A Proposal for a Non-perturbative Regularization of N = 2 Susy 4d Gauge Theory

In this letter we show that supersymmetry like geometry can be approximated using finite dimensional matrix models and fuzzy manifolds. In particular we propose a nonperturbative regularization of N = 2 supersymmetric U(n) gauge action in 4D. In some planar large N limits we recover exact SUSY together with the smooth geometry of Rθ. Noncommutative geometry [3] is the only known modification of field theory which preserves supersymmetry. In this note we will go one step further beyond the infinite dimensional matrix algebras of noncommutative Moyal-Weyl spacetimes and show that supersymmetry ( like geometry itself ) can be approximated using finite dimensional matrix models and fuzzy manifolds [1, 2]. In particular we propose a non-perturbative regularization of N = 2 supersymmetric U(n) gauge action in 4 dimensions. In some planar large N limits we will recover exact SUSY action together with the smooth geometry of spacetime Rθ. Motivated by 1) the IKKT matrix models approach [4, 5] to spacetime generation and 2) the noncommutative fuzzy geometry approach [1,2] to i) quantum geometry and to ii) the nonperturbative quantum field theory we are led to the following considerations and a proposal for a non-perturbative regularization of N = 2 SUSY in 4 dimensions using finite dimensional N ×N matrix algebras. Let us now consider the following bosonic actions [7]