  We briefly review these low-energy effective theories for the quantum Hall
effect, with emphasis and language familiar to field theorists. Two models have
been proposed for describing the most stable Hall plateaus (the Jain series):
the multi-component Abelian theories and the minimal W-infinity models. They
both lead to a-priori classifications of quantum Hall universality classes.
Some experiments already confirmed the basic predictions common to both
effective theories, while other experiments will soon pin down their detailed
properties and differences. Based on the study of partition functions, we show
that the Abelian theories are rational conformal field theories while the
minimal W-infinity models are not.
