A new development of operator algebras and mathematical physics

2015 Fiscal Year Final Research Report

• Project/Area Number: 23244016
• Research Category: Grant-in-Aid for Scientific Research (A)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Global analysis
• Research Institution: The University of Tokyo
• Principal Investigator: Kawahigashi Yasuyuki 東京大学, 数理(科)学研究科(研究院), 教授 (90214684)
• Co-Investigator(Renkei-kenkyūsha): IZUMI Masaki 京都大学, 大学院理学研究科, 教授 (80232362) ; OZAWA Narutaka 京都大学, 数理解析研究所, 教授 (60323466) ; MATUI Hiroki 千葉大学, 大学院理学研究科, 教授 (40345012) ; UEDA Yoshimichi 九州大学, 大学院数理学研究院, 准教授 (00314724)
• Project Period (FY): 2011-04-01 – 2016-03-31
• Keywords: 作用素環 / 共形場理論 / 部分因子環 / 頂点作用素代数 / 数理物理学 / 超対称性 / モジュラーテンソル圏 / 境界共形場理論

Outline of Final Research Achievements

Vertex operator algebras and local conformal nets (of operator algebras) are two mathematical frameworks to study chiral conformal field theory. Many analogies between the two have been known, but no directi relations were known so far. With Carpi, Longo and Weiner, we have proved that we can construct a local conformal net from a strongly local vertex operator algebra and we can also recover the original vertex operator algebra from this resulting local conformal net. We have further given a simple sufficient condition for strong locality. This gives a solution to an important problem studied over more than ten years. We have also shown that the automorpshim group of a vertex operator algebra and that of the corresponding local conformal net coincide. This result applies to many examples including the Moonshine vertex operator algebra. (The case of the Moonshine vertex operator algebra was known before.)

Free Research Field

作用素環論