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

Question

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

Comments

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

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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

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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

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any comments math.stackexchange.com/questions/3777000/… ? thanks!

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

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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

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who is Kephart ...?

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

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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