WILSON LOOPS AND NON-ABELIAN STATISTICS IN THE QUANTUM HALL-EFFECT

There is a topological connection between the boundary excitations of a quantum Hall fluid and the quantum numbers of its vortex-like bulk quasi-particles. I use this connection to examine the group properties of vortex excitations in a generalized quantum Hall fluid, and show how the vortex trajectories become Wilson lines interacting via Chern-Simons fields. As a result, I argue that non-abelian statistics, if they exist, should be independent of the detailed properties of the many-body wavefunction and will depend only on the bulk Hall conductivity tensor.