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Imagine one has a truly Scale-invariant theory (I mean not classical scale invariance but quantum mechanical, beta function vanishing one), can this symmetry become localized?

If yes, what can be the spin of the new particle emerging out of the local symmetry? And can one break such local symmetry by means of some Spontaneous Symmetry Breaking phenomenon?

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  • $\begingroup$ Related: physics.stackexchange.com/q/91528 $\endgroup$
    – Nihar Karve
    Feb 26, 2021 at 3:19
  • $\begingroup$ Honestly, I could not understand the clear answer to my question from the similar question link you shared. But thanks. @NiharKarve $\endgroup$
    – Bastam Tajik
    Feb 28, 2021 at 22:04
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    $\begingroup$ For the second part of the question, you can certainly break the dilatation and special CT generators (but not the other two, because you want the vacuum to stay Poincaré-invariant). The interesting thing is that you only get one Goldstone boson $\endgroup$
    – Nihar Karve
    Mar 3, 2021 at 9:27
  • $\begingroup$ It's interesting. And can you elaborate on the symmetries related to that generator? And I'd be grateful if you could clarify if it's possible to localize the scale-invariance symmetry in general? And what kind of particles should be added as the result of localization(first part of the question) Thanks $\endgroup$
    – Bastam Tajik
    Mar 4, 2021 at 15:55

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