# Is Connes model a composite Higgs in disguise?

Most of the 5-dimensional Higgs models can be seen, if I understand correctly, as models where the Higgs is a composite.

Now, is this true for Connes models? It is a model of extra dimensions too, in some sense. And when you look at the papers, at some moment a product of two symbols is substituted by a single $\phi$, so it seems that some composition is at work.

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why is the Higgs composite in extra dimension models? Do you mean little Higgs. –  Ron Maimon Jul 26 '12 at 5:33
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## 1 Answer

I just looked over Connes paper, and his Lagrangian is expressed with a Higgs field H. This makes H fundamental at energies where the Lagrangian is correct, which is everywhere below the scale where he has new structure. This is the scale where he gets the weird constraints in his model, and he puts this at the GUT scale, so it makes no sense to call it a composite Higgs model. It's a fundamental Higgs, like in the standard model or in a usual GUT where the Higgs is part of a larger multiplet, but is split at low energies.

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If you look it with most detail, you will notice that H is first got from a sumatory on indeterminate (arbitrary?) fields. –  arivero Jul 26 '12 at 21:37
@arivero: I looked for an expression like this in the paper, I didn't see it. I was looking at the earliest relevant paper linked on his site. Were you looking at a different paper? The H arose from some big high energy matrix thingy he was considering, not from products of fermionic (or bosonic) fields (at least I didn't see anyplace where this happened). –  Ron Maimon Jul 27 '12 at 2:38
Fascinating, you are right it is not mentioned in most of the supposedly definitive papers. But look eg at page 616 in the red book, alainconnes.org/docs/book94bigpdf.pdf The Higgs apears as combinations of products of pairs of complex numbers. –  arivero Jul 27 '12 at 13:38
@arivero: I didn't see the Higgs in that page, I saw a lot of "H"'s, but these are quaternions. I don't really like Connes presentation, I don't think it adds anything, and it is very unclear compared to standard presentations. –  Ron Maimon Jul 27 '12 at 13:56
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