An Algebraic Roadmap of Particle Theories

An optimal algebraic framework of particle physics has a number of checkpoints to pass. As a minimum, models should $⟨1⟩$ conform to the Coleman-Mandula theorem (or establish a loophole), $⟨2⟩$ evade familiar fermion doubling problems, $⟨3⟩$ naturally explain the Standard Model's chirality, $⟨4⟩$ exclude B-L gauge symmetry at low energy, and $⟨5⟩$ explain the existence of three generations. The framework introduced in ref. [1] is shown to passes checkpoints $⟨1⟩,⟨2⟩,⟨3⟩,⟨4⟩$, and has yet to cross $⟨5⟩$. The discussion is concluded by elucidating an unexpected appearance of spacetime symmetries.