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

Hello physics people,

I hope all is well, and that everyones feeling festive even though i dont celebrate xmas lol!

Iv got some wierd questions, at least for me. Iv been working on Kaluza-Klein theory and have found wierd things. Essentially I have been working on the basic $$M_{4} \times S^{1}$$ topology. I have a zeroth mode 4d Action; and an equation of motion in which i find vacuum expectation values at $$\eta_{\mu\nu} , A_{\mu}=0, and \phi = 1$$. 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 im pretty sure it is due to the generators of the pioncare group - but im 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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