Supersymmetric Integrable Theory and String Moedl

在本研究项目中，我们研究了通过数学和理论物理的相互作用而发展起来的可积系统。我们把注意力集中在超对称可积系统的结构和超空间中的微扰理论上开始了我们的研究。第一年，我们在超空间微扰理论的框架下，结合可解模型，研究了超对称Sine-Gordon理论。在N=2情形的结果的基础上，我们与东京大学的工作人员合作，应用N=4手征超空间形式，研究了Sine-Gorden理论推广到N=4情形的可能性。利用微扰理论研究了经典能级和量子能级的守恒律。进一步，我们研究了具有…的超对称四元群的非对易微积分更多的是通过超对称量子平面(空间)实现的。在文献[1]中，对量子空间和时空对称性的量子形变进行了综述。另一方面，在本研究项目的第二年和第三年(最后)，我们在微扰QCD和重整化群方法的框架下，研究了出现在核子自旋结构函数g_1和g_2中的高扭度算符twist-3和twist-4。这是与广岛大学的人们一起进行的。在过去的一年里，我们在前一年的基础上，与阿贡国家实验室的C.K.Zachos博士合作，研究了超对称西格玛模型的对偶性。我们进一步探索了N=2情形的可能扩展。在目前的研究过程中，与相关领域的人进行讨论和交流是非常有用的。特别感谢与东京大学、广岛大学、横滨国立大学和德岛大学的研究人员的交流。我们在这个项目中所取得的成果已经在日本物理学会年会、国内外研究机构的研讨会和研讨会上进行了宣传。这些结果已经发表在上面列出的期刊上。较少

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