Non-perturbative construction of 2D and 4D supersymmetric Yang–Mills theories with 8 supercharges Original Research Article

In this paper, we consider two-dimensional image supersymmetric Yang–Mills (SYM) theory and deform it by a mass parameter M with keeping all supercharges. We further add another mass parameter m in a manner to respect two of the eight supercharges and put the deformed theory on a two-dimensional square lattice, on which the two supercharges are exactly preserved. The flat directions of scalar fields are stabilized due to the mass deformations, which gives discrete minima representing fuzzy spheres. We show in the perturbation theory that the lattice continuum limit can be taken without any fine tuning. Around the trivial minimum, this lattice theory serves as a non-perturbative definition of two-dimensional image SYM theory. We also discuss that the same lattice theory realizes four-dimensional image image SYM on image around the minimum of k-coincident fuzzy spheres.