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We used Bands 6 and 7 of the Atacama Large Millimeter/submillimeter Array(ALMA) in Cycles 7 and 8 to search for $\mathrm{CO}\,(3-2)$ emission from asample of five fast radio burst (FRB) host galaxies discovered by the CommensalReal-time ASKAP Fast Transients (CRAFT) survey and the Fast and Fortunate forFRB Follow-up (F$^4$) team. These galaxies have redshifts $z \approx0.16-0.48$, masses log$(M_{\rm star}/M_{\odot})\approx 9.30-10.4$characteristic of field galaxies, and emission lines indicative of ongoing starformation. We detected three of the five galaxies with luminosities$L'(3-2)\approx0.2-4\times10^8\,\rm K\,km \, s^{-1}\,pc^2$ and set upper limitsfor the other two. Adopting standard metallicity-dependent CO-to-H$_2$conversion factors, we estimate molecular gas masses $M_{\rm gas}\approx0.2-3\times 10^9 \, M_{\odot}$. As a population, FRB host galaxies track themain $M_{\rm star}-M_{\rm gas}$ locus of star-forming galaxies in thepresent-day universe, with gas fractions of $\mu_{\rm gas}\approx0.1$ and gasdepletion times $t_{\rm dep} \gtrapprox 1\,$Gyr. We employ the Kaplan-Meierestimator to compare the redshift-corrected $\mu_{\rm gas}$ and $t_{\rm dep}$for all known FRB hosts with measurements or upper limits with those from thexCOLD GASS survey and find statistically different gas fractions. Thedifference is not statistically significant when we consider only the fivehosts studied here with consistently determined properties, suggesting more FRBhosts with measured molecular gas masses are needed to robustly study thepopulation. Lastly, we present a multi-wavelength analysis of one host(HG20180924B) combining high-spatial resolution imaging and integral fieldspectroscopy to demonstrate that future high-resolution observations will allowus to study the host galaxy environments local to the FRBs.

Constraining the Molecular Gas Content of Fast Radio Burst (FRB) Host Galaxies