The standard model, left/right symmetry, and the "magic square"

          @misc{ scivideos_PIRSA:21050005,
            doi = {10.48660/21050005},
            url = {https://pirsa.org/21050005},
            author = {Boyle, Latham},
            keywords = {Mathematical physics, Particle Physics, Quantum Fields and Strings},
            language = {en},
            title = {The standard model, left/right symmetry, and the "magic square"},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2021},
            month = {may},
            note = {PIRSA:21050005 see, \url{https://scivideos.org/pirsa/21050005}}
          }
          

Abstract

Recently, an intriguing connection between the exceptional Jordan algebra h_3(O) and the standard model of particle physics was noticed by Dubois-Violette and Todorov (with further interpretation by Baez). How do the standard model fermions fit into this story? I will explain how they may be neatly incorporated by complexifying h_3(O) or, relatedly, by passing from RxO to CxO in the so-called "magic square" of normed division algebras. This, in turn, suggests that the standard model, with gauge group SU(3)xSU(2)xU(1), is embedded in a left/right-symmetric theory, with gauge group SU(3)xSU(2)xSU(2)xU(1). This theory is not only experimentally viable, but offers some explanatory advantages over the standard model (including an elegant solution to the standard model's "strong CP problem"). Ramond's formulation of the magic square, based on triality, provides further insights, and possible hints about where to go next.