### SU(3)xSU(2)xU(1)/Z6… wait, Z6?

Recently I remembered something that mentioned a few years ago during the SLAC Summer Institute at the end of Prof. Dienes’ first lecture on grand unification. (Wait until the end of the video, then you’ll hear a famous Cosmic Variance blogger ask about this.) The gauge group for the Standard Model is apparently SU(3)xSU(2)xU(1)/Z6. The Z6 is a discrete group that was ~~first~~ discussed by Bakker, Veselov, Zubkov:

A Hidden Symmetry in the Standard Model (Phys. Lett. **B583**, 379)

**Update** (12 Mar 08): *Dr. Carroll points out that the Z6 was known before this paper, e.g. hep-ph/9312254. The paper looks like a lot of fun for the solitonic-ly inclined. I know of one Non Perturbative Physics lecturer in Durham who will be asked about this after class tomorrow.*

I don’t understand the details, but it has to do with the fermion and higgs sectors and something about the centres of the SU(3) and SU(2) groups. The authors derive the extra symmetry from a lattice perspective and then take the limit as the lattice becomes a continuum. (I’m not sure if this means that the Z6 gets an asterisk like the Spurs’ NBA championship in the lockout-truncated-season of 1999.)

This is apparently not just an intellectual exercise, as a follow up paper by Zubkov explains that this would have consequences on the structure of monopoles. (As one would expect, since solitons are the kinds of things that depend on the topology of the gauge group.)

The lattice-language is a bit far from what I’m used to, so I’m not sure if I’ll get around to properly digesting the paper. But in the now I can say “… and mod Z6” when time someone mentions the standard model gauge group.

**Update 2** (12 Mar 08): *Yet another well-known physics blogger has pointed out the following from Professor Baez’s 2003 quantum gravity seminar: The True Internal Symmetry Group of the Standard Model.*

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This famous blogger would like to point out that the Z_6 subgroup was certainly known before that — we wrote about it here:

http://arxiv.org/abs/hep-ph/9312254

But we didn’t make a big deal of it; we figured everyone knew, or at least someone knew.

(It’s not really an extra symmetry, of course; it’s

lesssymmetry, since the Z_6 is being modded out.)