Conformal field theory construction for non-Abelian hierarchy wave functions

The fractional quantum Hall effect is the paradigmatic example of topologically ordered phases. One of its most fascinating aspects is the large variety of different topological orders that may be realized, in particular non-Abelian ones. Here we analyze a class of non-Abelian fractional quantum Hall model states which are generalizations of the Abelian Haldane-Halperin hierarchy. We derive their topological properties and show that the quasiparticles obey non-Abelian fusion rules of type su(q)(k). For a subset of these states we are able to derive the conformal field theory description that makes the topological properties-in particular braiding-of the state manifest. The model states we study provide explicit wave functions for a large variety of interesting topological orders, which may be relevant for certain fractional quantum Hall states observed in the first excited Landau level.