## some references

Posted Mar27-11 at 08:59 PM by arivero

J.H. Schwarz, Phys.Lett.B37:315-319,1971 (also anticipated in a small comment in Phys. Rev. D 4, 1109–1111 (1971) )

EDIT: other references using "fermion-meson": http://dx.doi.org/10.1016/0550-3213(74)90529-X Nuclear Physics B Volume 74, Issue 2, 25 May 1974, Pages 321-342 L. Brink and D. B. Fairlie; http://www.slac.stanford.edu/spires/...=NUCIA,A11,749 Nuovo Cim.A11:749-773, 1972 by Edward Corrigan and David I. Olive.

http://vixra.org/abs/1102.0034
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## this could be useful...

Posted Oct4-10 at 12:09 PM by arivero
Updated Oct4-10 at 12:27 PM by arivero

If both F(s) and G(s) are absolutely convergent for s > a and s > b then we have

$$\frac{1}{2T}\int_{-T}^{T}\,F(a+it)G(b-it)\,dt= \sum_{n=1}^{\infty} f(n)g(n)n^{-a-b} \text{ as }T \sim \infty.$$

... in the context of dirichlet series, to decompose the Riemann zeta, finding a pair of functions where f(n)g(n)=1 for all n. Note that they not need to be multiplicate, do they?

The simplest not trivial case, had we absolute convergence, would...
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## Could it be Pati-Salam, at the end?

Posted May14-10 at 06:43 PM by arivero

Both
U(1)xSU(3)xSU(2)xSU(2)
and the full
SU(4)xSU(2)xSU(2)
live in 8 extra dimensions, as F-theory lives, and they probably need one of the extra dimensions to be infinitesimal, because U(1) B-L is not gauged, at least not at the scales we know.

The manifolds, by the way, are
S1 x CP2 x S3
and
S5 x S3
respectively.

The later is more complete and it allows to generate Witten's manifols almost automagically. But...
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## Koide doublets?

Posted Oct20-09 at 04:30 AM by arivero

From a point of view, there are no Koide doublets. If we define Koide's relationship as coming from three matrix conditions:

$$M^{1/2}= A + B$$ with
1) A multiple of the identity
2) B traceless
3) $$Tr (A^2) = Tr (B^2)$$

Then the 3 in the 3/2 factor is really the dimension of the matrix, and thus the factor is 2/2 for Koide's doublets and 1/2 for Koide "singlets". So in this sense there are no Koide doublets.

...
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