Representation Theoretic Study of Two Dimensional Quantum Field Theory

二维量子场论的表示理论研究

基本信息

批准号：
11440020
负责人：
TSUCHIYA Akihiro
金额：
$ 4.1万
依托单位：
Nagoya University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B)
财政年份：
1999
资助国家：
日本
起止时间：
1999 至 2001
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-11440020/
关键词：
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 Sei

项目摘要

I. Conformed field theory associated with vertex operator algebraIn 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 blocksP^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 parameterWe 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 2-form 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.

I. Conformed field theory associated with vertex operator algebraIn the middle of 80's, Borchers, 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在与大阪大学的Kiyokazu Nagatomo合作中，我定义了与手性顶点代数相关的通用包围代数和零mod Algebra，并改革了Vertex操作员Algebra的代表理论。在规律性的条件下，我们开发了理论的构型块^1，并显示了有限的维度，KZ连接的定义和沿模量空间边界边界的保形块的定义特性。这些结果在2001年11月在UCLA的会议上宣布。我们撰写了有关此主题的论文。拓扑场理论及其与质量参数的变形发展了理性椭圆形表面的时期理论，因为n = 2的扩展是由塞伯格（Seiberg -witten）于1994年开发的。我们表明，这一时期图的单构图可以由E_8^<（1）>型椭圆形韦伊尔组描述。我们展示了这种理论与E_8^<（1）>的变形理论之间的关系船，而Kyoji Saito简单地椭圆形奇异性。