Research abstract of Y. Kawahigashi for 2010-11

With Carpi, Hillier, Longo and Xu, we construct the N=2 super Virasoro net from the vacuum representation of the Neveu-Schwarz algebra for the central charge in the discrete series c < 3. We then identify the even part of this superconformal net with the coset net for the inclusions U(1)2m+4 \subset SU(2)m \otimes U(1)4. We identify the chiral ring and the spectral flow in the context of the representation theory of this superconformal net. We further classify all of their extensions using \alpha-induction modular invariants. We have a mixture of the coset construction and the mirror extension in the sense of Xu and obtain a new type of simple current extensions with cyclic groups of large orders.

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