2018 Fiscal Year Final Research Report
Operator Algebras and their Applications to Mathematical Physics
| Project/Area Number |
15H02056
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| Research Category |
Grant-in-Aid for Scientific Research (A)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | The University of Tokyo |
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Principal Investigator |
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| Research Collaborator |
Izumi Masaki
Ozawa Narutaka
Matui Hiroki
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| Project Period (FY) |
2015-04-01 – 2019-03-31
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| 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 |
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| 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.
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| Free Research Field |
作用素環論
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| 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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