  Kitaev materials are promising for realizing exotic quantum spin liquid
phases, such as a non-Abelian chiral spin liquid. Motivated by recent
experiments in these materials, we theoretically study the novel field-induced
quantum phase transitions from the non-Abelian chiral spin liquid to the
symmetry-broken zigzag phase and to the trivial polarized state. Utilizing the
recently developed dualities of gauge theories, we find these transitions can
be described by critical bosons or gapless fermions coupled to emergent
non-Abelian gauge fields, and the critical theories are of the type of a
QCD$_3$-Chern-Simons theory. We propose that all these exotic quantum phase
transitions can potentially be direct and continuous in Kitaev materials, and
we present sound evidence for this proposal. Therefore, besides being systems
with intriguing quantum magnetism, Kitaev materials may also serve as table-top
experimental platforms to study the interesting dynamics of emergent strongly
interacting quarks and gluons in $2+1$ dimensions.
