I found on some susy lectures (Bertolini, Lectures on Supersymmetry) that R-symmetry definition is:

The largest possible internal symmetry group which can act non trivially on the $Q$’s is thus $U(N)$, and this is called the R-symmetry group

So my question is: why the largest is $U(N)$ and not something else? There are two things that I don't understand

  • why it has to be an $N$-dimensional group (complex dimensions)?

  • why the structure has to be exactly $U(N)$ and not something else with the same dimension?

I split the two points because the intuitive reason behind the first one has to be "because there are $N$ indices on the supercharges" but I don't know how show that this implies the statement.

On the second point I have no ideas at all.



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