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Rezaderex

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**Kaluza Klein, Goldstone Bosons, symmetries obliging masslessness?**

Hello physics people,

I hope all is well, and that everyones feeling festive even though i don't celebrate xmas lol!

Iv got some weird questions, at least for me. Iv been working on Kaluza-Klein theory and have found weird things. Essentially I have been working on the basic [tex] M_{4} \times S^{1}[/tex] topology. I have a zeroth mode 4d Action; and an equation of motion in which i find vacuum expectation values at [tex]\eta_{\mu\nu} , A_{\mu}=0, and \phi = 1[/tex]. Now, how i understand it, this 4d action is Weyl Scaling invariant; however, the vacuum isnt! which implies a broken symmetry. This leads to the goldstone boson (massless) in introduces the scalar field(dilaton). Could someone possibly eloborate on this?

Also, in my spectrum I have a graviton and a photon, each of which massless... apparently, general covariance keeps the graviton massless, and gauge invariance keeps the photon massless. This is pretty wierd, and I am pretty sure it is due to the generators of the pioncare group - but I am just not sure.

If anyone could give me a helping hand i would be incredibly appreciative!

Cheers

edit: I know this could be in standard model beyond or SR and GR section; but this is more QFT related i think.

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