Emergence of Integrability in Gauge Theory and String Theory and Nonperturbative Effects

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1) Elucidated the deviation from BDS conjecture first in the world analytically. 2) Established the low energy theorem for the NG fermion in the model of Fujiwara-Itoyama-Sakaguchi. 3) In the USp matrix model of Itoyama - Tokura, we showed that the self-interaction between a spacetime point and its image is attractive in the long distances and repulsive in the short distances. Suggests the formation of 4 dimensional spacetime in this model. 4) 2d-4d connection, equivalence established between the spectral curve of the quiver matrix model and that of SW curve of Gaiotto-Witten type. 0d-4d dictionary was established.