A nonperturbative regularization of the supersymmetric Schwinger model

TL;DR

This paper demonstrates that noncommutative geometry can serve as a nonperturbative regularization method for supersymmetric gauge theories, preserving supersymmetry and gauge symmetry with finite degrees of freedom.

Contribution

It introduces a nonperturbative regularization approach using noncommutative geometry that maintains supersymmetry and gauge invariance in supersymmetric gauge theories.

Findings

Noncommutative geometry preserves supersymmetry during regularization.

Finite degrees of freedom are achieved without breaking symmetries.

Detailed example of N=1 U(1) supergauge theory on the sphere.

Abstract

It is shown that noncommutative geometry is a nonperturbative regulator which can manifestly preserve a space supersymmetry and a supergauge symmetry while keeping only a finite number of degrees of freedom in a theory. The simplest N=1 case of an U(1) supergauge theory on the sphere is worked out in detail.