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

Sébastien Palcoux (1)

1 IML - Institut de mathématiques de Luminy

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

Mots clés: von Neumann algebra; conformal field theory; primary fields; intertwining operator; subfactors; Connes fusion; unitary representations; local algebra; III$_{1}$ factor; bimodules; braiding; supersymmetry; boson; fermion; vertex algebra; Virasoro algebra

Domaines: Algèbres d'opérateurs [math.OA]; Analyse fonctionnelle [math.FA]; Théorie des représentations [math.RT]

Sébastien Palcoux. Neveu-Schwarz and operators algebras III: Subfactors and Connes fusion.. 2010. ⟨hal-00522528v2⟩