CHERN-SIMONS GAUGE-THEORIES FOR THE FRACTIONAL-QUANTUM-HALL-EFFECT HIERARCHY AND ANYON SUPERCONDUCTIVITY

It is shown that Chern-Simons gauge theories describe both the fractional-quantum-Hall effect (FQHE) hierarchy and anyon superconductivity (AS), simply by field-theoretically extracting the effects of vortex excitations. Vortices correspond to Laughlin's quasiparticles or bound states of anyons. Both of these phenomena are explained by the condensations of these vortices. We clarify why the anyon systems become incompressible (FQHE) or compressible (AS) depending on the statistics. It is to be emphasized that we can derive an effective Lagrangian describing fully the FQHE hierarchy from a basic Chern-Simons gauge theory.