Quantum mechanics

Magnetic field

Pure mathematics

Mathematical physics

Sigma model

Phase transition

Critical point (mathematics)

Scaling limit

Scaling

Current algebra

Physics

Nonlinear system

Renormalization group

Mathematics

Critical exponent

Geometry

Conformal field theory

Conformal map

Wave function

Quantum Hall effect

Renormalization

Algebra over a field

Nuclear Physics B

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 (NLσM). 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 Δq=q(1−q)/4. The Lagrangian of the RG-fixed point theory for r retarded and r advanced replicas is proposed to be the GL(r|r)n=4 Wess-Zumino-Witten model deformed by a truly marginal perturbation. The latter emerges from the NLσM by a natural scenario of spontaneous symmetry breaking.

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