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

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.