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The algebra of grand unified theories

Authors: John Baez and John Huerta
Journal: Bull. Amer. Math. Soc. 47 (2010), 483-552
MSC (2000): Primary 20C35, 81R05; Secondary 81-02
Published electronically: March 11, 2010
MathSciNet review: 2651086
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Abstract: The Standard Model is the best tested and most widely accepted theory of elementary particles we have today. It 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 $ \mathrm{U}(1) \times \mathrm{SU}(2) \times \mathrm{SU}(3)$ to a larger group. These three are Georgi and Glashow's $ \mathrm{SU}(5)$ theory, Georgi's theory based on the group $ \Spin(10)$, and the Pati-Salam model based on the group $ \mathrm{SU}(2) \times \mathrm{SU}(2) \times \mathrm{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.

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Additional Information

John Baez
Affiliation: Department of Mathematics, University of California, Riverside, California 92521

John Huerta
Affiliation: Department of Mathematics, University of California, Riverside, California 92521

Keywords: Grand unified theory, standard model, representation theory
Received by editor(s): May 8, 2009
Received by editor(s) in revised form: October 16, 2009
Published electronically: March 11, 2010
Additional Notes: This research was supported by a grant from the Foundational Questions Institute.
Article copyright: © Copyright 2010 John C. Baez and John Huerta