Noncommutative standard model

In theoretical particle physics, the non-commutative Standard Model (best known as Spectral Standard Model ^{[1] [2]} ), is a model based on noncommutative geometry that unifies a modified form of general relativity with the Standard Model (extended with right-handed neutrinos).

The model postulates that space-time is the product of a 4-dimensional compact spin manifold ${\displaystyle {\mathcal {M}}}$ by a finite space ${\displaystyle {\mathcal {F}}}$. The full Lagrangian (in Euclidean signature) of the Standard model minimally coupled to gravity is obtained as pure gravity over that product space. It is therefore close in spirit to Kaluza–Klein theory but without the problem of massive tower of states.

The parameters of the model live at unification scale and physical predictions are obtained by running the parameters down through renormalization.

It is worth stressing that it is more than a simple reformation of the Standard Model. For example, the scalar sector and the fermions representations are more constrained than in effective field theory.