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The title of the question is almost self-contained: I'd like to know if an internal symmetry group of a gauge theory could act non-trivially on supercharges.

I try to make my question clear with an example: in $\mathcal{N}=1$ supersymmetry, but also in extended cases, I could have $U(1)$ as R-symmetry group, so could those $U(1)$ transformation coincide with the $U(1)$ of QED, or I am always free to think that the two are distinct? (i.e. if my theory is symmetric under simultaneous action on electric charges and supercharges then is also symmetric under the action of each that separately)

In this sense I'm speaking of global symmetries, but if it is relevant for the question whether they could be gauged or not maybe one could consider the SUGRA analogue question (is only an hint, I don't know if it is reasonable).

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  • $\begingroup$ There is a concept of "twisting" a global symmetry (or perhaps a gauge symmetry) by the R-symmetry, that might be relevant. $\endgroup$ Commented Apr 6, 2018 at 10:45
  • $\begingroup$ I don't understand what you mean (in particular with the word "twisting"), sorry; could you suggest some references? $\endgroup$
    – Annibale
    Commented Apr 6, 2018 at 13:27
  • $\begingroup$ It's something about finding identical subgroups of the Lorentz group and the R-symmetry group, and somehow reducing their product to the diagonal subgroup, in order to produce a "topological sigma model" (Witten). $\endgroup$ Commented Apr 8, 2018 at 3:18

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The conventional wisdom appears to be that R-symmetry can only be gauged if supersymmetry becomes a local symmetry, thus requiring supergravity.

I can't remember any conventional proposal in which one of the standard model gauge groups is a gauging of an R-symmetry; but there are some extensions of the supersymmetric standard model in which there is a gauged R-symmetry that has phenomenological implications.

"The Other Fermion Compositeness" is an odd proposal in which some or all of the standard model fermions are goldstinos, and the gauge groups are subgroups of R-symmetry. Nothing is said about the usual argument requiring supergravity, and the more ambitious forms of the proposal require extended supersymmetry far beyond the usual limit of N=8.

"Embedding Standard Model Symmetries in K(E10)", released today, wants to do something with an exotic infinite R-symmetry, but I'm not quite sure what, and perhaps the authors aren't quite sure, either.

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