The Algebra of Grand Unified Theories
read the original abstract
The Standard Model of particle physics may seem complicated and arbitrary, but it has hidden patterns that are revealed by the relationship between three "grand unified theories": theories that unify forces and particles by extending the Standard Model symmetry group U(1) x SU(2) x SU(3) to a larger group. These three theories are Georgi and Glashow's SU(5) theory, Georgi's theory based on the group Spin(10), and the Pati-Salam model based on the group SU(2) x SU(2) x SU(4). In this expository account for mathematicians, we explain only the portion of these theories that involves finite-dimensional group representations. This allows us to reduce the prerequisites to a bare minimum while still giving a taste of the profound puzzles that physicists are struggling to solve.
This paper has not been read by Pith yet.
Forward citations
Cited by 3 Pith papers
-
How well can the QCD axion hide?
Multi-axion models relax the E/N bound on QCD axion photon coupling and allow subdominant dark matter contribution, but an axion-like particle is typically visible to next-generation experiments.
-
A Superalgebra Within: representations of lightest standard model particles form a $\mathbb{Z}_2^5$-graded algebra
Representations of lightest Standard Model particles form a Z_2^5-graded superalgebra isomorphic to H_16(C) and generated by division algebras.
-
Octonions, complex structures and Standard Model fermions
The Standard Model gauge group is characterized as a subgroup of Spin(10) via two suitably aligned commuting complex structures on R^10 encoded in orthogonal pure spinors whose sum is pure, described efficiently with ...
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.