Stable Hierarchical Quantum Hall Fluids as W1+∞ Minimal Models

In this paper, we pursue our analysis of the W1+∞ symmetry of the lowenergy edge excitations of incompressible quantum Hall fluids. These excitations are described by (1 + 1)-dimensional effective field theories, which are built by representations of the W1+∞ algebra. Generic W1+∞ theories predict many more fluids than the few, stable ones found in experiments. Here we identify a particular class of W1+∞ theories, the minimal models, which are made of degenerate representations only a familiar construction in conformal field theory. The W1+∞ minimal models exist for specific values of the fractional conductivity, which nicely fit the experimental data and match the results of the Jain hierarchy of quantum Hall fluids. We thus obtain a new hierarchical construction, which is based uniquely on the concept of quantum incompressible fluid and is independent of Jain’s approach and hypotheses. Furthermore, a surprising non-Abelian structure is found in the W1+∞ minimal models: they possess neutral quark-like excitations with SU(m) quantum numbers and nonAbelian fractional statistics. The physical electron is made of anyon and quark excitations. We discuss some properties of these neutral excitations which could be seen in experiments and numerical simulations.