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

我们构造了二维N=(2，2)超对称QCD的两种晶格模型，每种模型都保持一个超电荷。接下来，我们通过引入质量项，建立了二维N=(8，8)超Yang-Mills理论的无不稳定性晶格理论。应用由矩阵产生空间维度的方法，我们讨论了在没有任何微调的情况下获得四维N=4个超杨-米尔斯理论的过程。同时，我们还发现了超对称双势垒矩阵模型与二维IIA型超弦理论在非平凡背景下的对应关系。

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.