Universal structure of the edge states of the fractional quantum Hall states

We present an effective theory for the bulk fractional quantum Hall states on the Jain sequences on closed surfaces and show that it has a universal f orm whose structure does not change from fraction to fraction. The structur e of this effective theory follows from the condition of global consistency of the flux attachment transformation on closed surfaces. We derive the th eory of the edge states on a disk that follows naturally from this globally consistent theory on a torus. We find that, for a fully polarized two-dime nsional electron gas, the edge states for all the Jain filling fractions v = p/(2np + 1) have only one propagating edge field that carries both energy and charge, and two nonpropagating edge fields of topological origin that are responsible for the statistics of the excitations. Explicit results are derived for the electron and quasiparticle operators and for their propaga tors at the edge. We show that these operators create states with the corre ct charge and statistics. It is found that the electron tunneling density o f states for all the Jain states scales with frequency as /omega/((1 - v)/v ). [S0163-1829(99)02124-4].