Supersymmetric QCD in the Noncommutative Geometry

TL;DR

This paper explores the integration of supersymmetry into noncommutative geometry by proposing a new Dirac operator that respects supersymmetry and deriving the supersymmetric QCD action via the spectral action principle.

Contribution

It introduces a novel Dirac operator invariant under supersymmetry and demonstrates how supersymmetric QCD can be formulated within noncommutative geometry.

Findings

New Dirac operator invariant under supersymmetry

Spectral action correctly reproduces supersymmetric QCD

Inner automorphisms generate vector supermultiplets

Abstract

Introduction of supersymmetry into the noncommutative geometry is investigated. We propose a new Dirac operator which plays the role of the metric over the extended algebra of chiral and antichiral supermultiplets and is invariant under the supersymmetry transformations. Inner automorphisms for the algebra generate vector supermultiplets as an internal fluctuation of the metric. We show that the supersymmetric QCD action for these supermultiplets is correctly given by the spectral action principle.