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2018 Fiscal Year Final Research Report

Operator Algebras and their Applications to Mathematical Physics

Research Project

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Project/Area Number 15H02056
Research Category

Grant-in-Aid for Scientific Research (A)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionThe University of Tokyo

Principal Investigator

Kawahigashi Yasuyuki  東京大学, 大学院数理科学研究科, 教授 (90214684)

Research Collaborator Izumi Masaki  
Ozawa Narutaka  
Matui Hiroki  
Project Period (FY) 2015-04-01 – 2019-03-31
Keywords作用素環論 / 部分因子環 / 場の量子論 / 共形場理論 / 頂点作用素代数 / モジュラーテンソル圏 / トポロジカル相 / エニオン
Outline of Final Research Achievements

We have two mathematical theories to study chiral conformal field theory. One is a theory of vertex operator algebras and the other is one of local conformal nets. The direct relations of the two was not known, but we have proved that one can construct a local conformal net from a strongly local vertex operator algebra and recover the original vertex operator algebra from the local conformal net, with Carpi, Longo and Weiner. We have also given a simple sufficient condition for strong locality.
We also studied topological phases of matter from an operator algebraic viewpoint. We studied gapped domain walls and anyon systems using operator algebras.

Free Research Field

作用素環論

Academic Significance and Societal Importance of the Research Achievements

場の量子論は,時空と物質を記述する物理学の根本理論であるが,数学的な基礎づけは今も不十分であり,21世紀数学の重要な研究テーマである.場の量子論の特別な例であるカイラル共形場理論については,数学的理解がかなり進んできている.本研究ではそのうち二つの流儀が本質的に等価であることを示した.
また最近物理学で大きな注目を集めている物質のトポロジカル相について,数学的立場から研究を進めた.

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Published: 2020-03-30  

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