The algebra of grand unified theories

Baez, John; Huerta, John

doi:10.1090/S0273-0979-10-01294-2

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ISSN 1088-9485(online) ISSN 0273-0979(print)

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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