Representation Theoretic Study of Two Dimensional Quantum Field Theory
Project/Area Number 
11440020

Research Category 
GrantinAid for Scientific Research (B)

Allocation Type  Singleyear Grants 
Section  一般 
Research Field 
Geometry

Research Institution  Nagoya University 
Principal Investigator 
TSUCHIYA Akihiro Nagoya Uni., graduate school of Mathematics, professor, 大学院・多元数理科学研究科, 教授 (90022673)

CoInvestigator(Kenkyūbuntansha) 
KANNO Hiroaki Nagoya Uni., graduate school of Mathematics, assistant professor, 大学院・多元数理科学研究科, 助教授 (90211870)
OHTA Hiroshi Nagova Uni., graduate school of Mathematics, assistant professor, 大学院・多元数理科学研究科, 助教授 (50223839)
AWATA Hidetoshi Nagoya Uni., graduate school of Mathematics, assistant professor, 大学院・多元数理科学研究科, 助教授 (40314059)
HAYASHI Takahiro Nagoya Uni., graduate school of Mathematics, assistant professor, 大学院・多元数理科学研究科, 助教授 (60208618)
NAKANISHI Tomoli Nagoya Uni., graduate school of Mathematics, assistant professor, 大学院・多元数理科学研究科, 助教授 (80227842)
青本 和彦 名古屋大学, 大学院・多元数理科学研究科, 教授 (00011495)

Project Period (FY) 
1999 – 2001

Project Status 
Completed (Fiscal Year 2001)

Budget Amount *help 
¥6,400,000 (Direct Cost: ¥6,400,000)
Fiscal Year 2001: ¥2,000,000 (Direct Cost: ¥2,000,000)
Fiscal Year 2000: ¥2,000,000 (Direct Cost: ¥2,000,000)
Fiscal Year 1999: ¥2,400,000 (Direct Cost: ¥2,400,000)

Keywords  conformal field theory / vertex operator algebra / E_8 type elliptic Weyl group / primitive form / period of rational elliptic surface / E_8^<(1)> type simple elliptic singulations / E_8型Elliptic Wey1群 / 有利楕円曲面の周期理論 / 楕円型リー環 / 楕円型Weyl群 / 有理楕円曲面の周期理論 / SeibergWitten微分 / 有理楕円曲面のMordellWeil Lattice / N=2 Virasoro代数 
Research Abstract 
I. Conformed field theory associated with vertex operator algebra In the middle of 80's, Borcherds, Frenkel, etc. founded the theory of chiral vertex operator algebra using the operator product expansion in the conformal field theory and apply it to study Monster in finity group theory. But there has not studied conformal field theory associated with vertex operator algebra except case of minimal series of Virasoro algebra and integral representation of Affine Lie algebra. In the collaboration with Kiyokazu Nagatomo at Osaka University, I defined the universal enveloping algebra and zero mod algebra associated with chiral vertex algebra, and reformulated the representation theory of vertex operator algebra. And under the regularity condition we developed the theory the conformed blocks P^1 and showed finite dimensionality, definition of KZ connection and family factorization properties of conformal blocks along the boundary of Moduli spaces. These results was announsed at the meeting at UCLA in November 2001. We wrote a paper on this subject. II. Topological field theory and their deformation with mass parameter We developed the period theory of rational elliptic surfaces as extension of N=2 super Yang Mills theory developed by Seiberg  Witten in 1994. The period integral of the Mordel  Weil lattice along the meromorphic 2form which has order 1 pole on the fiber at ∞ on P^1, can be regarded as mass parameters. We showed that monodromy of this period map can be described by E_8^<(1)> type elliptic Weyl group. And we showed the relation ship between this theory and deformation theory of E_8^<(1)> simply elliptic singularity by Kyoji Saito.

Report
(4 results)
Research Products
(5 results)