Why Are There No 15 Representations for Fermions in SU(5) Grand Unification?

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SUMMARY

The discussion centers on the absence of a 15 representation for fermions within the SU(5) grand unification framework. Participants reference key papers, including arXiv:0803.4156v2 and arXiv:1504.03695, highlighting that the Higgs scalars have representations of 5, 24, 45, and 15, while fermions are limited to 5, 10, and 24. The chirality of the Standard Model (SM) and its embedding in SU(5) are identified as critical factors that eliminate the 15 and 35 representations as viable candidates for fermions.

PREREQUISITES
  • Understanding of SU(5) symmetry group
  • Familiarity with representations in particle physics
  • Knowledge of Standard Model chirality
  • Basic comprehension of Higgs scalars and fermions
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  • Research the implications of SU(5) symmetry on particle representations
  • Study the role of chirality in the Standard Model
  • Examine the significance of Majorana fermions in grand unification theories
  • Explore the detailed discussions in arXiv:1504.03695 regarding representation candidates
USEFUL FOR

This discussion is beneficial for theoretical physicists, particle physicists, and researchers focused on grand unification theories, particularly those interested in the SU(5) model and its implications for fermion representations.

Safinaz
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Hi there,

My question about grand unification based on SU(5) symmetry group ..

I read in some papers, like that
http://arxiv.org/pdf/0803.4156v2.pdf

The Higgs scalars grand representation are only 5, 24, 45, and 15, while the fermions grand representations are only 5, 10 , and 24..

I wonder why there is no for instance 15 representation for fermions ? do anyone has an idea ..

best
 
Safinaz said:
I wonder why there is no for instance 15 representation for fermions ? do anyone has an idea ..

If I recall well, it has to do with the chirality of the SM and how it's embedded within SU(5)?
http://arxiv.org/abs/1504.03695
check the discussion in 2.2 for example and how the 15 (and 35) is killed as a candidate.
I hope it helps... although I don't understand why you'd use the 24 repr for the fermions; are they majorana?
 
Thanx for the replies.
 

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