Three generations, two unbroken gauge symmetries, and one eight-dimensional algebra

Furey, C.

doi:10.1016/j.physletb.2018.08.032

Cited by 73 publications

(97 citation statements)

References 42 publications

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“…Interestingly then, what Eq. (21) suggests is that the fundamental symmetries of S are the same as those of O, although the factor of S 3 suggests we get three copies. This is exactly what we want in order to describe the observed three generations of fermions.…”

Section: Why Sedenions?mentioning

confidence: 99%

“…Given that a considerable amount of the SM structure for a single generation of fermions can be realised in terms of the complex octonions C ⊗ O, and its associated adjoint algebra of left actions (C ⊗ O) L ∼ = C (6), a natural question is how to extend these encouraging results from a single generation to exactly three generations. Although it is possible to represent three generations of fermion states inside a single copy of C (6) [20,21], in that case the physical states are no longer the basis states of minimal left ideals as for the case of a single generation. A three generation representation in terms of C (6) therefore comes at the cost of giving up the elegant construction of minimal left ideals giving rise to a single generation.…”

Section: Introductionmentioning

confidence: 99%

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Three fermion generations with two unbroken gauge symmetries from the complex sedenions

Gillard

Gresnigt

2019

Eur. Phys. J. C

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We show that three generations of leptons and quarks with unbroken Standard Model gauge symmetry SU (3) c × U (1) em can be described using the algebra of complexified sedenions C ⊗ S. A primitive idempotent is constructed by selecting a special direction, and the action of this projector on the basis of C ⊗ S can be used to uniquely split the algebra into three complex octonion subalgebras C ⊗ O. These subalgebras all share a common quaternionic subalgebra. The left adjoint actions of the 8 C-dimensional C ⊗ O subalgebras on themselves generates three copies of the Clifford algebra C (6). It was previously shown that the minimal left ideals of C (6) describe a single generation of fermions with unbroken SU (3) c × U (1) em gauge symmetry. Extending this construction from C ⊗ O to C ⊗ S naturally leads to a description of exactly three generations.

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Section: Why Sedenions?mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Three fermion generations with two unbroken gauge symmetries from the complex sedenions

Gillard

Gresnigt

2019

Eur. Phys. J. C

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“…The deepest ideas of math, if shown to be true, would almost invariably have consequences for physics and manifest themselves in nature in general, in providing (in part) a resolution to the theoretical questions which have resonated in the physics community for some time -as echoed by Peskin 96 and Furey 78,79,ii What makes SU (3) ⊗ SU (2) ⊗ U (1) so special 78 ?…”

Section: Discussionmentioning

confidence: 99%

The underlying geometry of the CAM gauge model of the Standard Model of particle physics

Wolk¹

2020

Int. J. Mod. Phys. A

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The Composition Algebra-based Methodology (CAM) [B. Wolk, Pap. Phys. 9, 090002 (2017); Phys. Scr. 94, 025301 (2019); Adv. Appl. Clifford Algebras 27, 3225 (2017); J. Appl. Math. Phys. 6, 1537 (2018); Phys. Scr. 94, 105301 (2019), Adv. Appl. Clifford Algebras 30, 4 (2020)], which provides a new model for generating the interactions of the Standard Model, is geometrically modeled for the electromagnetic and weak interactions on the parallelizable sphere operator fiber bundle [Formula: see text] consisting of base space, the tangent bundle [Formula: see text] of space–time [Formula: see text], projection operator [Formula: see text], the parallelizable spheres [Formula: see text] conceived as operator fibers [Formula: see text] attaching to and operating on [Formula: see text] [Formula: see text] as [Formula: see text] varies over [Formula: see text], and as structure group, the norm-preserving symmetry group [Formula: see text] for each of the division algebras which is simultaneously the isometry group of the associated unit sphere. The massless electroweak [Formula: see text] Lagrangian is shown to arise from [Formula: see text]’s generation of a local coupling operation on sections of Dirac spinor and Clifford algebra bundles over [Formula: see text]. Importantly, CAM is shown to be a new genre of gauge theory which subsumes Yang–Mills Standard Model gauge theory. Local gauge symmetry is shown to be at its core a geometric phenomenon inherent to CAM gauge theory. Lastly, the higher-dimensional, topological architecture which generates CAM from within a unified eleven [Formula: see text]-dimensional geometro-topological structure is introduced.

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“…9 In addition to top quark condensation, the model involves tau neutrino and tau lepton condensations as well. The approach is based on the framework of Clifford algebra Cℓ 0, 6 10 (note that there is an interesting connection between Clifford algebra Cl (6) and octonions via left-action maps 11 ), whereby standard model fermions are represented by algebraic spinors. There are two global chiral symmetries on top of the local gauge symmetries.…”

Section: Introductionmentioning

confidence: 99%

Dynamical symmetry breaking and negative cosmological constant

Lu¹

2019

Int. J. Mod. Phys. A

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In the context of Clifford functional integral formalism, we revisit the Nambu-Jona-Lasinio-type dynamical symmetry breaking model and examine the properties of the dynamically generated composite bosons. Given that the model with 4-fermion interactions is nonrenormalizable in the traditional sense, the aim is to gain insight into the divergent integrals without resorting to explicit regularization. We impose a restriction on the linearly divergent primitive integrals, thus resolving the long-standing issue of momentum routing ambiguity associated with fermion-antifermion condensations. The removal of the ambiguity paves the way for the possible calculation of the true ratio of Higgs boson mass to top quark mass in the top condensation model. In this paper, we also investigate the negative vacuum energy resulted from dynamical symmetry breaking and its cosmological implications. In the framework of modified Einstein-Cartan gravity, it is demonstrated that the late-time acceleration is driven by a novel way of embedding the Hubble parameter into the Friedmann equation via an interpolation function, whereas the dynamically generated negative cosmological constant only plays a minor role for the current epoch. Two cosmic scenarios are proposed, with one of which suggesting that the universe may have been evolving from an everlasting coasting state towards the accelerating era characterized by the deceleration parameter approaching -0.5 at low redshift. One inevitable outcome of the modified Friedmannian cosmology is that the directly measured local Hubble parameter should in general be larger than the Hubble parameter calibrated from the conventional Friedmann equation. This Hubble tension becomes more pronounced when the Hubble parameter is comparable or less than a characteristic Hubble scale.

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Three generations, two unbroken gauge symmetries, and one eight-dimensional algebra

Cited by 73 publications

References 42 publications

Three fermion generations with two unbroken gauge symmetries from the complex sedenions

Three fermion generations with two unbroken gauge symmetries from the complex sedenions

The underlying geometry of the CAM gauge model of the Standard Model of particle physics

Dynamical symmetry breaking and negative cosmological constant

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