Landau-Ginzburg theories for non-abelian quantum Hall states

We construct Landau-Ginzburg effective field theories for fractional quantu m Hall states such as the Pfaffian state - which exhibit non-abelian statis tics. These theories rely on a Meissner construction which increases the le vel of a non-abelian Chem-Simons theory while simultaneously projecting out the unwanted degrees of freedom of a concomitant enveloping abelian theory . We describe this construction in the context of a system of bosons at Lan dau level filling factor nu = 1, where the non-abelian symmetry is a dynami cally generated SU(2) continuous extension of the discrete particle-hole sy mmetry of the lowest Landau level. We show how the physics of quasiparticle s and their non-abelian statistics arises in this Landau-Ginzburg theory. W e describe its relation to edge theories - where a coset construction plays the role of the Meissner projection - and discuss extensions to other stat es. (C) 1999 Published by Elsevier Science B.V.