CONNECTIONS BETWEEN THE QUANTUM HALL-EFFECT AND CONFORMAL FIELD-THEORY

The quantum Hall effect (QHE) is studied in the context of a conformal field theory (CFT). Winding state vertex operators for an effective field of N "spins" associated with the cyclotron motion of particles are defined. The effective field of spins may be used to define an effective Hamiltonian. This effective Hamiltonian describes the collective motion of the N particles (with coupling kappa0) together with a current-current interaction (of strength kappa1). Such a system gives rise to a CFT in the large-N limit when kappa0 = kappa1. The Laughlin wave function is derived from this CFT as an N'-point correlation function of winding state vertex operators.