The integer quantum Hall plateau transition is a current algebra after all

The scaling behavior near the transition between plateaus of the Integer Quantum Hall Effect (IQHE) has traditionally been interpreted on the basis of a two-parameter renormalization group (RG) flow conjectured from Pruisken's non-linear sigma model (NL sigma M). Yet, the conformal field theory (CFT) describing the critical point remained elusive, and only fragments of a quantitative analytical understanding existed up to now. In the present paper we carry out a detailed analysis of the current-current correlation function for the conductivity tensor, initially in the Chalker-Coddington network model for the IQHE plateau transition and then in its exact reformulation as a supersymmetric vertex model. We develop a heuristic argument for the continuum limit of the non-local conductivity response function at criticality and thus identify a non-Abelian current algebra at level n = 4. Based on precise lattice expressions for the CFT primary fields we predict the multifractal scaling exponents of critical wavefunctions to be Delta(q) = q(1 - q)/4. The Lagrangian of the RG-fixed point theory for rretarded and radvanced replicas is proposed to be the GL(r vertical bar r)(n= 4) Wess-Zumino-Witten model deformed by a truly marginal perturbation. The latter emerges from the NLsM by a natural scenario of spontaneous symmetry breaking. (C) 2019 The Author. Published by Elsevier B.V.