Gravity and the standard model with neutrino mixing

Alain Connes; Ali H. Chamseddine; Matilde Marcolli

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Gravity and the standard model with neutrino mixing

Ali H. Chamseddine, Alain Connes, Matilde Marcolli

High Energy Physics - Theory · Submitted 23 Oct 2006

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We present an effective unified theory based on noncommutative geometry for the standard model with neutrino mixing, minimally coupled to gravity.

how it is stated · asserted 1.00 read the record →

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arXiv IDhep-th/0610241 (version 1)

Pith IDOFWQCEX2, Pith's permanent record of this paper and its review

CitationAlain Connes, Ali H. Chamseddine, Matilde Marcolli. "Gravity and the standard model with neutrino mixing." arXiv:hep-th/0610241 (2006). https://pith.science/paper/OFWQCEX2

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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,611 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.07 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.98 · compares with prior results 0.27 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

We present an effective unified theory based on noncommutative geometry for the standard model with neutrino mixing, minimally coupled to gravity. The unification is based on the symplectic unitary group in Hilbert space and on the spectral action. It yields all the detailed structure of the standard model with several predictions at unification scale. Besides the familiar predictions for the gauge couplings as for GUT theories, it predicts the Higgs scattering parameter and the sum of the squares of Yukawa couplings. From these relations one can extract predictions at low energy, giving in particular a Higgs mass around 170 GeV and a top mass compatible with present experimental value. The geometric picture that emerges is that space-time is the product of an ordinary spin manifold (for which the theory would deliver Einstein gravity) by a finite noncommutative geometry F. The discrete space F is of KO-dimension 6 modulo 8 and of metric dimension 0, and accounts for all the intricacies of the standard model with its spontaneous symmetry breaking Higgs sector.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We present an effective unified theory based on noncommutative geometry for the standard model with neutrino mixing, minimally coupled to gravity.	contribution 1.00	0.93	0.40	asserted 1.00
s1	The unification is based on the symplectic unitary group in Hilbert space and on the spectral action.	method 0.91	0.54	0.09	asserted 1.00
s2	It yields all the detailed structure of the standard model with several predictions at unification scale.	result 0.79	0.85	0.30	asserted 1.00
s3	Besides the familiar predictions for the gauge couplings as for GUT theories, it predicts the Higgs scattering parameter and the sum of the squares of Yukawa couplings.	result 0.96	0.83	0.14	asserted 1.00
s4	From these relations one can extract predictions at low energy, giving in particular a Higgs mass around 170 GeV and a top mass compatible with present experimental value.	result 1.00	0.85	0.21	asserted 0.82
s5	The geometric picture that emerges is that space-time is the product of an ordinary spin manifold (for which the theory would deliver Einstein gravity) by a finite noncommutative geometry F.	interpretation 0.89	0.69	0.13	asserted 0.99
s6	The discrete space F is of KO-dimension 6 modulo 8 and of metric dimension 0, and accounts for all the intricacies of the standard model with its spontaneous symmetry breaking Higgs sector.	interpretation 0.72	0.68	0.13	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.98.

What was examined, and what was not

sources read

arXiv listing abstract v1

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

We present an effective unified theory based on noncommutative geometry for the standard model with neutrino mixing, minimally coupled to gravity. The unification is based on the symplectic unitary group in Hilbert space and on the spectral action. It yields all the detailed structure of the standard model with several predictions at unification scale. Besides the familiar predictions for the gauge couplings as for GUT theories, it predicts the Higgs scattering parameter and the sum of the squares of Yukawa couplings. From these relations one can extract predictions at low energy, giving in particular a Higgs mass around 170 GeV and a top mass compatible with present experimental value. The geometric picture that emerges is that space-time is the product of an ordinary spin manifold (for which the theory would deliver Einstein gravity) by a finite noncommutative geometry F. The discrete space F is of KO-dimension 6 modulo 8 and of metric dimension 0, and accounts for all the intricacies of the standard model with its spontaneous symmetry breaking Higgs sector.

Human review

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References

Forward citations

Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

On the spectral characterization of manifolds
math.OA 2008-10 conditional novelty 9.0 of 10

Five spectral axioms, strengthened by strong regularity and an antisymmetric cycle, force a commutative spectral triple to come from a smooth compact oriented manifold.
The CKM sector of the exceptional-Jordan programme: finite-Dirac mass moduli, two conditional angle estimates, and the weak-to-mass bridge
hep-ph 2026-08 conditional novelty 6.0 of 10

A conditional algebraic scheme derives two CKM entries and a mass-ratio operator from octonionic chains, but the setup leaves two angles fitted and the key suppression rule unproven.
Neutron star mergers as a probe of modifications of general relativity with finite-range scalar forces
gr-qc 2017-09 conditional novelty 6.0 of 10

Fully relativistic simulations of binary neutron star mergers in R-squared gravity show that a scalar force shorter than the neutron star leaves the inspiral nearly unchanged but shifts the post-merger gravitational w...
Fractal space-times under the microscope: A Renormalization Group view on Monte Carlo data
hep-th 2011-10 conditional novelty 6.0 of 10

Asymptotically safe quantum gravity predicts three scaling regimes for the spectral dimension of spacetime, and a two-parameter fit to 3D CDT data matches to about 1%, placing the simulations on the classical-to-semi-...
Spontaneous Symmetry Breakdown and Critical Perspectives of Higgs Mechanism
hep-ph 2006-03 unverdicted novelty 2.0 of 10

A review of the Higgs mechanism and mass generation that speculates, using the authors' earlier scalar-tensor gravity model, that Higgs bosons may couple only gravitationally.

How later papers used it

72 later papers cite it

Evidence: substantial. 70 of the citing papers share no author with it, and 9 of those carry a confident label from Pith's citation classifier.

Pith read 31 of the 193 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

1 later paper by other authors is listed below: 1 used its data or values.

Uses its data or values 1 paper

Used the minor mismatch between observed and predicted U(1) coupling constant shown in this paper's Figure 1 to suggest some new physics in the desert.

Non-compact spectral triples with finite volume (2009) · 0.80 · paraphrased: the licence does not allow quoting

How the literature uses it

64 arXiv papers cite this in 165 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 112 sentences without a confident label

Contests it 1 paper

Unfortunately, the restrictions of the running of the couplings, found in the literature [ref] , have neglected the nonminimal coupling of the Higgs to the geometry, which as we have seen is indeed crucial for the inflation to be successful.

Natural inflation mechanism in asymptotic noncommutative geometry · Elements of NCG · contest 0.80

Uses its method or tool 1 paper

Using the heat kernel method, the bosonic part of the spectral action can be expanded in powers of the scale $Λ$ in the form [ref]

Cosmological consequences of the noncommutative spectral geometry as an approach to unification · NCG spectral action · 0.85

Uses its data or values 1 paper

The minor mismatch between observed and predicted $U(1)$ coupling constant (see Figure 1 in [ref] ) might suggest some new physics in the desert.

Non-compact spectral triples with finite volume · Introduction · 0.80

Compares with it 4 papers

The extra-dimensional matrices are assumed to have a finite spectrum and no massless modes, similar in a sense to Connes approach to the standard model in noncommutative geometry [ref] .

Noncommutative gauge theory and symmetry breaking in matrix models · Introduction · 0.91
Fermions, gauge fields and Higgs field are all massive, with the Higgs mass slightly smaller than the prediction from noncommutative geometry [ref] .

Non-compact spectral triples with finite volume · Field equations · 0.94
The non-commutative geometrical approach has the virtue of preserving only universal terms in the induced action following the process of integrating out gravitational degrees of freedom [ref] , where as our result leaves a non-universal operator.

Pure gauge theory for the gravitational spin connection · Discussion · 1.00

Cites it as background 33 papers

I will focus on a model proposed by Connes and collaborators [ref] , aiming at describing the Standard Model of particle physics coupled with gravity.

Cosmological consequences of the NonCommutative Geometry Spectral Action · Introduction · 0.85
We do this using the spectral properties of the (generalized) Dirac operator, and in this respect this work can be seen in the framework of Connes and collaborators approach to the standard model [ref] , as well as of Sakharov induced gravity [ref] (for a modern review see [ref] ).

Spectral Action from Anomalies · Introduction · 0.90
The final version of the bosonic spectral action is given as [ref]

Clifford-based spectral action and renormalization group analysis of the gauge couplings · The minimal spectral action · 0.84

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