Effective Chern?Simons theories of pfaffian and parafermionic quantum Hall states, and orbifold conformal field theories

FRADKIN, EDUARDO; HUERTA, MARINA; ZEMBA, GUILLERMO

NUCLEAR PHYSICS B

ELSEVIER SCIENCE BV

Lugar: Amsterdam; Año: 2001

0550-3213

We present a pure Chern?Simons formulation of families of interesting conformal field theoriesdescribing edge states of non-Abelian quantum Hall states. These theories contain two AbelianChern?Simons fields describing the electromagnetically charged and neutral sectors of these models,respectively. The charged sector is the usual Abelian Chern?Simons theory that successfullydescribes Laughlin-type incompressible fluids. The neutral sector is a (2 + 1)-dimensional theoryanalogous to the (1 + 1)-dimensional orbifold conformal field theories. It is based on the gaugegroup O(2) which contains a Z 2 disconnected group manifold, which is the salient feature of thistheory. At level q, the Abelian theory of the neutral sector gives rise to a Z 2q symmetry, which isfurther reduced by imposing the Z 2 symmetry of charge-conjugation invariance. The remaining Z qsymmetry of the neutral sector is the origin of the non-Abelian statistics of the (fermionic) q-pfaffianstates.