Representation Theories of Superconformal Algebras and Superstring

超共形代数和超弦的表示论

• 批准号: 02640227
• 负责人: MATSUDA Satoshi
• 金额: $ 1.41万
• 依托单位: KYOTO UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (C)
• 财政年份: 1990
• 资助国家: 日本
• 起止时间: 1990 至 1992
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-02640227/
• 关键词: N=4 Superconformal Algebras; Superstring Models; Coulomb Gas Representations; Screening Operators; Compactification; Kac Determinants; Quantum Gravity; Solvable Models; 超共形代数; 表現論; クーロンガス表系; 共形対称性; ク-ロンガス表示; シュヴァルツ微分; 2次元量子重力

The representation theories of the Virasoro and Kac-Moody algebras originally developed from the study of elementary particle physics,is itself a very interesting topic of study. The present project has been pursued, particularly focusing on the fact that the results of the representation theories play an important key role in the general investigation of the construction of superstring theories and their compactification as well as the study of solvable models for critical phenomena. To be concrete, the mathematical aspects of the representation theories have been analyzed by providing the generic method (the Kato-Matsuda method) of constructing null states in the Verma modules of superconformal algebras with supercharge N. As the results of our investigation in 1990-1991, we succeeded in obtaining the Coulomb gas representations of the N = 4 superconformal algebras with the SU(2) Kac-Moody algebra, which allow for incorporating non-unitary representations of the algebras. In 1992 we … More futher developed the study, finding the charge screenign operators using the results obtained in the first two years. We constructed vertex operators in the N = 4 algebras and thereby suceeded in identifying the whole set of the screening operators which are the key tools for developing the complete representation theories of the N = 4 algebras. Our results provide the basis for achieving the rigorous proof of the N = 4 Kac determinant formulae. Also we have been pursuing the BRS cohomology of the N = 4 representations. We further developed our study on 2 dimesional quantum gravity and slovable models with an emphasis on the expected common features of 2 dimensional symmetry behind these topics. We made an active contact with researchers in physics and mathematics in order to have our deep understanding of the problem and also to achieve our goal of the project. Our obtained results have been published in the international juornals, and also put together in the Report of our project under Grant-in-Aid for Scientific Research (C). Less

Virasoro和Kac-Moody代数的表示理论最初是从基本粒子物理学的研究中发展起来的，本身就是一个非常有趣的研究课题。本项目一直在进行，特别关注这样一个事实，即表示理论的结果在超弦理论的构造及其紧化的一般研究以及临界现象的可解模型的研究中起着重要的关键作用。具体地说，通过提供在带超荷数N的超共形代数的Verma模中构造零态的一般方法（Kato-Matsuda方法），我们分析了表示理论的数学方面。作为我们在1990-1991年的研究结果，我们成功地获得了N = 4超共形代数与SU(2) Kac-Moody代数的库仑气体表示，它允许纳入代数的非幺正表示。1992年，我们进一步开展了这项研究，利用前两年的成果找到了电荷屏蔽算子。我们构造了N = 4代数中的顶点算子，从而成功地确定了一整套筛选算子，这是发展N = 4代数完全表示理论的关键工具。我们的结果为N = 4 Kac行列式的严格证明提供了依据。我们也一直在研究N = 4表示的BRS上同性。我们进一步发展了我们对二维量子引力和可解模型的研究，重点是在这些主题背后的二维对称的预期共同特征。为了对问题有更深入的了解，也为了实现我们的项目目标，我们与物理和数学方面的研究者进行了积极的接触。我们取得的成果已在国际期刊上发表，并被汇总在我们的科学研究资助项目报告(C)中。少

项目成果

S. Matsuda: "Coulomb Gas Representations and Screening Operators of the N=4 Superconformal Algebras" Phys. Letters B. B282. 56-62 (1992)

S. Matsuda：“N=4 超共形代数的库仑气体表示和筛选算子”Phys。

S.Matsuda: "Comments on Super Schwarzian Derivatives" Proceedings of the Workshop:"Topology,Field Theory and Superstrings",KEK,Tsukuba,Japan,November 6ー10,1989(KEK Report). 89ー22. 87-108 (1990)

S.Matsuda：“对超级 Schwarzian 导数的评论”研讨会论文集：“拓扑、场论和超弦”，KEK，日本筑波，1989 年 11 月 6-10 日（KEK 报告）87-22。 1990)

S.Matsuda 松田 哲: "Coulomb Gas Representations and Screening Operators of the N=4 Superconformal Algebras" Physics Letters B. B282. 56-62 (1992)

S.Matsuda Satoshi Matsuda：“N=4 超共形代数的库仑气体表示和筛选算子”《物理快报》B. B282 (1992)。

S.MATSUDA(松田 哲): "Comments on Super Schwarzian Derivatives" Proceeding of the Workshop″Topolohy,Field Theory and Superstring″,KEK,Tsukuba,Japan,November 6-10,1989(KEK Report). 89-22. 87-108 (1990)

S.MATSUDA (Tetsu Matsuda)：“对超级 Schwarzian 导数的评论”“拓扑学、场论和超弦”研讨会论文集，KEK，日本筑波，1989 年 11 月 6-10 日（KEK 报告）89-22。 -108 (1990)

S. Matsuda: "Comments on Super Schwarzian Derivatives" Proceedings of the Workshop: "Topology,Field Theory and Superstrings",KEK, Tsukuba, Japan Nov.6-10,1989. 89-22. 87-108 (1990)

S. Matsuda：“Comments on Super Schwarzian Derivatives”研讨会论文集：“拓扑、场论和超弦”，KEK，日本筑波，1989 年 11 月 6-10 日。