Non-Abelian fractional quantum Hall states and chiral coset conformal field theories

Abstract

We propose an effective Lagrangian for the low energy theory of the Pfaffian states of the fractional quantum Hall effect in the bulk in terms of non-Abelian Chern-Simons (CS) actions. Our approach exploits the connection between the topological Chern-Simons theory and chiral conformal field theories. This construction can be used to describe a large class of non-Abelian FQH states.

Revised manuscript, 17 pages; new section discusses parafermion states

References in corpus (8)

• Beyond paired quantum Hall states: parafermions and incompressible states in the first excited Landau level
• A Chern-Simons Effective Field Theory for the Pfaffian Quantum Hall State
• New Class of Non-Abelian Spin-Singlet Quantum Hall States
• Projective Construction of Non-Abelian Quantum Hall Liquids
• Landau-Ginzburg Theories for Non-Abelian Quantum Hall States
• A Unified Conformal Field Theory Description of Paired Quantum Hall States
• Topological Degeneracy of Quantum Hall Fluids
• Hamiltonian Formulation of the W-Infinity Minimal Models

Cited by in corpus (9)

• Topological Order and Conformal Quantum Critical Points
• Anyon Condensation and Continuous Topological Phase Transitions in Non-Abelian Fractional Quantum Hall States
• $U(1)\times U(1)⋊Z_2$ Chern-Simons Theory and Z_4 Parafermion Fractional Quantum Hall States
• Effective Field Theory and Projective Construction for the Z_k Parafermion Fractional Quantum Hall States
• Ground state degeneracy of non-Abelian topological phases from coupled wires
• Landau-Ginzburg Theories of Non-Abelian Quantum Hall States from Non-Abelian Bosonization
• Effective Chern-Simons Theories of Pfaffian and Parafermionic Quantum Hall States, and Orbifold Conformal Field Theories
• Effective Theories for 2+1 Dimensional Non-Abelian Topological Spin Liquids
• Chiral Edge States in 2+1 Dimensional Topological Phases