High-energy QCD and Supersymmetric Integrable Models

在本研究项目中，我们不仅从传统的微扰方法而且从适用于微扰区和非微扰区的边界区的框架来研究QCD的高能行为，以阐明它的动力学以及超对称可积理论的各个方面。第一年，我们结合超对称统一理论，研究了扩展的超对称的部分破缺，特别是N=2超共形对称性的自发破缺，直至N=1的超Poincare对称性。基于时空对称性的非线性实现的一般方法，我们得到了有效的拉格朗日。另一方面，在本研究项目的第二年和第三年(最后)，我们结合QCD的高能行为，研究了出现在核子自旋结构函数和自旋结构函数…中的高扭度算符在微扰QCD和重整化群方法框架下的更多虚光子。特别是在过去的一年里，我们计算了光子的极化结构函数，它可以通过高能下的极化电子-正电子碰撞来测量。这是通过计算QCD中的高阶来实现的，我们得到了QCD求和规则。我们进一步得到了极化虚光子内部与自旋相关的夸克和胶子分布，并研究了它与因式分解的关系。最后，我们对高能QCD的可积性及其有效的二维超对称理论寻求统一的认识。出于最近对ADS/CFT通信的兴趣，扩展的ADS超对称性的部分破缺也在调查中。在本研究过程中，与相关领域人士的讨论和交流非常有用。我们特别感谢与东京大学、广岛大学、横滨国立大学和理工学院的研究人员的交流，并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公布了我们在这个项目中取得的成果。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 high-energy behavior of QCD, not only from the conventional perturbative approach but also from the framework applicable for the boundary region between perturbative and non-perturbative regimes, in order to clarify its dynamics as well as the various aspects of the supersymmetric integrable theories. In the first year, in connection with supersymmetric unified theories, we have studied partial breaking of the extended supersymmetry, especially the spontaneous breaking of N=2 superconformal symmetry down to N=1 super-Poincare symmetry. Based on the general method of the nonlinear realization of space-time symmetries, we have obtained the effective lagrangian. On the other hand, in the second and the third(last)years of this research project, in connection with the high-energy behavior of QCD, we have investigated the higher-twist operators, which appear in the nucleon's spin structure functions as well as the spin structure func … More tions of the virtual photon in the framework of the perturbative QCD and the renormalization group method. Especially in the last year, we have calculated the polarized structure function of the photon which can be measured through the polarized electron-positron collision at high-energy. This was carried out by evaluating the higher order in QCD and we have obtained the QCD sum rule. We further obtained spin-dependent quark and gluon distributions inside the polarized virtual photon and also examined its factorization scheme dependence. Finally, we pursued unified understanding for the integrability of the high-energy QCD and its effective 2-dimensional supersymmetric theories. Motivated by the recent interest in the AdS/CFT correspondence, the partial breaking of the extended AdS supersymmetry is also under investigation. 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 RIKEN.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