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ABSTRACT FRB 20210912A is a fast radio burst (FRB), detected and localized to subarcsecond precision by the Australian Square Kilometre Array Pathfinder. No host galaxy has been identified for this burst despite the high precision of its localization and deep optical and infrared follow-up, to 5σ limits of R = 26.7 mag and Ks = 24.9 mag with the Very Large Telescope. The combination of precise radio localization and deep optical imaging has almost always resulted in the secure identification of a host galaxy, and this is the first case in which the line of sight is not obscured by the Galactic disc. The dispersion measure of this burst, DMFRB = 1233.696 ± 0.006 pc cm−3, allows for a large source redshift of z > 1 according to the Macquart relation. It could thus be that the host galaxy is consistent with the known population of FRB hosts, but is too distant to detect in our observations (z > 0.7 for a host like that of the first repeating FRB source, FRB 20121102A); that it is more nearby with a significant excess in DMhost, and thus dimmer than any known FRB host; or, least likely, that the FRB is truly hostless. We consider each possibility, making use of the population of known FRB hosts to frame each scenario. The fact of the missing host has ramifications for the FRB field: even with high-precision localization and deep follow-up, some FRB hosts may be difficult to detect, with more distant hosts being the less likely to be found. This has implications for FRB cosmology, in which high-redshift detections are valuable. 

Abstract We present high-resolution 1.5–6 GHz Karl G. Jansky Very Large Array and Hubble Space Telescope (HST) optical and infrared observations of the extremely active repeating fast radio burst (FRB) FRB 20201124A and its barred spiral host galaxy. We constrain the location and morphology of star formation in the host and search for a persistent radio source (PRS) coincident with FRB 20201124A. We resolve the morphology of the radio emission across all frequency bands and measure a star formation rate (SFR) ≈ 8.9M_⊙yr⁻¹, approximately ≈2.5–6 times larger than optically inferred SFRs, demonstrating dust-obscured star formation throughout the host. Compared to a sample of all known FRB hosts with radio emission, the host of FRB 20201124A has the most significantly obscured star formation. While HST observations show the FRB to be offset from the bar or spiral arms, the radio emission extends to the FRB location. We propose that the FRB progenitor could have formed in situ (e.g., a magnetar born from a massive star explosion). It is still plausible, although less likely, that the progenitor of FRB 20201124A migrated from the central bar of the host. We further place a limit on the luminosity of a putative PRS at the FRB position ofL_6.0GHz≲ 1.8 ×10²⁷erg s⁻¹Hz⁻¹, among the deepest PRS luminosity limits to date. However, this limit is still broadly consistent with both magnetar nebulae and hypernebulae models assuming a constant energy injection rate of the magnetar and an age of ≳10⁵yr in each model, respectively.