Three generations, two unbroken gauge symmetries, and one eight-dimensional algebra
Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
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Furey, C. (2018). Three generations, two unbroken gauge symmetries, and one eight-dimensional algebra. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, 785 84-89. https://doi.org/10.1016/j.physletb.2018.08.032
A considerable amount of the standard model's three-generation structure can be realised from just the 8C-dimensional algebra of the complex octonions. Indeed, it is a little-known fact that the complex octonions can generate on their own a 64C-dimensional space. Here we identify an su(3) + u(1) action which splits this 64C-dimensional space into complexi ed generators of SU(3), together with 48 states. These 48 states exhibit the behaviour of exactly three generations of quarks and leptons under the standard model's two unbroken gauge symmetries. This article builds on a previous one, , by incorporating electric charge.
This work has been partially supported by STFC consolidated grant ST/P000681/1. The au- thor is furthermore grateful for support from the NSERC Postdoctoral Fellowship, and from the Walter Grant Scott Research Fellowship in Physics at Trinity Hall, Uni- versity of Cambridge.
External DOI: https://doi.org/10.1016/j.physletb.2018.08.032
This record's URL: https://www.repository.cam.ac.uk/handle/1810/286191
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Licence URL: https://creativecommons.org/licenses/by/4.0/