Representation Theories of Superconformal Algebras and Superstring
Project/Area Number  02640227 
Research Category 
GrantinAid for Scientific Research (C).

Research Field 
核・宇宙線・素粒子

Research Institution  KYOTO UNIVERSITY 
Principal Investigator 
MATSUDA Satoshi Kyoto University, Faculty of Integrated Human Studies, Full Professor, 総合人間学部, 教授 (60025476)

Project Fiscal Year 
1990 – 1992

Project Status 
Completed(Fiscal Year 1992)

Budget Amount *help 
¥2,200,000 (Direct Cost : ¥2,200,000)
Fiscal Year 1992 : ¥700,000 (Direct Cost : ¥700,000)
Fiscal Year 1991 : ¥700,000 (Direct Cost : ¥700,000)
Fiscal Year 1990 : ¥800,000 (Direct Cost : ¥800,000)

Keywords  N=4 Superconformal Algebras / Superstring Models / Coulomb Gas Representations / Screening Operators / Compactification / Kac Determinants / Quantum Gravity / Solvable Models / N=4超共形代数 / 超弦模型 / クーロンガス表示 / 遮蔽演算子 / コンパクト化 / Kac行列式 / 量子重力 / 可解模型 / 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 
Research Abstract 
The representation theories of the Virasoro and KacMoody 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 KatoMatsuda method) of constructing null states in the Verma modules of superconformal algebras with supercharge N. As the results of our investigation in 19901991, we succeeded in obtaining the Coulomb gas representations of the N = 4 superconformal algebras with the SU(2) KacMoody algebra, which allow for incorporating nonunitary representations of the algebras. In 1992 we
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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 GrantinAid for Scientific Research (C). これらの研究遂行において,物理・数学の研究者との研究成果交換・研究討論を積極的に実行した。 これらの研究成果は,欧文学術論文として欧文雑誌に公表され,同時に,科学研究費補助金研究成果報告書にまとめた。 Less

Report
(5results)
Research Output
(14results)