Parafermion Hall states from coset projections of abelian conformal theories

The Zk-parafermion Hall state is an incompressible fluid of k-electron clusters generalizing the Pfaffian state of paired electrons. Extending our earlier analysis of the Pfaffian, we introduce two 'parent' abelian Hall states which reduce to the parafermion state by projecting out some neutral degrees of freedom. The first abelian state is a generalized (331) state which describes clustering of k distinguishable electrons and reproduces the parafermion state upon symmetrization over the electron coordinates. This description yields simple expressions for the quasi-particle wave functions of the parafermion state. The second abelian state is realized by a conformal theory with a (2k-1)-dimensional chiral charge lattice and it reduces to the Zk-parafermion state via the coset construction su(k)1-circumflex+su(k)1-circumflex/su(k)2-circumflex. The detailed study of this construction provides us with a complete account of the excitations of the parafermion Hall state, including the field identifications, the Zk symmetry and the partition function