Compactification of M theory and the origin of Higgs and matter fields

我们在这个研究项目的主题上取得了一些结果。1.我们坚持这样的观点，即希格斯场是由更高维的规范场通过紧致得到的。在这种方法中，为了建立标准模型，这个规范理论的群必须扩展到SU(3)×SU(3)×U(1)(3-3-1模型)或更高。我们研究了3-3-1模型的一个唯象结果。2.最近，在超弦理论的背景下，提出了超空间坐标为非对易超空间的超对称(SUSY)场论，并成功地在NC超空间上构造了SUSY CP^n非线性Sigma模型(NLSM)。我们进一步研究了将d=2中的SUSY Cp^n模型推广到NC超空间后，是否保留了该模型的一些“好性质”的问题。在微扰方面，我们得到了一些结果，如模型的可重整化。3.我们研究了规范理论/引力对应及相关问题，特别是利用矩阵模型(Dijkgraaf-Vafa)计算4D超杨-Mills理论中的有效超势。为此，我们构造了超对称本征值模型，并研究了它的运动方程。我们提出了Nekrasov配分函数与D-膜的模空间之间的关系。在本项目的三年中，我们发表了11篇论文。

We have achieved a few results on the subjects of this research project.1.We pursued the viewpoint that the Higgs field is obtained from a gauge field in higher dimensions by compactification. In this approach the group of this gauge theory has to be extended to SU (3)×SU (3)×U(1)(3-3-1 model) or higher in order for the standard model to be built in. We have studied a phenomenological consequence of the 3-3-1 model.2.Recently, in the context of superstring theory, supersymmetric (SUSY) field theories on superspace of which superspace coordinates are noncommutative (NC) have been proposed.We have succeeded in constructing SUSY CP^n nonlinear sigma model (NLSM) on NC superspace. We have further studied the question whether some of the "good properties" of the SUSY CP^n model in d=2 are preserved after extension to NC superspace. We have obtained results on the perturbative aspect, such as renormalizability of the model. We have also studied it's non-perturbative properties, instantons and integrability of the model.3.We have studied gauge theory/gravity correspondence and related problems, in particular the evaluation of the effective superpotential in 4D super Yang-Mills theory using the matrix model (due to Dijkgraaf-Vafa).To this end we have constructed supersymmetric eigenvalue model and studied it's equation of motion.We have proposed a relation between Nekrasov's partition function and the moduli space of D-branes.We have published 11 papers during the three years of this project term.