Supersymmetric Integrable Theory and String Moedl

在目前的研究项目中，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。我们的研究开始于超对称可积系统的结构和超空间中的微扰理论。第一年，我们结合可解模型，研究了在超空间中表述的微扰理论框架下的超对称正弦戈登理论。在N=2情况下得到的结果的基础上，我们与东京大学的人合作，通过应用N=4手性超空间形式主义，研究了sin - golden理论在N=4情况下的可能推广。利用微扰理论研究了经典水平和量子水平上的守恒定律。在此基础上，研究了超对称量子群的非交换微分问题，这些问题更多是通过超对称量子平面（空间）来实现的。在文献[1]中，对时空对称的量子空间和量子变形进行了综述。另一方面，在本研究项目的第二年和第三年（最后一年），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中的高捻算子twist-3和twist-4。这是与广岛大学的人一起进行的。去年，基于前一年的成果，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模型的对偶性。我们进一步探讨了N=2情况的可能推广。在目前的研究过程中，与相关领域人士的讨论和交流是非常有益的。我们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。我们在这个项目中获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。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