How SU(2)4 anyons are Z3 parafermions

Abstract

We consider the braid group representation which describes the non-abelian braiding statistics of the spin 1=2 particle world lines of an SU(2)4 Chern-Simons theory. Up to an abelian phase, this is the same as the non-Abelian statistics of the elementary quasiparticles of the k = 4 Read-Rezayi quantum Hall state. We show that these braiding properties can be represented exactly using Z3 parafermion operators.©