Nonperturbative effects in QFT and new supersymmetry

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This research project was planned for advancement of understanding of the nonperturbative effects in quantum theory and further explore new possibilities of supersymmetry. The analytical method that can handle nonperturbative effects was the valley method in imaginary path-integral formalism, developed a group including the current project leader, H. Aoyama. Using this method for an asymmetric double-well potential model in one-dimensional quantum mechanics, the N-fold supersymmetry had been found. Therefore it was intended to further explore this new supersymmetry, searching for new models.This four-year research project has just accomplished this task. The valley method was applied to various quantum mechanical models. From the nonperturbative effects obtained by this method, the large order behaviour of perturbative series were extracted. Some of them lead to success : a periodic model was found to have a form of N-fold supersymmetry, which were more general than the assymmetric double-well model, in a sense that its supercharge is not just the N-th power of the momentum, but an N-th order polynomial. Inspired by this finding, another model, a sextet model, was soon found to have an N-fold supersymmetry.All these N-fold supersymmetry models shared a special factorizable form of the supercharge. Motivated by this, we defined a subclass "type-A" of N-fold supersymmetry, and identified the necessary and sufficient conditions for N-fold supersymmetry. We solved these conditions completely, classified all the models of this type, and wrote down their potentials and supercharge.With these results, we now have a complete theory of type-A. Exploring models outside this subclass is one of the most important task for future.