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

Non-Abelian bosonization and modular transformation approach to superuniversality