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Gold Member
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?
jakob1111
arivero
arivero
jakob1111
Gold Member
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
\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 $SO(2) \times SU(5) \times SU(3) \times U(1)$
arivero
SO(2N) has in some sense a concept of antiparticle, say $x^\dagger$, inherited of SU(N) via $2N = N + \bar N$. 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 $SO(N) \times SO(N)$, or very similarly to U(N).
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 $x\pm x^\dagger$ 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.
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.
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 :-(
arivero