Clifford Structures in Noncommutative Geometry and the Extended Scalar Sector

TL;DR

This paper explores how incorporating Clifford structures into noncommutative geometry's spectral action extends the scalar sector of the standard model, potentially leading to new phenomenological insights and scalar fields.

Contribution

It demonstrates that Clifford structures naturally extend the scalar sector in noncommutative geometry, revealing new scalar fields and clarifying the fermionic doubling phenomenon.

Findings

Extended scalar sector includes new fields with weak isospin and color.

Fermionic doubling is a meaningful feature, not just spurious degrees of freedom.

New scalar fields influence the spectral action without affecting fermionic dynamics.

Abstract

We consider aspects of the noncommutative approach to the standard model based on the spectral action principle. We show that as a consequence of the incorporation of the Clifford structures in the formalism, the spectral action contains an extended scalar sector, with respect to the minimal Standard Model. This may have interesting phenomenological consequences. Some of these new scalar fields carry both weak isospin and colour indexes. We calculate the new terms in spectral action due to the presence of these fields. Our analysis demonstrates that the fermionic doubling in the noncommutative geometry is not just a presence of spurious degrees of freedom, but it is an interesting and peculiar property of the formalism, which leads to physically valuable conclusions. Some of the new fields do not contribute to the physical fermionic action, but they appear in the bosonic spectral action. Their contributions to the Dirac operator correspond to couplings with the spurious fermions, which are projected out.