Kaluza Klein and gauge symmetry breaking.

[arivero]

In standard, old-fashioned, Kaluza Klein theory we have new dimensionful parameters, the size of the compact dimensions, but they become dimensionless after quotient against the Plank size, so they become the adimensional coupling constants of the gauge groups associated to the symmetry of the compact dimensions.

Now, in the Standard Model we have another dimensional parameter, the electroweak scale (call it the electroweak vacuum, the mass of the Z, or the mass of the W; we can pass proportionally from one to another by using the adimensional coupling constants). When this parameter goes, in mass units, to zero the gauge group becomes SU(3)xSU(2)xU(1). When this parameter goes to infinity the gauge group becomes SU(3)xU(1). So in some sense this parameter interpolates between two different Kaluza Klein theories. But I can not see it in the standard setup. Can it be fitted somewhere? It should be of some value when considering GUT groups in the KK context.

 

[javierR]

What scenarios do you have in mind specifically? Internal spaces in which the gauge group is arising from the structure of the extra dimensions? Or cases in which the gauge group already exists in higher dimensions and symmetry breaking is ultimately tied to the compactification? Etc... The electroweak breaking scale depends on what specific type of extra dimensional scenario you're talking about.

In any case, if the EW breaking scale is directly tied to the energy scale of the extra dimension then generally you will find that increasing and decreasing this scale corresponds to the limits you're interested in.

If you meant a scenario in which the gauge group arises from the internal space's structure, then the limits could correspond to a group contraction associated with the internal space, in which case you would indeed be going from one space to another. In general you should be concerned whether a smooth limiting process is possible; e.g. you can't go from an AdS space to Minkowski space by a smooth limiting process (which are both homogeneous spaces of the form G/H).

 

[arivero]

What scenarios do you have in mind specifically? Internal spaces in which the gauge group is arising from the structure of the extra dimensions?

[/QUOTE]
Yes, the classical scenario, albeit some exotic internal spaces could be allowed in order to account for an SU(2) chiral.

I would not restricg to EW breaking, generically any GUT breaking mechanism is of interest here. The EW model is explicit because it has limits in two Kaluza Klein theories which could live in different dimension, so it seems that the scale parameter interpolates between them.

In any case, if the EW breaking scale is directly tied to the energy scale of the extra dimension then generally you will find that increasing and decreasing this scale corresponds to the limits you're interested in.

I was on such belief, but now I read that increasing and decreasing this scale corresponds to changes in the coupling constant associated to the gauge group. Note that in the original KK models the group is not broken.