Chiral algebras of class S and symplectic geometry

2020 Fiscal Year Final Research Report

• Project/Area Number: 17K18724
• Research Category: Grant-in-Aid for Challenging Research (Exploratory)
• Allocation Type: Multi-year Fund
• Research Field: Algebra, Geometry, and related fields
• Research Institution: Kyoto University
• Principal Investigator: Arakawa Tomoyuki 京都大学, 数理解析研究所, 教授 (40377974)
• Project Period (FY): 2017-06-30 – 2021-03-31
• Keywords: 頂点代数 / 4D/2D双対性

Outline of Final Research Achievements

We have achieved the main objective of this project. Namely, we have constructed the chiral algebras of class S and showed that there associated varieties are isomorphic to Moore-Symplectic varieties constructed by Braverman-Finkelberg-Nakajima.　This result gives a rigorous mathematical proof of the remarkable conjecture of Been and Rastelli with states that the associated variety of the vertex operator algebra associated with the 4D N=2 SCFT via 4D/2D duality is isomorphic to the Higgs branch of the corresponding 4D theory, for the class S theory.

Free Research Field

表現論

Academic Significance and Societal Importance of the Research Achievements

現代数学は, 前世紀後半から物理学における弦理論から多大な影響を受けてきた. 応募者が研究領域 とする頂点代数も弦理論を起源として持つ. しかし一方, 逆に数学の側から物理学への影響は少なかっ たように感じる. 本研究課題では頂点代数のシンプレック幾何との新しい関係を与えると共に、数学における頂点代数の理論の弦理論への応用をも同時に行うという挑戦的研究に成功した。