Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Silliest GUT ever.

  1. Apr 17, 2009 #1

    MTd2

    User Avatar
    Gold Member

    So, I was thinking, SM symmetry group is U(1)XSU(2)XSU(3), so, why not going on, that is:

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

    Did anyone ever try that?
     
  2. jcsd
  3. Apr 17, 2009 #2

    Haelfix

    User Avatar
    Science Advisor

    I'm not entirely positive, you should ask on the math forum, but isn't that just homomorphic to SU(N) N--> infinity anyway? Which is just the planar gauge theory.
     
  4. Apr 17, 2009 #3
    I would like to note that I have previously derived a much sillier GUT theory than this, outlined in the comments to this post.

    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)
     
  5. Apr 18, 2009 #4

    Haelfix

    User Avatar
    Science Advisor

    Actually it doesn't behave particularly "particulate" at all. Instead its quite stringy, and remarkable simplifications occur at the quantum level leading some people to expect it to be exactly soluble. Nevertheless it was discovered by 'T Hooft in the 70s before string theory was really popular.

    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).
     
  6. Apr 19, 2009 #5

    MTd2

    User Avatar
    Gold Member

    In fact, what I mean is really simple, silly indeed. As you go to higher and higher enegies, you would find that the best description of the particle zoo up to a point would be a new direct product with the next j of SU(j). I didn't mean an aproximation, but an almost exact aproximation at each enegry level and that's why I didnt ask in the math forums.
     
  7. Apr 19, 2009 #6

    Haelfix

    User Avatar
    Science Advisor

    That won't work, b/c for finite j you will have some leading order groups that admits only self conjugate irreps and are nonchiral. The effective theories thus cannot be broken up in such a way.
     
  8. Apr 19, 2009 #7

    MTd2

    User Avatar
    Gold Member

    I don't see the problem in having some of them non chiral. The standard model will always be a subgroup of the sequence.
     
  9. Apr 19, 2009 #8

    Haelfix

    User Avatar
    Science Advisor

    You always need a chiral gauge group. One physical reason it matters is b/c if you didn't you would have fermion masses completely at odds with experiment. Generically all the fermions in the theory would pick up large gauge invariant masses at some high energy scale instead of being massless (until electroweak symmetry breaking).

    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)
     
  10. Apr 20, 2009 #9
    N cannot go to infinity: there is no particle heavier than the total Universe energy.

    Bob.
     
  11. Apr 20, 2009 #10

    MTd2

    User Avatar
    Gold Member

    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?
     
  12. Apr 20, 2009 #11

    Haelfix

    User Avatar
    Science Advisor

    I don't really understand your first sentence. For instance E7 * G(standard model) is still unsuitable for phenomenology even if you are deadset on trying to complicate the high energy landscape for no suitable rewards!

    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.
     
  13. Apr 20, 2009 #12

    MTd2

    User Avatar
    Gold Member

    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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Silliest GUT ever.
  1. GUTS & Inflation (Replies: 4)

  2. Connes GUT? (Replies: 30)

  3. No gut? (Replies: 1)

  4. Geometrical GUT? (Replies: 1)

Loading...