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Supersymmetric Integrable Theory and String Moedl

超对称可积理论与弦模型

基本信息

批准号：
06640392
负责人：
UEMATSU Tsuneo
金额：
$ 1.28万
依托单位：
KYOTO UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1994
资助国家：
日本
起止时间：
1994 至 1996
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-06640392/
关键词：
Integrable System Supersymmetry N=4 Chiral Superspace Sine-Gordon Theory Quantum Space Duality Perturbative QCD Spin Structure Function N=4カライル超空間超空間シグマ模型正準変換

项目摘要

In the present research project, we have investigated the integrable system, that has been developed through the interaction between mathematics and theoretical physics. We started our research by focusing our attention on the structure of the supersymmetric version of the intergrable system and the perturbation theory in the superspace. In the first year, in connection with solvable models, we have studied the supersymmetric sine-Gordon theory in the framework of perturbation theory formulated in superspace. Based on the result which has been obtained for N=2 case, we have examined the possible extension of the sine-Gorden theory to the N=4 case, by applying the N=4 chiral superspace formalism in collaboration with the people at University of Tokyo. The conservation laws at the classical level as well as at the quantum level have been studied utilizing the perturbation theory. Further, we investigated the non-commutative differential calculus for the supersymmetric quatum groups which … More are realized by supersymmetric quantum plane (space). In the Iiterature [1], a review on the quantum space and quantum deformation of space-time symmetry has been given. On the other hand, in the second and the third (last) years of this research project, we have investigated the higher-twist operators, twist-3 and twist-4, which appear in the nucleon's spin structure functions g_1 and g_2, in the framework of the perturbative QCD and the renormalization group method. This was carried out with the people at Hiroshima University. In the last year, based on what we have obtained in the previous year, we studied the duality in the supersymmetric sigma models in collaboration with Dr.C.K.Zachos from the Argonne National Laboratory. We further explored the possble extention to the N=2 case.In the course of the present research, discussions and communications with the people in the related fields were very useful. Especially, we are very much indebted to the communications with the researchers at University of Tokyo, Hiroshima University, Yokohama National University, and Tokushima University. What we have obtained during this project have been publicized on the occasion of annual meeting of The Japan Physical Society, workshops and seminars at the domestic as well as foreign research Institutes. These results have been published in the journals listed above. Less

在本研究项目中，我们研究了通过数学和理论物理之间的相互作用而发展起来的可积系统。我们开始我们的研究，集中我们的注意力在超对称版本的可积系统的结构和微扰理论在超空间。在第一年，在可解模型方面，我们在超空间微扰理论的框架内研究了超对称sine-Gordon理论。基于N=2情况下获得的结果，我们与东京大学的研究人员合作，应用N=4手征超空间形式主义，研究了sine-Gorden理论到N=4情况的可能扩展。利用微扰理论研究了经典和量子两个层次的守恒律。进一步，我们研究了超对称quatum群的非交换微分， ...更多信息是由超对称量子平面（空间）实现的。文献[1]对时空对称性的量子空间和量子形变作了评述。另一方面，在本研究计划的第二年和第三年（最后一年），我们在微扰QCD和重整化群方法的框架下，研究了核子自旋结构函数g_1和g_2中的高扭算符twist-3和twist-4。这是和广岛大学的人一起进行的。在过去的一年中，基于我们在前一年中所获得的，我们与阿贡国家实验室的C.K.Zachos博士合作研究了超对称sigma模型中的对偶性。在本研究过程中，与相关领域的人士进行了有益的讨论和交流。特别是，我们非常感谢与东京大学、广岛大学、横滨国立大学和德岛大学研究人员的交流。我们在本项目中获得的成果已在日本物理学会年会、国内外研究机构的讲习班和研讨会上公布。这些结果已发表在上述期刊上。少