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

DOI:
https://doi.org/10.1090/S0273-0979-10-01294-2

Published electronically:
March 11, 2010

MathSciNet review:
2651086

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 $\textrm {Spin}(10)$, 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

Email:
baez@math.ucr.edu

**John Huerta**

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

Email:
huerta@math.ucr.edu

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