θ renormalization, electron electron interactions and super universality in the quantum Hall regime

The renormalization theory of the quantum Hall effect relies primarily on the non-perturbative concept of θ renormalization by instantons. Within the generalized non-linear σ model approach initiated by Finkelstein we obtain the physical observables of the interacting electron gas, formulate the general (topological) principles by which the Hall conductance is robustly quantized and derive—for the first time—explicit expressions for the non-perturbative (instanton) contributions to the renormalization group β and γ functions. Our results are in complete agreement with the recently proposed idea of super universality which says that the fundamental aspects of the quantum Hall effect are all generic features the instanton vacuum concept in asymptotically free field theory.