We explain how (perturbed) boundary conformal field theory allows us tounderstand the tunneling of edge quasiparticles in non-Abelian topologicalstates. The coupling between a bulk non-Abelian quasiparticle and the edge isdue to resonant tunneling to a zero mode on the quasiparticle, which causes thezero mode to hybridize with the edge. This can be reformulated as the flow fromone conformally-invariant boundary condition to another in an associatedcritical statistical mechanical model. Tunneling from one edge to another at apoint contact can split the system in two, either partially or completely. Thiscan be reformulated in the critical statistical mechanical model as the flowfrom one type of defect line to another. We illustrate these two phenomena indetail in the context of the nu=5/2 quantum Hall state and the critical Isingmodel. We briefly discuss the case of Fibonacci anyons and conclude byexplaining the general formulation and its physical interpretation.
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