scholarly journals Actions for twisted spectral triple and the transition from the Euclidean to the Lorentzian

2020 ◽  
Vol 17 (supp01) ◽  
pp. 2030001
Author(s):  
Agostino Devastato ◽  
Manuele Filaci ◽  
Pierre Martinetti ◽  
Devashish Singh
Keyword(s):  
Scalar Field ◽  
Standard Model ◽  
Noncommutative Geometry ◽  
Spectral Triple ◽  
Spectral Action ◽  
Lorentzian Signature ◽  
The Standard Model ◽  
Form Field

This is a review of recent results regarding the application of Connes’ noncommutative geometry to the Standard Model, and beyond. By twisting (in the sense of Connes-Moscovici) the spectral triple of the Standard Model, one does not only get an extra scalar field which stabilises the electroweak vacuum, but also an unexpected [Formula: see text]-form field. By computing the fermionic action, we show how this field induces a transition from the Euclidean to the Lorentzian signature. Hints on a twisted version of the spectral action are also briefly mentioned.

scholarly journals A DARK SECTOR EXTENSION OF THE ALMOST-COMMUTATIVE STANDARD MODEL

2014 ◽  
Vol 29 (01) ◽  
pp. 1450005 ◽  
Author(s):  
CHRISTOPH A. STEPHAN
Keyword(s):  
Scalar Field ◽  
Standard Model ◽  
Present Model ◽  
Higgs Field ◽  
Dark Sector ◽  
Spectral Action ◽  
Scalar Particles ◽  
A Value ◽  
The Standard Model ◽  
Model C

We consider an extension of the Standard Model within the framework of Noncommutative Geometry. The model is based on an older model [C. A. Stephan, Phys. Rev. D79, 065013 (2009)] which extends the Standard Model by new fermions, a new U(1)-gauge group and, crucially, a new scalar field which couples to the Higgs field. This new scalar field allows to lower the mass of the Higgs mass from ~170 GeV, as predicted by the Spectral Action for the Standard Model, to a value of 120–130 GeV. The shortcoming of the previous model lay in its inability to meet all the constraints on the gauge couplings implied by the Spectral Action. These shortcomings are cured in the present model which also features a "dark sector" containing fermions and scalar particles.

scholarly journals Spectral action and the electroweak θ-terms for the Standard Model without fermion doubling

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
A. Bochniak ◽  
A. Sitarz ◽  
P. Zalecki
Keyword(s):  
Standard Model ◽  
Symmetry Breaking ◽  
Dirac Operator ◽  
Noncommutative Geometry ◽  
Gauge Fields ◽  
Wick Rotation ◽  
Spectral Action ◽  
Geometry Model ◽  
The Standard Model ◽  
Cp Symmetry

Abstract We compute the leading terms of the spectral action for a noncommutative geometry model that has no fermion doubling. The spectral triple describing it, which is chiral and allows for CP-symmetry breaking, has the Dirac operator that is not of the product type. Using Wick rotation we derive explicitly the Lagrangian of the model from the spectral action for a flat metric, demonstrating the appearance of the topological θ-terms for the electroweak gauge fields.

scholarly journals Spectral Noncommutative Geometry Standard Model and all that

2019 ◽  
Vol 34 (19) ◽  
pp. 1930010 ◽  
Author(s):  
Agostino Devastato ◽  
Maxim Kurkov ◽  
Fedele Lizzi
Keyword(s):  
Standard Model ◽  
Noncommutative Geometry ◽  
Beyond The Standard Model ◽  
Particle Interactions ◽  
Spectral Action ◽  
The Standard Model

We review the approach to the Standard Model of particle interactions based on spectral noncommutative geometry. The paper is (nearly) self-contained and presents both the mathematical and phenomenological aspects. In particular, the bosonic spectral action and the fermionic action are discussed in detail, and how they lead to phenomenology. We also discuss the Euclidean versus Lorentz issues and how to go beyond the Standard Model in this framework.

scholarly journals INTERNAL SPACE FOR THE NONCOMMUTATIVE GEOMETRY STANDARD MODEL AND STRINGS

2007 ◽  
Vol 22 (07) ◽  
pp. 1317-1334 ◽  
Author(s):  
FEDELE LIZZI
Keyword(s):  
String Theory ◽  
Standard Model ◽  
Noncommutative Geometry ◽  
The Other ◽  
Vertex Operators ◽  
Internal Space ◽  
Renormalization Scale ◽  
Spectral Action ◽  
The Standard Model

In this paper I discuss connections between the noncommutative geometry approach to the Standard Model on one side, and the internal space coming from strings on the other. The Standard Model in noncommutative geometry is described via the spectral action. I argue that an internal noncommutative manifold compactified at the renormalization scale, could give rise to the almost commutative geometry required by the spectral action. I then speculate how this could arise from the noncommutative geometry given by the vertex operators of a string theory.

scholarly journals The 750 GeV diphoton excess in unified SU(2)L ×SU(2)R ×SU(4) models from noncommutative geometry

2016 ◽  
Vol 31 (18) ◽  
pp. 1650101 ◽  
Author(s):  
Ufuk Aydemir ◽  
Djordje Minic ◽  
Chen Sun ◽  
Tatsu Takeuchi
Keyword(s):  
Scalar Field ◽  
Large Hadron Collider ◽  
Standard Model ◽  
Noncommutative Geometry ◽  
Cross Sections ◽  
Hadron Collider ◽  
Gauge Coupling ◽  
The Standard Model

We discuss a possible interpretation of the 750 GeV diphoton resonance, recently reported at the large hadron collider (LHC), within a class of [Formula: see text] models with gauge coupling unification. The unification is imposed by the underlying noncommutative geometry (NCG), which in these models is extended to a left–right symmetric completion of the Standard Model (SM). Within such unified [Formula: see text] models the Higgs content is restrictively determined from the underlying NCG, instead of being arbitrarily selected. We show that the observed cross-sections involving the 750 GeV diphoton resonance could be realized through a SM singlet scalar field accompanied by colored scalars, present in these unified models. In view of this result, we discuss the underlying rigidity of these models in the NCG framework and the wider implications of the NCG approach for physics beyond the SM.

scholarly journals Missing the point in noncommutative geometry

Synthese ◽  
2021 ◽  
Author(s):  
Nick Huggett ◽  
Fedele Lizzi ◽  
Tushar Menon
Keyword(s):  
Scalar Field ◽  
Noncommutative Geometry ◽  
Smooth Manifold ◽  
Operational Definition ◽  
Spectral Triple ◽  
Fundamental Quantity

AbstractNoncommutative geometries generalize standard smooth geometries, parametrizing the noncommutativity of dimensions with a fundamental quantity with the dimensions of area. The question arises then of whether the concept of a region smaller than the scale—and ultimately the concept of a point—makes sense in such a theory. We argue that it does not, in two interrelated ways. In the context of Connes’ spectral triple approach, we show that arbitrarily small regions are not definable in the formal sense. While in the scalar field Moyal–Weyl approach, we show that they cannot be given an operational definition. We conclude that points do not exist in such geometries. We therefore investigate (a) the metaphysics of such a geometry, and (b) how the appearance of smooth manifold might be recovered as an approximation to a fundamental noncommutative geometry.

scholarly journals Weak scale from Planck scale: Mass scale generation in a classically conformal two-scalar system

2020 ◽  
Vol 2020 (3) ◽  
Author(s):  
Junichi Haruna ◽  
Hikaru Kawai
Keyword(s):  
Scalar Field ◽  
Standard Model ◽  
Planck Scale ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
The Other ◽  
Expectation Value ◽  
Weak Scale ◽  
The Standard Model ◽  
The One

Abstract In the standard model, the weak scale is the only parameter with mass dimensions. This means that the standard model itself cannot explain the origin of the weak scale. On the other hand, from the results of recent accelerator experiments, except for some small corrections, the standard model has increased the possibility of being an effective theory up to the Planck scale. From these facts, it is naturally inferred that the weak scale is determined by some dynamics from the Planck scale. In order to answer this question, we rely on the multiple point criticality principle as a clue and consider the classically conformal $\mathbb{Z}_2\times \mathbb{Z}_2$ invariant two-scalar model as a minimal model in which the weak scale is generated dynamically from the Planck scale. This model contains only two real scalar fields and does not contain any fermions or gauge fields. In this model, due to a Coleman–Weinberg-like mechanism, the one-scalar field spontaneously breaks the $ \mathbb{Z}_2$ symmetry with a vacuum expectation value connected with the cutoff momentum. We investigate this using the one-loop effective potential, renormalization group and large-$N$ limit. We also investigate whether it is possible to reproduce the mass term and vacuum expectation value of the Higgs field by coupling this model with the standard model in the Higgs portal framework. In this case, the one-scalar field that does not break $\mathbb{Z}_2$ can be a candidate for dark matter and have a mass of about several TeV in appropriate parameters. On the other hand, the other scalar field breaks $\mathbb{Z}_2$ and has a mass of several tens of GeV. These results will be verifiable in near-future experiments.

scholarly journals On catalyzed vacuum decay around a radiating black hole and the crisis of the electroweak vacuum

2020 ◽  
Vol 2020 (8) ◽  
Author(s):  
Takumi Hayashi ◽  
Kohei Kamada ◽  
Naritaka Oshita ◽  
Jun’ichi Yokoyama
Keyword(s):  
Black Hole ◽  
Scalar Field ◽  
Standard Model ◽  
Decay Rate ◽  
Early Universe ◽  
Hawking Radiation ◽  
False Vacuum ◽  
Vacuum Decay ◽  
Higgs Vacuum ◽  
The Standard Model

Abstract False vacuum decay is a key feature in quantum field theories and exhibits a distinct signature in the early Universe cosmology. It has recently been suggested that the false vacuum decay is catalyzed by a black hole (BH), which might cause the catastrophe of the Standard Model Higgs vacuum if primordial BHs are formed in the early Universe. We investigate vacuum phase transition of a scalar field around a radiating BH with taking into account the effect of Hawking radiation. We find that the vacuum decay rate slightly decreases in the presence of the thermal effect since the scalar potential is stabilized near the horizon. However, the stabilization effect becomes weak at the points sufficiently far from the horizon. Consequently, we find that the decay rate is not significantly changed unless the effective coupling constant of the scalar field to the radiation is extremely large. This implies that the change of the potential from the Hawking radiation does not help prevent the Standard Model Higgs vacuum decay catalyzed by a BH.

scholarly journals WHAT KIND OF NONCOMMUTATIVE GEOMETRY FOR QUANTUM GRAVITY?

2005 ◽  
Vol 20 (17n18) ◽  
pp. 1315-1326 ◽  
Author(s):  
PIERRE MARTINETTI
Keyword(s):  
Standard Model ◽  
Quantum Gravity ◽  
Noncommutative Geometry ◽  
Thermal Time ◽  
The Standard Model

We give a brief account of the description of the standard model in noncommutative geometry as well as the thermal time hypothesis, questioning their relevance for quantum gravity.

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