https://doi.org/10.1140/epjc/s10052-025-15160-3
Regular Article - Theoretical Physics
Kaluza–Klein ansatz from Lorentzian quantum gravity on the fuzzy sphere
School of Mathematical Sciences, Queen Mary University of London, Mile End Rd, E1 4NS, London, UK
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Received:
7
November
2025
Accepted:
3
December
2025
Published online:
24
December
2025
Abstract
If Kaluza–Klein ideas were correct as an explanation of Yang–Mills and General Relativity on spacetime, the extra fibre geometry would have to be a sphere of constant size of the order of 10 Planck lengths, hence subject to quantum gravity corrections. Conversely, it was shown in previous work that modelling such corrections by noncommutative fibre coordinates indeed forces the Kaluza–Klein cylinder ansatz form of the metric, and we now propose that the remaining restrictions needed come from quantum gravity on the fibre. Working with a fuzzy sphere fibre, we find that the expected value of the metric is indeed spherical and we propose that it can be taken as of constant size due to freedom in the renormalisation of divergences. In this way, we outline a mechanism whereby the observed structure of gravity plus Yang–Mills can emerge at low energies as a consequence of quantum gravity effects.
CL was supported by a China Scholarship and SM by Leverhulme Trust project grant RPG-2024-177.
© The Author(s) 2025
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