- #1

MTd2

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U(1)XSU(2)XSU(3)XSU(4)XSU(5)X...XSU(N), N-> infinity

Did anyone ever try that?

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- Thread starter MTd2
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- #1

MTd2

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U(1)XSU(2)XSU(3)XSU(4)XSU(5)X...XSU(N), N-> infinity

Did anyone ever try that?

- #2

Haelfix

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Haelfix, what would the "planar gauge theory" act like when you try to apply it as a particle gauge theory? (If this is a sensible question)

- #4

Haelfix

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Its also one of the founding and motivating examples for AdS/CFT (where you take a large N gauge theory over a Riemann surface in a lower dimension).

- #5

MTd2

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Haelfix

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- #7

MTd2

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- #8

Haelfix

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Thats one of the biggest constraints in GUT model building and why we don't use groups like say E7 for model building (even if it contains the SM as a subgroup)

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N cannot go to infinity: there is no particle heavier than the total Universe energy.

Bob.

Bob.

- #10

MTd2

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You always need a chiral gauge group.

These are just embendings of smaller groups into largers ones until infinity. It's not like searching a smaller group inside a bigger one, but making a bigger extending the smallerm, and see what happens. And isnt every SU(j) gauge group chiral invariant?

- #11

Haelfix

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Actually, the problem with SU(N) with N finite, is actually a little more complicated than I said above. In order to have a physically viable candidate, you need both a complex representation (and hence a chiral spectrum), which SU(N) does have, except that you also need to satisfy the additional requirement for anomaly cancellation. The only completely antisymmetric m fold representation for SU(N) then only contains the familiar SU(5) representation 1, 5, 5bar, 10bar. Which you can build up to get higher versions.

Unfortunately there again you run into certain choices for some fixed N, with a fixed representation r where you will have to explain why either fermions don't recieve large masses or why the theory doesn't possess possible gauge anomalies..

For N --> infinity, well thats a different story b/c of the aforementioned simplifications. But then thats not a candidate GUT either.

- #12

MTd2

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The only completely antisymmetric m fold representation for SU(N) then only contains the familiar SU(5) representation 1, 5, 5bar, 10bar. Which you can build up to get higher versions.

I don't get any of this. :tongue2:

Hmm. Fermions haing a huge mass is a desired effect, because I am adding a new force for every SU(j) added. They shouldn't be seen that easily.

I'd like to know how to unify that kind of inifinite sequence of forces.

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