Wednesday, November 09, 2005

Notes on two papers

Brustein and de Alwis study a thermodynamic description of the early cosmology and argue that the tunnelling tends to end up near extrema of the potential, and close to the "center" of the landscape where the coupling is of order one and the sizes of the internal manifold are close to the self-dual radii, taking KKLT as a moral example. This seems to agree with the observations of physicists such as Alon Faraggi that the self-dual dimensions of order one are preferred. I also believe in this kind of stuff - the vacuum selection mechanism that we will eventually find will favor the most "canonical" vacua which may be those that are close to the center. This idea is somewhat related to the "beauty is attractive" business but its focus is not on enhanced symmetries.

As far as I understand, John Baez:
  • rediscovered that the Standard Model group is SU(3) x SU(2) x U(1) divided by a certain Z_6 group
  • rediscovered that the complex spinor 16 of spin(10) is a good representation for a single generation of quarks and leptons - i.e. rediscovered one reason behind grand unified theories
  • realized that SU(5) is actually a subgroup of SO(10), not only spin(10), that moreover does not include the 2.pi-rotation and therefore the spinor is single-valued
  • rediscovered that manifolds with SU(5) holonomy are called Calabi-Yau five-folds
  • wants to study, for a very incomprehensible reason, manifolds whose holonomy coincides with the Standard Model gauge group

The last point seems rather unnatural to me because the holonomy is exactly the symmetry - a part of the tangential group - that is broken by the manifold’s curvature, while the gauge group of the Standard Model is a group that must be, on the contrary, completely unbroken to start with.




Comparing the dimensions 4+6 of the large and hidden dimensions in string theory with the (doubled - real) dimensions of the fundamental reps of SU(2) and SU(3) is pure numerology. The four dimensions of the space we know do not transform under the electroweak SU(2), and the six hidden dimensions cannot transform under the colorful SU(3).

Before the heterotic string theory was found, people wanted to create non-Abelian Kaluza-Klein theories with the isometry group giving you the Standard Model. They realized very soon that the required manifolds would have to have dimensions that exceed six. But as far as I can say, no one tried to interpret the Standard Model gauge group as a holonomy group because it seems to be a misunderstanding what the groups mean.

2 comments:

  1. Dear Lumos,

    What is wrong with John Baez coming up with a new formulation of something?

    You seem to have a problem with science going back to old ideas, sorting them out, and developing something useful from them.

    For example, Aristarchus came up with the solar system in 250 BC.

    According to you, this would tarnish Copernicus for developing this in 1500 AD. Similarly, someone else in the Greek age saw fossils up in the hills and realised that life had evolved, 2000 years before Darwin and Wallace. I think from memory that it was Anaximander.

    ‘(1). The idea is nonsense. (2). Somebody thought of it before you did. (3). We believed it all the time.’ - Professor R.A. Lyttleton's summary of inexcusable censorship (quoted by Sir Fred Hoyle in ‘Home is Where the Wind Blows’ Oxford University Press, 1997, p154).

    Best wishes,
    Nigel

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  2. yeah right, must be among 'today's finds or catches in mathematics', but please, don't put it in today's find in physics.
    going back to old ideas, sorting them out is called scientific archaeology.

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