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I need to know if conformal symmetry can be localized in the same manner that global symmetries like $SU(2)$ is localized and gauge bosons pop up?(I assume the trace anomaly doesn't violate the scale invariance symmetry)

If so what is the particle that appears after localization? Is such symmetry compatible with the rest of the Standard Model symmetries? (In other words, if it can create any violation of mixed vectorial current anomaly via triangle diagrams)

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    $\begingroup$ Gauging a spacetime symmetry is very different from gauging an internal symmetry. I would look up conformal supergravity. $\endgroup$ Nov 25 at 13:19
  • $\begingroup$ You can't just "localize" Lorentz invariance and get gravity either - the usual procedure of "gauging" global internal symmetries produces a Yang-Mills theory, but the Einstein-Hilbert action of gravity is not of Yang-Mills type. Without specifying what exactly you mean by "localizing" here, this question is not really answerable. $\endgroup$
    – ACuriousMind
    Nov 25 at 13:58
  • $\begingroup$ I never said it's a Yang-Mills action. Localizing a global symmetry no matter if internal or a symmetry of spacetime, is viable as it modifies the covariant derivative by the inclusion of a connection. I guess this is the only sense that can be made out of the "localization" of a symmetry. @ACuriousMind $\endgroup$ Nov 25 at 14:13
  • $\begingroup$ But you have to state what the action is in order to even have a symmetry, since a symmetry (global or local) is defined as a property of the action, after all. And just saying "replace the derivative by a covariant derivative" doesn't cut it - you need an additional term in the action that produces a non-trivial e.o.m. for the gauge field. $\endgroup$
    – ACuriousMind
    Nov 25 at 14:22
  • $\begingroup$ I barely guess that actions define the symmetries, in fact, symmetries uniquely define the action or lagrangian! @ACuriousMind But for the sake of clarity let's take a scalar boson on a flat background. Trivially trace anomaly vanishes in two-dimensional flat spacetime. Is such symmetry localizable in the sense that I meant? why? $\endgroup$ Nov 25 at 14:43

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