Neveu-Schwarz and operators algebras I: Vertex operators superalgebras.

Sébastien Palcoux (1)

1 IML - Institut de mathématiques de Luminy

This paper is the first of a series giving a self-contained way from the Neveu-Schwarz algebra to a new series of irreducible subfactors. Here we present an elementary, progressive and self-contained approch to vertex operator superalgebra. We then build such a structure from the loop algebra $Lg$ of any simple finite dimensional Lie algebra $g$. The Neveu-Schwarz algebra $Vir_{1/2}$ emerges naturally on. As application, we obtain a unitary action of $Vir_{1/2}$ on the unitary discrete series of $Lg$.

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 I: Vertex operators superalgebras.. 2010. ⟨hal-00522526v2⟩