  Given the absence of directly detected dark matter (DM) as weakly interacting
massive particles, there is strong interest in the possibility that DM is an
ultra-light scalar field, here denoted as fuzzy DM. Ultra-diffuse galaxies,
with the sizes of giant galaxies and the luminosities of dwarf galaxies, have a
wide range of DM halo masses, thus providing new opportunities for exploring
the connections between galaxies and their DM halos. Following up on new
integral field unit spectroscopic observations and dynamics modeling of the
DM-dominated ultra-diffuse galaxy Dragonfly 44 in the outskirts of the Coma
Cluster, we present models of fuzzy DM constrained by the stellar dynamics of
this galaxy. We infer a scalar field mass of $\sim 3 \times 10^{-22}$ eV,
consistent with other constraints from galaxy dynamics but in tension with
constraints from Ly$\alpha$ forest power spectrum modeling. While we are unable
to statistically distinguish between fuzzy DM and normal cold DM models, we
find that the inferred properties of the fuzzy DM halo satisfy a number of
predictions for halos in a fuzzy DM cosmology. In particular, we find good
agreement with the predicted core size--halo mass relation and the predicted
transition radius between the quantum pressure-dominated inner region and the
outer halo region.
