We made the following study on algebraic quantum foeld theory.
We have revised paper [45] which was originally written in 2004. We had a construction of local conformal nets of von Neumann algebras analogous to the one of framed vertex operator algebras with Longo, and as an example, we had a local conformal net corresponding to the moonshine vertex operator algebra in 2004. This year, we have shown that the automorphism group of this local conformal net is indeed the Monster group, as expected.
In [46], we completely classified irreducible, but possibly non-local extensions of the Virasoro net with central charge less than 1 with Longo, Pennig and Rehren. By general theory of Longo and Rehren, this amounts to a complete classification of algebraic boundary CFT with central charge less than 1 satisfying the Haag duality.