A CHERN-SIMONS EFFECTIVE-FIELD THEORY FOR THE PFAFFIAN QUANTUM HALL STATE

We present a low-energy effective field theory describing the universa lity class of the Pfaffian quantum Hall state. To arrive at this theor y, we observe that the edge theory of the Pfaffian state of bosons at v = 1 is an SU(2)(2) Kac-Moody algebra. It follows that the correspond ing bulk effective field theory is an SU(2) Chern-Simons theory with c oupling constant k = 2, The effective field theories for other Pfaffia n states, such as the fermionic one at v = 1/2 are obtained by a flux- attachment procedure. We discuss the non-Abelian statistics of quasipa rticles in the context of this effective field theory. (C) 1998 Elsevi er Science B.V.