Effective Chern-Simons theories of pfaffian and parafermionic quantum Hallstates, and orbifold conformal field theories

We present a pure Chern-Simons formulation of families of interesting confo rmal field theories describing edge states of non-Abelian quantum Hall stat es. These theories contain two Abelian Chern-Simons fields describing the e lectromagnetically charged and neutral sectors of these models, respectivel y. The char,oed sector is the usual Abelian Chern-Simons theory that succes sfully describes Laughlin-type incompressible fluids. The neutral sector is a (2 + 1)-dimensional theory analogous to the (1 + 1)-dimensional orbifold conformal field theories. It is based on the gauge group O(2) which contai ns a Z(2) disconnected group manifold, which is the salient feature of this theory. At level q, the Abelian theory of the neutral sector gives rise to a Z(2q) Symmetry, which is further reduced by imposing the Z2 symmetry of charge-conjugation invariance. The remaining Z(q) symmetry of the neutral s ector is the origin of the non-Abelian statistics of the (fermionic) q-pfaf fian states. (C) 2001 Published by Elsevier Science B.V.