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 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 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 SU(8) family unification with boson–fermion balance

2014 ◽  
Vol 29 (22) ◽  
pp. 1450130 ◽  
Author(s):  
Stephen L. Adler
Keyword(s):  
Perturbation Theory ◽  
Standard Model ◽  
Symmetry Breaking ◽  
Gauge Field ◽  
Gauge Coupling ◽  
Dynamical Symmetry ◽  
Gauge Fields ◽  
Yukawa Couplings ◽  
Gauge Symmetries ◽  
The Standard Model

We formulate an SU(8) family unification model motivated by requiring that the theory should incorporate the graviton, gravitinos, and the fermions and gauge fields of the standard model, with boson–fermion balance. Gauge field SU(8) anomalies cancel between the gravitinos and spin ½ fermions. The 56 of scalars breaks SU(8) to SU(3) family × SU(5) × U(1)/Z5, with the fermion representation content needed for "flipped" SU(5) with three families, and with residual scalars in the 10 and [Formula: see text] representations that break flipped SU(5) to the standard model. Dynamical symmetry breaking can account for the generation of 5 representation scalars needed to break the electroweak group. Yukawa couplings of the 56 scalars to the fermions are forbidden by chiral and gauge symmetries, so in the first stage of SU(8) breaking fermions remain massless. In the limit of vanishing gauge coupling, there are N = 1 and N = 8 supersymmetries relating the scalars to the fermions, which restrict the form of scalar self-couplings and should improve the convergence of perturbation theory, if not making the theory finite and "calculable." In an Appendix we give an analysis of symmetry breaking by a Higgs component, such as the (1, 1)(-15) of the SU(8) 56 under SU(8) ⊃ SU(3) × SU(5) × U(1), which has nonzero U(1) generator.

scholarly journals Chiral anomaly in SU(2)R-axion inflation and the new prediction for particle cosmology

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Azadeh Maleknejad
Keyword(s):  
Standard Model ◽  
Symmetry Breaking ◽  
Particle Physics ◽  
Cosmological Parameters ◽  
Chiral Anomaly ◽  
Dark Matter Candidate ◽  
Neutrino Sector ◽  
Matter Creation ◽  
The Standard Model ◽  
Non Gaussian

Abstract Upon embedding the axion-inflation in the minimal left-right symmetric gauge extension of the SM with gauge group SU(2)L × SU(2)R × U(1)B−L, [1] proposed a new particle physics model for inflation. In this work, we present a more detailed analysis. As a compelling consequence, this setup provides a new mechanism for simultaneous baryogenesis and right-handed neutrino creation by the chiral anomaly of WR in inflation. The lightest right-handed neutrino is the dark matter candidate. This setup has two unknown fundamental scales, i.e., the scale of inflation and left-right symmetry breaking SU(2)R × U(1)B−L→ U(1)Y. Sufficient matter creation demands the left-right symmetry breaking scale happens shortly after the end of inflation. Interestingly, it prefers left-right symmetry breaking scales above 1010 GeV, which is in the range suggested by the non-supersymmetric SO(10) Grand Unified Theory with an intermediate left-right symmetry scale. Although WR gauge field generates equal amounts of right-handed baryons and leptons in inflation, i.e. B − L = 0, in the Standard Model sub-sector B − LSM ≠ 0. A key aspect of this setup is that SU(2)R sphalerons are never in equilibrium, and the primordial B − LSM is conserved by the Standard Model interactions. This setup yields a deep connection between CP violation in physics of inflation and matter creation (visible and dark); hence it can naturally explain the observed coincidences among cosmological parameters, i.e., ηB ≃ 0.3Pζ and ΩDM ≃ 5ΩB. The new mechanism does not rely on the largeness of the unconstrained CP-violating phases in the neutrino sector nor fine-tuned masses for the heaviest right-handed neutrinos. The SU(2)R-axion inflation comes with a cosmological smoking gun; chiral, non-Gaussian, and blue-tilted gravitational wave background, which can be probed by future CMB missions and laser interferometer detectors.

Flavons and LFV decays and productions of pseudoscalar mesons

2019 ◽  
Vol 34 (35) ◽  
pp. 1950288
Author(s):  
Tian-Qi Li ◽  
Chong-Xing Yue
Keyword(s):  
Standard Model ◽  
Symmetry Breaking ◽  
Flavor Symmetry ◽  
Lepton Flavor ◽  
Flavor Changing ◽  
Pseudoscalar Mesons ◽  
The Standard Model

Flavons are the dynamic agent of flavor symmetry breaking and have flavor changing couplings to the Standard Model (SM) fermions. We consider their contributions to the lepton flavor violating (LFV) decays [Formula: see text] and [Formula: see text] with [Formula: see text], [Formula: see text] or [Formula: see text] and [Formula: see text] in the simplest flavon model without Higgs-flavon mixing. We find that flavons can produce significant contributions to some of these LFV decay processes.

scholarly journals STRINGS, NONCOMMUTATIVE GEOMETRY AND THE SIZE OF THE TARGET SPACE

1999 ◽  
Vol 14 (28) ◽  
pp. 4501-4517 ◽  
Author(s):  
FEDELE LIZZI
Keyword(s):  
String Theory ◽  
Dirac Operator ◽  
Noncommutative Geometry ◽  
Low Energy ◽  
Target Space ◽  
World Sheet ◽  
Crucial Point ◽  
Spectral Action ◽  
Energy Eigenvalues ◽  
The World

We describe how the presence of the antisymmetric tensor (torsion) on the world sheet action of string theory renders the size of the target space a gauge noninvariant quantity. This generalizes the R ↔ 1/R symmetry in which momenta and windings are exchanged, to the whole O(d,d,ℤ). The crucial point is that, with a transformation, it is possible always to have all of the lowest eigenvalues of the Hamiltonian to be momentum modes. We interpret this in the framework of noncommutative geometry, in which algebras take the place of point spaces, and of the spectral action principle for which the eigenvalues of the Dirac operator are the fundamental objects, out of which the theory is constructed. A quantum observer, in the presence of many low energy eigenvalues of the Dirac operator (and hence of the Hamiltonian) will always interpreted the target space of the string theory as effectively uncompactified.

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