Conformal field theory of composite fermions

We show that the quantum Hall wave functions for the ground states in the Jain series Î =n/(2np+1) can be exactly expressed in terms of correlation functions of local vertex operators Vn corresponding to composite fermions in the nth composite-fermion (CF) Landau level. This allows for the powerful mathematics of conformal field theory to be applied to the successful CF phenomenology. Quasiparticle and quasihole states are expressed as correlators of anyonic operators with fractional (local) charge, allowing a simple algebraic understanding of their topological properties that are not manifest in the CF wave functions. Moreover, our construction shows how the states in the Î =n/(2np+1) Jain sequence may be interpreted as condensates of quasiparticles.