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Georgi statements about the symmetry breaking of $rm SO(10)$

Physics Asked on January 6, 2022

Here is a paragraph with some statements about the Gauge Symmetry Breaking from Georgi’s book Lie Algebras in Particle Physics 2nd ed — From Isospin to Unified Theories (Georgi, 1999) p.285.

Georgi wrote:

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His claim is too quick. Can some experts explain which symmetry breaking pattern he is thinking of? In particular, he uses three Higgs fields in three representations:

  • 24 should be the adjoint representation of SU(5).

  • 5 should be the fundamental representation of SU(5).

  • 45 should be EITHER the adjoint representation of SO(10) or some (what kind?) representation of SU(5).

question: How do we use representation 24, 5, and 45 to break from $SO(10)$ to $SU(5)$ to $SU(3) times SU(2) times U(1)$?

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