Noncommutative Geometry and the Physics of the LHC Era

Abstract

Noncommutative geometry allows to unify the basic building blocks of particle physics, Yang-Mills-Higgs theory and General relativity, into a single geometrical framework. The resulting effective theory constrains the couplings of the particle model and reduces the number of degrees of freedom. After briefly introducing the basic ideas of noncommutative geometry, I will present its predictions for the Standard Model (SM) and the few known models beyond the Standard Model. Most of these models, including the Standard Model, are now ruled out by LHC data. But interesting extensions of the Standard Model which agree with the presumed Standard Model Scalar (SMS) mass and predict new particles are still very much alive and await further experimental data.

A Dark Sector Extension of the Almost-Commutative Standard Model

“…Therefore one would expect more kinetic mixing. This model will be investigated further in an upcoming publication [St13]. One could also imagine to extend the Standard Model group by a non-abelian group in the spirit of [St07] and [SS07].…”

Lorentz signature and twisted spectral triples

“…Such an outcome is difficult to achieve however as the extra geometric constraints imposed by the NCG formalism severely restrict any allowed addition to the Standard Model. Early attempts in [15,16] to generate an extra scalar field within the framework required the adjunction of new fermions. More recently, there have been a number of phenomenologically viable Standard Model extensions singled out by the NCG framework which preserve the fermionic sector.…”