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

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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:

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 $$SU(3) \times SU(2) \times U(1)$$?

This post imported from StackExchange Physics at 2020-12-01 17:43 (UTC), posted by SE-user annie marie heart
It's all in Slansky, equation (3.4) and Table 43 but you must learn the language... The WP article on the SO(10) GUT: the antisym 45 of SO(10) breaks it down to SU(5) GG and contains the 24 of GG for further breaking to the SM. I think the higgs doublet of the SM is coming out of the 5 of SU(5) , etc... I'm not sure why you'd care about the 45 of SU(5), though--its YTableau, 4column & 2column is in Table 28. Really, there are no easy summaries...

This post imported from StackExchange Physics at 2020-12-01 17:43 (UTC), posted by SE-user Cosmas Zachos
Answering my own question of the 45 of SU(5). Georgi and Jarlskog, PhysLett B86 (1979) 297 use it for the Yukawas of SU(5) which yield better mass relations. It has a Young tableau of a 4-story column and a 2-story column next to it. Lots of them in the 120 of SO(10).

This post imported from StackExchange Physics at 2020-12-01 17:43 (UTC), posted by SE-user Cosmas Zachos
MANY THANKS FOR PRECIOUS COMMENTS - <3 thanks ~

This post imported from StackExchange Physics at 2020-12-01 17:43 (UTC), posted by SE-user annie marie heart

This post imported from StackExchange Physics at 2020-12-01 17:43 (UTC), posted by SE-user annie marie heart
Frankly, emailing Kephart should produce a superior answer....! There can be a self-dual and an anti-self-dual one...

This post imported from StackExchange Physics at 2020-12-01 17:43 (UTC), posted by SE-user Cosmas Zachos
who is Kephart ...?

This post imported from StackExchange Physics at 2020-12-01 17:43 (UTC), posted by SE-user annie marie heart
Tom Kephart, an author of that link. Great guy... In any case, these tensors split nicely into dual and antidual pieces...

This post imported from StackExchange Physics at 2020-12-01 17:43 (UTC), posted by SE-user Cosmas Zachos

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