Stable hierarchical quantum Hall fluids as W _{1+∞} minimal models
Abstract
In this paper, we pursue our analysis of the W _{1+∞} 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 W _{1+∞} algebra. Generic W _{1+∞} theories predict many more fluids than the few, stable ones found in experiments. Here we identify a particular class of W _{1+∞} theories, the minimal models, which are made of degenerate representations only  a familiar construction in conformal field theory. The W _{1+∞} minimal models exist for specific values of the fractional Hall 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 nonabelian structure is found in the W _{1+∞} minimal models: they possess neutral quarklike 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.
 Publication:

Nuclear Physics B
 Pub Date:
 February 1995
 DOI:
 10.1016/05503213(95)00233I
 arXiv:
 arXiv:hepth/9502021
 Bibcode:
 1995NuPhB.448..470C
 Keywords:

 High Energy Physics  Theory;
 Condensed Matter
 EPrint:
 Latex file, 41 pages