A Dual 2D Model for the Quantum Hall Fluid

Abstract
We present a dual 2D statistical model to describe the physical properties of a Quantum Hall Fluid. Such a model depends on a coupling constant g and an angular variable , which couples the electric and the magnetic charges. We show that it has topologically non trivial vacua (corresponding to rational values of the filling), which are infrared stable fixed points of the renormalization group. Moreover its partition function has a dual infinite discrete symmetry, SL( 2, Z), which reproduces the phenomenological laws of corresponding states. Such a symmetry allows for an unified description of its fixed points in terms of a 2D Conformal Field Theory with central charge c = 1.