Division algebraic symmetry breaking

          @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.