A Conformal Field Theory for the Quantum Hall Effect

Abstract

The QHE is studied in the context of a CFT. An effective field of $N$ ``spins" associated with the cyclotron motion of particles is taken as an order parameter from which an effective Hamiltonian may be defined. This effective Hamiltonian describes the COM motion of the $N$ particles (with coupling $κ_0$) together with a current-current interaction (of strength $κ_1$). Such a system gives rise to a CFT in the large $N$ limit when $κ_0 = κ_1$. The Laughlin wavefunction is derived from this CFT as an $N'$-point correlation function of winding state vertex operators.