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arXiv · 2409.06668

Fermions in the fuzzy sphere Kaluza-Klein model

Chengcheng Liu·Shahn Majid
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Abstract

We consider spinors on the total space of a Kaluza-Klein model with fuzzy sphere fibre and geometrically realised Dirac operator on the product. We show that a single massless spinor on the product appears on spacetime as multiplets of spinors with a particular signature of differing masses and $SU(2)$ Yang-Mills charges. For example, for the reduced fuzzy sphere isomorphic to $M_2(\mathbb{C})$, a massless spinor appears as two $SU(2)$ doublets and an $SU(2)$ quadruplet in mass ratios $1:5/3:7/3$. Although such signatures do not appear to exactly match the Standard Model, the paper provides proof of concept of the approach, which can be applied to other noncommutative fibre algebras.

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Chengcheng Liu, Shahn Majid. 2024-09-10. Fermions in the fuzzy sphere Kaluza-Klein model. https://arxiv.org/abs/2409.06668

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