| Research Abstract |
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
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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
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