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arivero
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arivero

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Second instalment, I do not know how to title it. The topic is "reorganizing 496" to see if we can go down to SSM, or sideways to E8 Sep 2, 2017

arivero was last seen:
Sep 23, 2017 at 6:06 PM
    1. arivero
      arivero
      Second instalment, I do not know how to title it. The topic is "reorganizing 496" to see if we can go down to SSM, or sideways to E8
      1. arivero
        arivero
        \begin{array}{llll}
        496=\\
        {\bf (1,24,1^c) }&+{\bf [1,15,\bar 3^c]}&+{\bf [1, \bar {15}, 3^c]}&+\\
        1,24,8^c&+[1,10,\bar 6^c]&+[1,\bar {10},6^c]&+\\
        (1,1,8^c)&&&+\\&(2,5,3^c)&+(2,\bar 5,\bar 3^c)&+\\
        &(1,1,1^c)&+[1,1,1^c]\\
        \end{array}
        This is straight from a Gellmann-Ramond-Slansky https://inspirehep.net/record/112502?ln=es
        We apply (2.18) to get SO(32)
        to [itex]SO(2) \times SU(5) \times SU(3) \times U(1)[/itex]
        Sep 2, 2017
      2. arivero
        arivero
        SO(2N) has in some sense a concept of antiparticle, say [itex] x^\dagger[/itex], inherited of SU(N) via [itex]2N = N + \bar N[/itex]. We can use it to rearrange group elements, for instance the combinations that are going to branch into (N,N) and (Adj N, 1)+(1,Adj N) under decomposition to [itex]SO(N) \times SO(N)[/itex], or very similarly to U(N).
        Sep 3, 2017
      3. arivero
        arivero
        So for SO(32) we have 496 = 256 + (120+120), but somehow this 256 does not seem to be the one that is divided in 128+128 by stringers. On the other hand we can also recombine as [itex]x\pm x^\dagger[/itex] but we get (120 + 120) + (120 + 136). It adds to 240 + 256 but it doesnt look as E8xE8; no SO(16) spinor :-(
        Sep 3, 2017
    2. arivero
      arivero
      Ok, so lets go: "Some symmetries of the scalar sector of the SSM" The three generations supersymmetric standard model.
      1. View previous comments...
      2. arivero
        arivero
        Another way to escalate: just colouring the 5 of SU(5) upgrades it to a 15 of SU(5)xSU(3), and a SU(15) invites to organize the whole stuff at least in SO(30). And the whole thing of pairing two charges is pretty much -neglecting orientability issues- as an open string terminating in Chan Paton charges.
        Sep 2, 2017
      3. arivero
        arivero
        This is a direct invitation to check the organization of SO(32), isn't it? Well, it did not ocurred me until this year :-(
        Sep 2, 2017
      4. arivero
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