Supersymmetry and noncommutative geometry Part III: The noncommutative supersymmetric Standard Model

TL;DR

This paper explores the construction of a noncommutative geometric version of the MSSM, identifying its particle content and interactions, but finds that the standard action functional is not supersymmetric.

Contribution

It applies a formalism for supersymmetric theories in noncommutative geometry to the MSSM, revealing limitations of the standard action functional.

Findings

Particle content of the noncommutative MSSM is obtained

Interactions are identified but not supersymmetric

Standard action functional does not preserve supersymmetry

Abstract

In a previous paper we developed a formalism to construct (potentially) supersymmetric theories in the context of noncommutative geometry. We apply this formalism to explore the existence of a noncommutative version of the minimal supersymmetric Standard Model (MSSM). We obtain the exact particle content of the MSSM and identify (in form) its interactions but conclude that their coefficients are such that the standard action functional used in noncommutative geometry is in fact not supersymmetric.