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We study the non-Abelian statistics of quasiparticles in the Ising-typequantum Hall states which are likely candidates to explain the observed Hallconductivity plateaus in the second Landau level, most notably the one atfilling fraction nu=5/2. We complete the program started in Nucl. Phys. B 506,685 (1997) and show that the degenerate four-quasihole and six-quasiholewavefunctions of the Moore-Read Pfaffian state are orthogonal with equalconstant norms in the basis given by conformal blocks in a c=1+1/2 conformalfield theory. As a consequence, this proves that the non-Abelian statistics ofthe excitations in this state are given by the explicit analytic continuationof these wavefunctions. Our proof is based on a plasma analogy derived from theCoulomb gas construction of Ising model correlation functions involving bothorder and (at most two) disorder operators. We show how this computation alsodetermines the non-Abelian statistics of collections of more than sixquasiholes and give an explicit expression for the corresponding conformalblock-derived wavefunctions for an arbitrary number of quasiholes. Our methodalso applies to the anti-Pfaffian wavefunction and to Bonderson-Slingerlandhierarchy states constructed over the Moore-Read and anti-Pfaffian states.

Plasma Analogy and Non-Abelian Statistics for Ising-type Quantum Hall States