A Proposal for a Non-Perturbative Regularization of {\cal N}=2 SUSY 4D Gauge Theory

TL;DR

This paper proposes a non-perturbative regularization method for four-dimensional { m N}=2 supersymmetric U(n) gauge theories using matrix models and fuzzy manifolds, enabling the recovery of exact SUSY and smooth geometry in certain limits.

Contribution

It introduces a novel regularization approach for { m N}=2 SUSY gauge theories via matrix models, capturing SUSY and geometry non-perturbatively.

Findings

Exact SUSY recovered in large N limits

Smooth geometry of R^4_{theta} obtained

Matrix models approximate supersymmetric geometries

Abstract

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 non-perturbative regularization of {\cal 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 R^4_{theta}.