Domain walls, fusion rules, and conformal field theory in the quantum Hall regime.
We provide a simple way to obtain the fusion rules associated with elementary quasiholes over quantum Hall wave functions, in terms of domain walls. The knowledge of the fusion rules is helpful in the identification of the underlying conformal field theory describing the wave functions. We show that, for a certain two-parameter family (k,r) of wave functions, the fusion rules are those of su(r)k. In addition, we give an explicit conformal field theory construction of these states, based on the Mk(k+1,k+r) "minimal" theories. For r=2, these states reduce to the Read-Rezayi states. The "Gaffnian" wave function is the prototypical example for r>2, in which case the conformal field theory is nonunitary.
Ardonne
Eddy
E
Nordita, Roslagstullsbacken 23, SE-106 91 Stockholm, Sweden.