Last year I was studying supersymmetry and since them I'm regularly thinking to one question for which I don't have answer: when one looks at the susy algebra with N generators, one sees that there is a U(N) R-symmetry. But for N=4, the group is in fact SU(4).(adsbygoogle = window.adsbygoogle || []).push({});

To explain this, one generally argues (Terning's book, McGreevy's lectures, problem set 2) using the form of the lagrangian, e.g. that the scalars are in the real antisymmetric 6 representation, and so a phase transformation is clearly not a symmetry of the lagrangian.

But I'm remember to have read somewhere a computation at the level of the algebra (with N generators) which leads to a term with (N-4) and this explains why the case N=4 is special. Unfortunately I'm not able to remember the steps of the computation or to find again the place where I have read this; it's not in usual books (Terning, Weinberg, Wess/Bagger, West, Binétruy, Freund, Müller-Kirsten/Wiedemann) nor reviews (Sohnius, Bilal, etc.). Does someone have an idea or a hint about this?

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# R-symmetry for N=4 susy

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