# Quirks and exta dimensions.

1. Apr 9, 2009

### arivero

Kaluza Klein in 8 dimensions with the 4 dimensional compact space being the homogeneous space H=SU(3)/SU(2)xU(1), so that the resulting KK bosons are those of SU(3). Similarly, KK in 10 dimensions with H x T^2 as compactified space will produce a SU(3)xU(1)^2 gauge theory.

For energies smaller that the compactificacion scale, this theory is QCD. So it has (empirically, at least) confinement, and it has an implicit string theory, the one of the QCD flux tube. One could even tell of two open string theories: an oriented one, where pairs of particle and antiparticle lie in the extremes of the string, and an unoriented one, where the extremes can be of the same SU(3) irrep, say two quarks or two antiquarks. Are the extremes of these strings confined to live in the 3-brane of space-time?

I pondered how relevant QCD was to strings after a post http://www.nonequilibrium.net/108-how-stringy-is-qcd-string/

I wonder why the forces coming from KK are not considered in most models of superstring theory. Or are they considered but in a hidden way?

Last edited by a moderator: Apr 24, 2017
2. Apr 11, 2009

### blechman

KK modes in string theory are at the Planck scale! Their effects on ultra-ULTRA low-energy physics (a.k.a. electroweak scale) are hence suppressed except in rather exceptional compactifications, brane-world scenarios, etc. In such cases, there are additional forces (Brans-Dicke type forces, for example) and "fifth-force" experiments can be very constraining.

3. Apr 11, 2009

### arivero

The (most usual) compactification scale is near the Planck scale, yes. But the gauge fields from kaluza klein come via the massless modes, so the scale is not relevant to get the gauge structure; it could be relevant if the compactification scale were related to symmetry breaking.

On other hand, as you say, there are models "strings at TeV" wher the KK modes are near the electroweak scale.

The point I was intrigued here, in any case, is that it seems that almost any KK theory (besides T^n or K3) would produce a SU(n) theory and then a "QCD" string theory.

4. Apr 13, 2009

### blechman

Ah, so you are referring not to the "KK modes" of the theory, but the higher dimensional polarizations (like $g_{5\mu}$) in the original KK idea.

This has been done in the context of brane-world scenarios. However, such models that try to accurately describe nature (UED, for example) have problems, such as a very low cutoff; stabilization issues; etc.