## Saturday, September 24, 2011

### Theory Update 112

For many years, kneemo has tried to get me interested in the classical geometry much beloved by traditional M theorists. An early push on this front included Szabo's 2002 paper on tachyons and K-homology. So when number 26 made a few remarks at the viXra log neutrino post, sounding for all the world like a numerology robot, it nonetheless caught my attention, because robots don't usually know that $120$ is a very, very interesting number.

Recall that, back in 2006, we were very excited that the orbifold Euler characteristic of the moduli space $M_{2,0}$ of the genus $2$ Riemann surface with no punctures was $-1/120 = 2 \zeta(-7)$, in terms of a zeta value. This is because $M_{2,0}$ belongs to the triplet $(M_{0,6}, M_{1,3}, M_{2,0})$ of moduli spaces of twistor dimension. We already knew that the number of generations for mass quantum number came from the $-6$ for the moduli $M_{0,6}$, by halving. Similarly, we halve the $-1/120$ to get the $\zeta (-7)$ much beloved by number 26.

Not being an expert in classical geometry, I am still rather unsure about some of the things that number 26 said, but I am quite certain that some of the things that number 26 said are in fact closely related to mass generation in quantum gravity. Long live tachyonic neutrinos.

1. We do not assume that ordinary antineutrinos, such as those observed from supernova 1987A, are the same as these special neutrinos. After all, we have yet to sort out this neutrino mirror neutrino business. Taking the three observations (1987A, MINOS and OPERA) at face value, $\overline{\nu}$ (mass) states are NOT tachyonic while the $\nu$ ones are.

2. Then the MiniBooNE low E excess for ν states (arising as predicted from our neutrino vacuum) notably contrasts with different characteristics for the antineutrinos.

3. I am sorry, but OPERA experiment has done other bluff. I think the OPERA team has forgotten an important systematic error indeed. Einstein was right, again. I am tempted to think they have donde that due to some cut threat in their budget. I can not believe they have not realized that correction in their analyses.

Best wishes.

4. Juan, try to post comments on the right post.

5. Also recall the K-matrix theory papers from 2002 which explore the interplay between spectral triples, K-homology and D-brane geometry (hep-th/0108085). The modern view is to interpret such ideas through the lens of motivic cohomology.

6. Yes, kneemo, I would be much happier discussing motivic cohomology. As you know, this allows a much simpler description of M theory, and hence the tachyon sector.

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