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

[Safinaz]

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

 

[ChrisVer]

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?

 

[Safinaz]

Thanx for the replies.