We present high-resolution 1.5--6 GHz Karl G. Jansky Very Large Array (VLA)
and Hubble Space Telescope (HST) optical and infrared
observations of the extremely active repeating fast radio burst (FRB)
FRB20201124A 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 FRB20201124A. We resolve the morphology of the
radio emission across all frequency bands and measure a star formation rate SFR
≈8.9M⊙​ yr−1, a factor of ≈4−6 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 FRB20201124A has the most significant 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 central
engine born from the explosion of a massive star). It is still plausible,
although less likely, that the progenitor of FRB20201124A migrated from the
central bar of the host, e.g., via a runaway massive star. We further place a
limit on the luminosity of a putative PRS at the FRB position of $L_{\rm 6.0 \
GHz}\lesssim2.6\times10^{27}ergs^{-1}Hz^{-1},twoordersofmagnitudebelowanyPRSknowntodate.However,thislimitisstillbroadlyconsistentwithbothmagnetarnebulaeandhypernebulaemodelsassumingaconstantenergyinjectionrateofthemagnetarandanageof\gtrsim 10^{5}$
yr in each model, respectively.Comment: 21 pages, 6 figures, 3 tables, Submitte