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

2000/11/08 by Eduardo Fradkin, Marina Huerta, Guillermo R. Zemba +1
Physics and Astronomy · #Abelian group #Conformal field theory #Field (mathematics) #Gauge group #Gauge theory #Orbifold #Physics of Superconductivity and Magnetism #Quantum Hall effect #Quantum and electron transport phenomena #Quantum field theory #Topological Materials and Phenomena #cond-mat.mes-hall #hep-th

paper · pdf · doi:10.1016/s0550-3213(01)00077-3

published as Nucl.Phys. B601 (2001) 591-606

arxiv created 2000/11/08 · openalex publication_date 2001/05/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

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 \bf 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 \bf Z_2q symmetry, which is further reduced by imposing the \bf Z₂ symmetry of charge-conjugation invariance. The remaining \bf Z_q symmetry of the neutral sector is the origin of the non-Abelian statistics of the (fermionic) q-Pfaffian states.

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