Due to their relation to massive stars, long-duration gamma-ray bursts (GRBs) allow pinpointing star formation in galaxies independently of redshift, dust obscuration, or galaxy mass/size, thus providing a unique tool to investigate the star-formation history over cosmic time. About half of the optical afterglows of long-duration GRBs are missed due to dust extinction, and are primarily located in the most massive GRB hosts. In order to understand this bias it is important to investigate the amount of obscured star-formation in these GRB host galaxies. Radio emission of galaxies correlates with star-formation, but does not suffer extinction as do the optical star-formation estimators. We selected 11 GRB host galaxies with either large stellar mass or large UV-/optical-based star-formation rates (SFRs) and obtained radio observations of these with the Australia Telescope Compact Array and the Karl Jansky Very Large Array. Despite intentionally selecting GRB hosts with expected high SFRs, we do not find any star-formation-related radio emission in any of our targets. Our upper limit for GRB 100621A implies that the earlier reported radio detection was due to afterglow emission. We do detect radio emission from the position of GRB 020819B, but argue that it is in large parts, if not all, due to afterglow contamination. Half of our sample has radio-derived SFR limits which are only a factor 2--3 above the optically measured SFRs. This supports other recent studies that the majority of star formation in GRB hosts is not obscured by dust.
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