W-1-THEORIES FOR THE EDGE EXCITATIONS IN THE QUANTUM HALL-EFFECT(INFINITY FIELD)

We briefly review these low-energy effective theories for the quantum Hall effect, with emphasis and language familiar to field theorists. T wo models have been proposed for describing the most stable Hall plate aus (the Jain series): the multi-component Abelian theories and the mi nimal W-1+infinity models. They both lead to a-priori classifications of quantum Hall universality classes. Some experiments already confirm ed the basic predictions common to both effective theories, while othe r experiments will soon pin down their detailed properties and differe nces. Based on the study of partition functions, we show that the Abel ian theories are rational conformal field theories while the minimal W -1+infinity models are not.