Effective Chern–Simons theories of pfaffian and parafermionic quantum Hall states, and orbifold conformal field theories Original Research Article

We present a pure Chern–Simons formulation of families of interesting conformal field theories describing edge states of non-Abelian quantum Hall states. These theories contain two Abelian Chern–Simons fields describing the electromagnetically charged and neutral sectors of these models, respectively. The charged sector is the usual Abelian Chern–Simons theory that successfully 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 contains a Z2 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 Z2q symmetry, which is further reduced by imposing the Z2 symmetry of charge-conjugation invariance. The remaining Zq symmetry of the neutral sector is the origin of the non-Abelian statistics of the (fermionic) q-pfaffian states.