With Carpi and Longo, we have studied boundary conformal field theory from an operator algebraic viewpoint. We have shown how to construct boundary CFT nets which are locally isomorphic to A⊗A from a completely rational net of the form A⊗A on the 2-dimensional Minkowski space.
With Suthichitranont, we have constructed a holomorphic local conformal framed nets extended from a tensor power of the Virasoro net with c=1/2 with a pair of binary codes (C,D) satisfying certain conditions. This is an operator algebraic counterpart of the result of Lam-Yamauchi on vertex operator algebras.
With Ogata and Stømer, we have shown that for a type III factor M, its finite dimensional C*-algebra A and finitely many normal states φi, i=0,1,...,n, with φ0 faithful on it, we have a unitary u in M such that we have Ad u φi=φi on A for i=1,2,...,n.