The Standard Model from the Shadow of a 5 Dimensional Cube

          @misc{ scivideos_PIRSA:25030186,
            doi = {10.48660/25030186},
            url = {https://pirsa.org/25030186},
            author = {Coughlin, Cole},
            keywords = {Other Physics},
            language = {en},
            title = {The Standard Model from the Shadow of a 5 Dimensional Cube},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2025},
            month = {mar},
            note = {PIRSA:25030186 see, \url{https://scivideos.org/pirsa/25030186}}
          }
          

Abstract

In this episode, we continue our exploration of Lie Groups and weight diagrams of their representations as a means of understanding the very specific field content and Gauge Groups of the Standard Model. Previously we presented a novel perspective of the Electroweak sector of the Standard Model as a shadow of 3 dimensional polytopes, which correspond to representations of a rank 3 group, and who's shadow corresponds to a specific embedding of the Electroweak Gauge Group. While interesting, we highlighted the theories inability to include colour as a simple extension, which motivated our search for higher rank unifying groups. Today, we present an algorithm for determining the Gauge quantum numbers of all SM chiral fermions from nothing but a projection of a 5 dimensional cube. We will discuss how previous unifications such as Georgi-Glashow, Pati-Salam, and others can be seen as different aspects of this rank 5 group and what conditions are used to fix the embedding corresponding to unbroken symmetries of the Standard Model. While our approach does violate common necessary conditions for Grand Unification, we use these difficulties to motivate our search for connections between the violation of spacetime symmetries such as Parity, and symmetry breaking in the Gauge sector.