Chiral algebras of class S and symplectic geometry
| 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 |
|
|---|
| Project Period (FY) |
2017-06-30 – 2021-03-31
|
| Project Status |
Completed (Fiscal Year 2020)
|
| Budget Amount *help |
¥6,370,000 (Direct Cost: ¥4,900,000、Indirect Cost: ¥1,470,000)
Fiscal Year 2019: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Fiscal Year 2018: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2017: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
|
|---|
| Keywords | 頂点代数 / 4D/2D双対性 / 頂点作用素代数 / 群の表現論 / 場の理論 / 群論(含群の表現論) / シンプレクティック幾何 / 弦理論 / シンプレック幾何 / 表現論 |
|---|
| 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.
|
| 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。
|
Report
(5 results)
Research Products
(91 results)
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
[Presentation] W-algebras (four talks)2019
Author(s)
Arakawa Tomoyuki
Organizer
Program on Vertex Operator Algebras and Related Topics, Tianyuan Mathematical Center in Southwest China
Related Report
Int'l Joint Research / Invited
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
