N=2 superconformal nets

Abstract

We provide an Operator Algebraic approach to N=2 chiral Conformal Field Theory and set up the Noncommutative Geometric framework. Compared to the N=1 case, the structure here is much richer. There are naturally associated nets of spectral triples and the JLO cocycles separate the Ramond sectors. We construct the N=2 superconformal nets of von Neumann algebras in general, classify them in the discrete series c<3, and we define and study an operator algebraic version of the N=2 spectral flow. We prove the coset identification for the N=2 super-Virasoro nets with c<3, a key result whose equivalent in the vertex algebra context has seemingly not been completely proved so far. Finally, the chiral ring is discussed in terms of net representations.

42 pages. Final version to be published in Communications in Mathematical Physics

References in corpus (4)

• Structure and Classification of Superconformal Nets
• Thermal States in Conformal QFT. II
• Representations of Conformal Nets, Universal C*-Algebras and K-Theory
• Conformal nets and KK-theory

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• Energy bounds for vertex operator algebra extensions
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• From vertex operator superalgebras to graded-local conformal nets and back
• Unitarity and strong graded locality of holomorphic vertex operator superalgebras with central charge at most 24
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