  There has been a recent surge of interest in dualities relating theories of
Chern-Simons gauge fields coupled to either bosons or fermions within the
condensed matter community, particularly in the context of topological
insulators and the half-filled Landau level. Here, we study the application of
one such duality to the long-standing problem of quantum Hall inter-plateaux
transitions. The key motivating experimental observations are the anomalously
large value of the correlation length exponent $\nu \approx 2.3$ and that $\nu$
is observed to be super-universal, i.e., the same in the vicinity of distinct
critical points. Duality motivates effective descriptions for a fractional
quantum Hall plateau transition involving a Chern-Simons field with $U(N_c)$
gauge group coupled to $N_f = 1$ fermion. We study one class of theories in a
controlled limit where $N_f \gg N_c$ and calculate $\nu$ to leading non-trivial
order in the absence of disorder. Although these theories do not yield an
anomalously large exponent $\nu$ within the large $N_f \gg N_c$ expansion, they
do offer a new parameter space of theories that is apparently different from
prior works involving abelian Chern-Simons gauge fields.
