An Algebraic Roadmap of Particle Theories

Since the 1970s, physicists have worked to fuse the fragmented pieces of the Standard Model of particle physics into something known as a (grand) unified theory. In this context, six models have appeared again and again over the last fifty years. They are known as the Spin(10) model, the Georgi-Glashow model, the Pati-Salam model, the Left-Right Symmetric model, the Standard Model pre-Higgs, and the Standard Model post-Higgs. In recent work, we have demonstrated that these six models are in fact each related to one another in algebraic cascades. Specifically, we have shown that it is possible to move from one theory to the next by considering a form of reflection that generalizes the notion of complex conjugation.