Coset Construction of Parafermionic Hall States

Fractional quantum Hall fluids with fillings 2 < ν < 3 have been recently proposed which generalize the Pfaffian state (ν = 2 + 1/2) into a hierarchy of states with parafermionic excitations. We describe here the corresponding Zk-parafermion conformal field theory by means of the coset construction ŝu(k)1⊕ ŝu(k)1/ŝu(k)2. This extends our earlier derivation of the Pfaffian state from a “parent” state with abelian affine symmetry plus a projection of degrees of freedom. The numerator of the coset is actually a rational conformal field theory made out of (2k − 2) scalar fields and a specific extended symmetry. The coset construction projects out some neutral Hall edge excitations while preserving the filling fraction; it also respects the Zk parity rule coupling neutral and charged excitations in the parent abelian theory.