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arivero
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    Hi, in your paper "The strange formula of Dr. Koide" you mention your list of
    phenomenologically inspired relationships, which is supposed to be available at http://www.physcomments.org/wiki/index.php?title=Bakery:HdV . This site is no longer online and I was wondering if it is still available somewhere?
    J
    jakob1111
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    arivero
    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
    arivero
    arivero
    Gold Member
    \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]
    arivero
    arivero
    Gold Member
    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).
    arivero
    arivero
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    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 :-(
    Gold Member
    Ok, so lets go: "Some symmetries of the scalar sector of the SSM" The three generations supersymmetric standard model.
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