## Abstract

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 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 Z_{2} symmetry of charge-conjugation invariance. The remaining Z_{q} symmetry of the neutral sector is the origin of the non-Abelian statistics of the (fermionic) q-pfaffian states.

Original language | English (US) |
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Pages (from-to) | 591-606 |

Number of pages | 16 |

Journal | Nuclear Physics B |

Volume | 601 |

Issue number | 3 |

DOIs | |

State | Published - May 14 2001 |

## ASJC Scopus subject areas

- Nuclear and High Energy Physics