N=2 superconformal nets

TL;DR

This paper develops an operator algebraic framework for N=2 superconformal nets, classifies them in the discrete series, and establishes key structural and spectral properties, advancing the mathematical understanding of N=2 superconformal field theories.

Contribution

It introduces a novel operator algebraic approach to N=2 superconformal nets, including classification, spectral flow, and coset identification, which were not fully established before.

Findings

Constructed N=2 superconformal nets of von Neumann algebras

Classified nets in the discrete series c<3

Proved coset identification for N=2 super-Virasoro 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.