Research abstract of Y. Kawahigashi for 2014-15

We have studied phase boundaries and topological defects in conformal field theory from the operator algebraic viewpoints with Bischoff, Longo and Rehren. We defined phase boundaries in algebraic quantum field theory and studied their basic properties. In particular, we proved all phase boundaries arise from irreducible decompositions of a braided product of two Q-systems. We also proved that phase boundaries exactly correpond to bimodules over two Q-systems.

We also developed a general theory of Q-systems without assuming factoriality with Bischoff, Longo and Rehren.

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