  Quantum Hall inter-plateaux transitions are physical exemplars of quantum
phase transitions. Near each of these transitions, the measured electrical
conductivity scales with the same correlation length and dynamical critical
exponents, i.e., the critical points are superuniversal. In apparent
contradiction to these experiments, prior theoretical studies of quantum Hall
phase transitions within the framework of Abelian Chern-Simons theory coupled
to matter found correlation length exponents that depend on the value of the
quantum critical Hall conductivity. Here, we use non-Abelian bosonization and
modular transformations to theoretically study the phenomenon of
superuniversality. Specifically, we introduce a new effective theory that has
an emergent $U(N)$ gauge symmetry with any $N > 1$ for a quantum phase
transition between an integer quantum Hall state and an insulator. We then use
modular transformations to generate from this theory effective descriptions for
transitions between a large class of fractional quantum Hall states whose
quasiparticle excitations have Abelian statistics. We find the correlation
length and dynamical critical exponents are independent of the particular
transition within a controlled 't Hooft large $N$ expansion, i.e.,
superuniversal! We argue that this superuniversality could survive away from
this controlled large $N$ limit using recent duality conjectures.
