Clifford Structures in Noncommutative Geometry and the Extended Scalar Sector

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.

24 pages, no figures, final version, accepted for publication in PRD, references added

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Cited by in corpus (5)

• Horizon-scale tests of gravity theories and fundamental physics from the Event Horizon Telescope image of Sagittarius A${}^{\ast }$
• Lorentz signature and twisted spectral triples
• A survey of spectral models of gravity coupled to matter
• Spectral Noncommutative Geometry, Standard Model and all that
• Clifford-based spectral action and renormalization group analysis of the gauge couplings