Supersymmetry and the Spectral Action. On a geometrical interpretation of the MSSM

TL;DR

This thesis explores the integration of noncommutative geometry with supersymmetry, aiming to geometrically interpret the MSSM through spectral action analysis.

Contribution

It develops a framework to identify almost-commutative geometries with supersymmetric spectral actions, specifically applying this to formulate a non-commutative version of the MSSM.

Findings

Identifies conditions for supersymmetry in spectral actions

Constructs a non-commutative MSSM model

Analyzes supersymmetry breaking mechanisms

Abstract

This PhD thesis aims at combining the framework of noncommutative geometry and supersymmetry. A particular class of non-commutative geometries called almost-commutative geometries can be used to describe particle theories. This thesis contains a systematic search for such almost-commutative geometries whose corresponding spectral action exhibits supersymmetry. Chapter 2 discusses extensions of the Standard Model in the context of noncommutative geometry in general. In Chapter three a framework is developed to build and analyze potential supersymmetric theories. Chapter 4 covers supersymmetry breaking mechanisms in this context. Finally, the approach of Chapter three is applied to what is to yield the non-commutative version of the MSSM in Chapter 5.