Non-Abelian fermionization and fractional quantum Hall transitions

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 interplateaux transitions. The key motivating experimental observations are the anomalously large value of the correlation length exponent ν≈2.3 and that ν is observed to be superuniversal, i.e., the same in the vicinity of distinct critical points [Sondhi, Rev. Mod. Phys. 69, 315 (1997)RMPHAT0034-686110.1103/RevModPhys.69.315]. Duality motivates effective descriptions for a fractional quantum Hall plateau transition involving a Chern-Simons field with U(Nc) gauge group coupled to Nf=1 fermion. We study one class of theories in a controlled limit where Nf Nc and calculate ν to leading nontrivial order in the absence of disorder. Although these theories do not yield an anomalously large exponent ν within the large Nf Nc expansion, they do offer a new parameter space of theories that is apparently different from prior works involving Abelian Chern-Simons gauge fields [Wen and Wu, Phys. Rev. Lett. 70, 1501 (1993)PRLTAO0031-900710.1103/PhysRevLett.70.1501; Chen, Phys. Rev. B 48, 13749 (1993)PRBMDO0163-182910.1103/PhysRevB.48.13749].