Clifford-based spectral action and renormalization group analysis of the gauge couplings

Abstract

The Spectral Action Principle in noncommutative geometry derives the actions of the Standard Model and General Relativity (along with several other gravitational terms) by reconciling them in a geometric setting, and hence offers an explanation for their common origin. However, one of the requirements in the minimal formalism, unification of the gauge coupling constants, is not satisfied, since the basic construction does not introduce anything new that can change the renormalization group (RG) running of the Standard Model. On the other hand, it has been recently argued that incorporating structure of the Clifford algebra into the finite part of the spectral triple, the main object that encodes the complete information of a noncommutative space, gives rise to five additional scalar fields in the basic framework. We investigate whether these scalars can help to achieve unification. We perform a RG analysis at the one-loop level, allowing possible mass values of these scalars to float from the electroweak scale to the putative unification scale. We show that out of twenty configurations of mass hierarchy in total, there does not exist even a single case that can lead to unification. In consequence, we confirm that the spectral action formalism requires a model-construction scheme beyond the (modified) minimal framework.

arXiv comment20 pages, 1 figure, 1 table of results; matches the published version

References in corpus (30)

• Heat kernel expansion: user's manual
• Test of lepton universality using $B^{+}\to K^{+}{\ell }^{+}{\ell }^{-}$ decays
• Evidence for an excess of B -> D(*) Tau Nu decays
• Gravity coupled with matter and foundation of non-commutative geometry
• Measurement of an Excess of B -> D(*) Tau Nu Decays and Implications for Charged Higgs Bosons
• The Spectral Action Principle
• Measurement of the branching ratio of $\bar{B}\to D^{(\ast )}{\tau }^{-}{\bar{\nu }}_{\tau }$ relative to $\bar{B}\to D^{(\ast )}{\ell }^{-}{\bar{\nu }}_{\ell }$ decays with hadronic tagging at Belle
• Measurement of the ratio of branching fractions $\mathcal{B}({\overline{B}}^0\to D^{\ast +}{\tau }^{-}{\overline{\nu }}_{\tau })/\mathcal{B}({\overline{B}}^0\to D^{\ast +}{\mu }^{-}{\overline{\nu }}_{\mu })$
• Measurement of the $\tau$ lepton polarization and $R(D^{\ast })$ in the decay $\bar{B}\to D^{\ast }{\tau }^{-}{\bar{\nu }}_{\tau }$
• Gravity and the standard model with neutrino mixing
• Measurement of the branching ratio of ${\bar{B}}^0\to D^{\ast +}{\tau }^{-}{\bar{\nu }}_{\tau }$ relative to ${\bar{B}}^0\to D^{\ast +}{\ell }^{-}{\bar{\nu }}_{\ell }$ decays with a semileptonic tagging method
• Measurement of the ratio of the $B^0\to D^{\ast -}{\tau }^{+}{\nu }_{\tau }$ and $B^0\to D^{\ast -}{\mu }^{+}{\nu }_{\mu }$ branching fractions using three-prong $\tau$-lepton decays
• Test of Lepton Flavor Universality by the measurement of the $B^0\to D^{\ast -}{\tau }^{+}{\nu }_{\tau }$ branching fraction using three-prong $\tau$ decays
• A Universal Action Formula
• Why the Standard Model
• Resilience of the Spectral Standard Model
• Noncommutative Geometry as a Framework for Unification of all Fundamental Interactions including Gravity. Part I
• Beyond the Spectral Standard Model: Emergence of Pati-Salam Unification
• Inner Fluctuations in Noncommutative Geometry without the first order condition
• Grand Unification in the Spectral Pati-Salam Model
• Gauge Coupling Unification in Left-Right Symmetric Models
• Wick Rotation and Fermion Doubling in Noncommutative Geometry
• $B$-decay anomalies and scalar leptoquarks in unified Pati-Salam models from noncommutative geometry
• Pati-Salam Unification from Non-commutative Geometry and the TeV-scale $W_R$ boson
• The Standard Model in Noncommutative Geometry and Morita equivalence
• The 750 GeV diphoton excess in unified $SU(2{)}_L\times SU(2{)}_R\times SU(4)$ models from noncommutative geometry
• Spectral Action in Noncommutative Geometry
• Clifford Structures in Noncommutative Geometry and the Extended Scalar Sector
• Unification of Coupling Constants, Dimension six Operators and the Spectral Action
• LHC probes of TeV-scale scalars in $\mathrm{SO}(10)$ grand unification

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• A survey of spectral models of gravity coupled to matter
• Spectral Noncommutative Geometry, Standard Model and all that