超共形网的结构与分类
Structure and Classification of Superconformal Nets
摘要：
研究了圆上von Neumann代数的Fermi共形网的一般结构，考虑了一类拓扑表示，即一般表示，我们将其刻画为Neveu-Schwarz表示或Ramond表示，特别地，Jones指数可以与它们中的每一个相关联.然后，我们考虑一个超对称一般表示与费米模网，并给出一个公式，涉及Fredholm指数的超荷运营商和琼斯指数。然后考虑与超维拉索罗代数相关联的网并讨论其结构。若中心荷c属于离散级数，则此网可模F的功. Xu和我们得到了一个例子，其中我们的设置通过考虑具有最低权重c/24的Ramond不可约表示来验证。我们分类的所有不可约费米扩展的任何super-Virasoro网的离散系列，从而提供了一个分类的所有超共形网的中心荷小于3/2。
英文摘要：
We study the general structure of Fermi conformal nets of von Neumann algebras on the circle, consider a class of topological representations, the general representations, that we characterize as Neveu-Schwarz or Ramond representations, in particular a Jones index can be associated with each of them. We then consider a supersymmetric general representation associated with a Fermi modular net and give a formula involving the Fredholm index of the supercharge operator and the Jones index. We then consider the net associated with the super-Virasoro algebra and discuss its structure. If the central charge c belongs to the discrete series, this net is modular by the work of F. Xu and we get an example where our setting is verified by considering the Ramond irreducible representation with lowest weight c/24. We classify all the irreducible Fermi extensions of any super-Virasoro net in the discrete series, thus providing a classification of all superconformal nets with central charge less than 3/2.
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