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

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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.