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This paper is the third of a series giving a self-contained way from theNeveu-Schwarz algebra to a new series of irreducible subfactors. Here weintroduce the local von Neumann algebra of the Neveu-Schwarz algebra, to obtainJones-Wassermann subfactors for each representation of the discrete series.Then using primary fields we prove the irreducibility of these subfactors; tonext compute the Connes fusion ring and obtain the explicit formula of thesubfactors indices.

Neveu-Schwarz and operators algebras III: Subfactors and Connes fusion