation could solve the parameter degeneracy in the pulsar-driven SN model for optical/UV light curves, and could also give us clues to young neutron star scenarios for SLSNe-I and fast radio bursts.
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