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

我们在这个研究项目的课题上取得了一些成果。我们坚持希格斯场是由一个更高维度的规范场通过紧化得到的观点。在这种方法中，该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，以便建立标准模型。我们研究了3-3-1模型的一个现象学结果。近年来，在超弦理论的背景下，提出了超空间上的超对称场论，其中超空间坐标是非对易的。我们成功地在NC超空间上构造了SUSY CP^n非线性σ模型（NLSM）。我们进一步研究了d=2中的SUSY CP^n模型在扩展到NC超空间后是否保留一些“好性质”的问题。我们在微扰方面得到了一些结果，例如模型的重整性。我们还研究了它的非微扰性质、瞬态和模型的可积性。我们研究了规范理论/重力对应及其相关问题，特别是利用矩阵模型（由于Dijkgraaf-Vafa）评价4D超Yang-Mills理论中的有效超势。为此，构造了超对称本征值模型，并研究了其运动方程。提出了d膜模空间与Nekrasov配分函数的关系。在这个项目的三年里，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.