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.

Dear Lumos,

ReplyDeleteWhat 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

yeah right, must be among 'today's finds or catches in mathematics', but please, don't put it in today's find in physics.

ReplyDeletegoing back to old ideas, sorting them out is called scientific archaeology.