## Wednesday, November 2, 2011

### Theory Update 121

As noted in McElrath's 2008 paper, gravitational condensates involving neutrinos must also consider the electroweak bosons. From the braid diagrams, one obtains the mirror sector by flipping all twisted ribbon charges. The neutrinos, mirror neutrinos and photons are the only particles invariant under this process. The $Z$ boson, although neutral, consists of a colored triplet of $(+,-,0)$ ribbons. This triplet is the Fourier dual of the right handed leptons. Observe that a $Z$ boson is the only braid object composing with its mirror braid to form a massless photon, a dual to the left handed neutrino.

1. Meanwhile on the arxiv, people are digging into nonperturbative EW explanations for the CDF Wjj anomaly. Nonperturbativity is simpler with braids.

2. I'd like to point out, for the benefit of any skeptical readers, that if there is an extended supersymmetry at work in the background here, then there will be relationships between the known particles which cut across familiar barriers. For example, in Gell-Mann's 1983 proposal, the photon and the 8 gluons are superpartners of the 9 up-type quarks (3 flavors x 3 colors).

What I still can't say is whether the correspondences above are 100% consistent with Gell-Mann 1983, or whether there is a point of difference. I can already tentatively map Gell-Mann's goldstinos onto these mirror neutrinos, and Gell-Mann's gravitinos onto the whole of Riofrio's dark sector. In the place of a conventional weak interaction, Gell-Mann also has a lot of massive gauge bosons which are superpartners to his "dark energy gravitinos". So it's mysterious but suggestive.

3. Thank you, Mitchell.

Ultimately, however, the usual multiplets emerge from braids, which are more fundamental in so many ways, and so the usual multiplets have limited, if any, utility, except for providing a mathematical proof that string theory is incorrect. In physics, though, mathematical proof means nothing, and experimental proof is everything.

4. At the moment I'm thinking that the triplet/antitriplet gravitinos (which are a geometric embedding of the mirror neutrinos) couple to the hadrons, and the singlet gravitinos couple to the leptons.

I still don't speak Braid, but as we discussed elsewhere, the latter may have something to do with the states on the diagonal of your (1,9,9) circulant matrix. The difference is that "Gell-Mann" (by which I mean, my interpretation of Gell-Mann) has two such objects, and you have three. Finally, a point of difference?

5. That sounds right, Mitchell. The $2$ usually comes from the $56 = 54 + 2$, whereas we have $57 = 54 + 3$ in a $3 \times 3$ triality setup. See Gunaydin et al.

6. BIG leap in my understanding there. E8 acts on the 57-dimensional space of nonassociative paths, which includes the standard model fermions, the mirror neutrinos, and these other three objects. !!