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Fast radio bursts (FRBs) represent an exciting frontier in the study ofgravitational lensing, due to their brightness, extragalactic nature, and thecompact, coherent characteristics of their emission. In a companion work[Kader, Leung+2022], we use a novel interferometric method to search forgravitationally lensed FRBs in the time domain using bursts detected byCHIME/FRB. There, we dechannelize and autocorrelate electric field data at atime resolution of 1.25 ns. This enables a search for FRBs whose emission iscoherently deflected by gravitational lensing around a foreground compactobject such as a primordial black hole (PBH). Here, we use our non-detection oflensed FRBs to place novel constraints on the PBH abundance outside the LocalGroup. We use a novel two-screen model to take into account decoherence fromscattering screens in our constraints. Our constraints are subject to a singleastrophysical model parameter -- the effective distance between an FRB sourceand the scattering screen, for which we adopt a fiducial distance of 1 parsec.We find that coherent FRB lensing is a sensitive probe of sub-solar masscompact objects. Having observed no lenses in $172$ bursts from $114$independent sightlines through the cosmic web, we constrain the fraction ofdark matter made of compact objects, such as PBHs, to be $f \lesssim 0.8$, iftheir masses are $\sim 10^{-3} M_{\odot}$.

Constraining Primordial Black Holes using Fast Radio Burst Gravitational-Lens Interferometry with CHIME/FRB