RECENT DEVELOPMENT OF SUPERSYMMETRIC GAUGE THEORIES ON LATTICE

Abstract

First, we give a brief review of recent development of lattice formulations for supersymmetric Yang-Mills (SYM) theories with extended supersymmetry, which preserves a part of supersymmetry on lattice. For cases of two dimensions, we can see that lattice models in such formulations lead to the target continuum theories with no fine-tuning. Namely, supersymmetries or some other symmetries not realized on the lattice are automatically restored in the continuum limit. Next, we consider a mass deformation to [Formula: see text] and present its lattice formulation with keeping two supercharges. It provides a nonperturbative framework to investigate IIA matrix string theory. Moreover, since it has fuzzy sphere solutions around which four-dimensional theory is deconstructed, it will serve a nonperturbative formulation of four-dimensional [Formula: see text] which requires no fine-tuning. The rank of the gauge group is not restricted to large N. It opens a quite interesting possibility to test AdS/CFT correspondence in a stringy regime where string loop effects cannot be neglected. Also, for two-dimensional [Formula: see text], a similar argument is possible to obtain four-dimensional [Formula: see text] on noncommutative space.