Study of lattice formulations for supersymmetric gauge theories and their nonperturbative aspects

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We constructed two kinds of lattice models for two-dimensional N=(2,2) supersymmetric QCD each of which preserves one of supercharges. Next, we formulated a lattice theory without instability for two-dimensional N=(8,8) super Yang-Mills theory by introducing mass terms. Applying to the above result a method that creates spatial dimensions from matrices, we discussed a procedure to obtain N=4 super Yang-Mills theory in four dimensions without any fine tuning. Also, we found correspondence of a supersymmetric double-well matrix model with two-dimensional type IIA superstring theory on a nontrivial background.