Pseudo-Riemannian structures in Pati-Salam models

Bochniak, Arkadiusz; Williams, Thomas; Zalecki, Paweł

doi:10.1007/jhep07(2020)072

Cited by 3 publications

(4 citation statements)

References 28 publications

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“…Furthermore, possible relations of non-product geometries with bundle-like structures over noncommutative manifolds [26] as well to the inclusion of gravity for this non-product geometry (see [27] for a link between nonproduct geometries and gravity) shall also be explored and examined. Finally, it shall be interesting to see possible extensions of the model, both in the direction of scalar conformal modifications that can help to fix the Higgs mass as well as extensions of the Pati-Salam type [28,29].…”

Section: Discussionmentioning

confidence: 99%

Spectral geometry for the standard model without fermion doubling

Bochniak

Sitarz

2020

Phys. Rev. D

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We propose a simple model of noncommutative geometry to describe the structure of the Standard Model, which satisfies spin c condition, has no fermion doubling, does not lead to the possibility of color symmetry breaking and explains the CP-violation as the failure of the reality condition for the Dirac operator. I. INTRODUCTIONThe Standard Model of particle interactions is certainly one of the most successful and best tested theory about the fundamental constituents of matter and the forces between them.Even though we still have no satisfactory description of the strong interactions in low-energy regime and there are some puzzles concerning masses and character of neutrinos as well as there are some experimental signs that could point out to new physics, the Standard Model appears to be robust and verified. Yet neither the content of fermion sector, the mixing between the families and the fundamentally different character of the Higgs boson from other gauge bosons appear to have a satisfactory geometrical explanation.One of the few theories that aimed to provide a sound geometrical basis for the structure of the Standard Model, explaining the appearance of the Higgs and symmetry-breaking potential, was noncommutative geometry (see [1][2][3]). Constructed with the core idea that spaces with points can be replaced with algebras provided a plausible explanation of the gauge group of the Standard Model and the particles in its representation as linked to the unitary group of a finite-dimensional algebra. Merged with the Kaluza-Klein idea that the physical spacetime has extra dimensions, the geometry of the finite-dimensional algebra (in the noncommutative sense) gave rise to the Higgs field understood as a connection, and the Higgs symmetry-breaking potential appeared as the usual Yang-Mills term in the action.The original model, which is based on the construction of a product geometry, with the resulting geometry being the tensor product of a usual "commutative" space with the finitedimensional noncommutative geometry suffers from two problems. Firstly, in the original

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Section: Discussionmentioning

confidence: 99%

Spectral geometry for the standard model without fermion doubling

Bochniak

Sitarz

2020

Phys. Rev. D

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“…In this section, we briefly discuss a method that allows for the reduction of possible Dirac operators describing the content of the Standard Model and its extension. This discussion is mostly based on the results obtained in [32][33][34]. We work here only with finite spectral triples.…”

Section: Towards Pseudo-riemannian Spectral Triplesmentioning

confidence: 99%

“…The above analysis was extended in [34] to the family of Pati-Salam models. They are potential extensions of the Standard Model with the gauge group 𝑆𝑈 (2) × 𝑆𝑈 (2) × 𝑆𝑈 (4).…”

Section: Pos(modave2022)001mentioning

confidence: 99%

Modave lectures on Noncommutative Geometry and its applications to physics

Bochniak¹

2023

Proceedings of Modave Summer School in Mathematical Physics — PoS(Modave2022)

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“…Furthermore, possible relations of non-product geometries with bundle-like structures over noncommutative manifolds [30] as well to the inclusion of gravity for this non-product geometry (see [31] for a link between nonproduct geometries and gravity) shall also be explored and examined. Finally, it shall be interesting to see possible extensions of the model, both in the direction of scalar conformal modifications that can help to fix the Higgs mass as well as extensions of the Pati-Salam type [32,33].…”

Section: Jhep12(2021)142mentioning

confidence: 99%

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

Bochniak

Sitarz

Zalecki

2021

J. High Energ. Phys.

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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.

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Pseudo-Riemannian structures in Pati-Salam models

Cited by 3 publications

References 28 publications

Spectral geometry for the standard model without fermion doubling

Spectral geometry for the standard model without fermion doubling

Modave lectures on Noncommutative Geometry and its applications to physics

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

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