PIRSA:21030013 Conference Mathematical physics Particle Physics Quantum Fields and Strings

DOI10.48660/21030013

Conference/School: Octonions and the Standard Model

Furey, C. & Hughes, M. (2021). Division algebraic symmetry breaking. Perimeter Institute. https://pirsa.org/21030013

Furey, Cohl, and Mia Hughes. Division algebraic symmetry breaking. Perimeter Institute, Mar. 15, 2021, https://pirsa.org/21030013 

@misc{ pirsa_PIRSA:21030013,
  doi = {10.48660/21030013},
  url = {https://pirsa.org/21030013},
  author = {Furey, Cohl and Hughes, Mia},
  keywords = {Mathematical physics, Particle Physics, Quantum Fields and Strings},
  language = {en},
  title = {Division algebraic symmetry breaking},
  publisher = {Perimeter Institute},
  year = {2021},
  month = {mar},
  note = {PIRSA:21030013 see, \url{https://pirsa.org}}
}

Abstract

Can the 32C-dimensional algebra R(x)C(x)H(x)O offer anything new for particle physics? Indeed it can. Here we identify a sequence of complex structures within R(x)C(x)H(x)O which sets in motion a cascade of breaking symmetries: Spin(10) -> Pati-Salam -> Left-Right symmetric -> Standard model + B-L (both pre- and post-Higgs-mechanism). These complex structures derive from the octonions, then from the quaternions, then from the complex numbers. Finally, we describe a left-right symmetric Higgs system which exhibits, we believe for the first time, an explicit demonstration of quaternionic triality.

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