GUTs: Understanding SU(5), SO(10) & E6

[Jim Kata]

I don't have access to Georgi's and Wilcheck's work, if somebody has some good links to an overview of the su(5), so(10), and e6 GUTS that would be awesome.

Anyways, there's something I really don't get, let's take su(5) for example, su(5) has the root system A_4 now there is 4(4+2) = 24 generators of the lie algebra. Now I know they didn't use all 24 of the generators because it would mean that there were 24 gauge bosons, not including the Higgs. So I heard they used a diagonal representation of su(5). Something like

[su(3)0]
[0 su(2)]

Does that entail just using the Cartan subalgebra or what? What did they do?

 

[Avodyne]

All 24 gauge bosons are there, but SU(5) is spontaneously broken to SU(3)xSU(2)xU(1) by a vacuum expectation value for a Higgs fields in the adjoint representation.

Srednicki's QFT book (available free on his website) has a good basic discussion of the SU(5) model.

 

[Barmecides]

I don't have access to Georgi's and Wilcheck's work, if somebody has some good links to an overview of the su(5), so(10), and e6 GUTS that would be awesome.

Anyways, there's something I really don't get, let's take su(5) for example, su(5) has the root system A_4 now there is 4(4+2) = 24 generators of the lie algebra. Now I know they didn't use all 24 of the generators because it would mean that there were 24 gauge bosons, not including the Higgs. So I heard they used a diagonal representation of su(5). Something like

[su(3)0]
[0 su(2)]

Does that entail just using the Cartan subalgebra or what? What did they do?

I'm not at all a specialist of GUT, but I think only generators from SU3 x SU2 x U1 are diagonal and commute. Other generators are non-diagonal and entail the breaking of SU5 into SU3 x SU2 x U1.
If you have good www ressources, I'm also interested.