  In this paper, we generalize Witten's non-abelian bosonization in $(1+1)$-D
to two and three spatial dimensions. Our theory applies to fermions with
relativistic dispersion. The bosonized theories are non-linear sigma models
with level-1 Wess-Zumino-Witten terms. We apply the bosonization results to the
$SU(2)$ gauge theory of the $\pi$-flux phase, critical spin liquids in 1,2,3
spatial dimensions, and twisted bilayer graphene.
