- For a general N the R-symmetry group is U(N) but for the N=2 case why is it SU(2) ? I guess it is again different for N=4. How does one understand this?
One denotes the generators of the R-symmetry group by Bi and let α be the spinor index and let a,b be the R-charge indices in a N=2 theory. Then one writes the defining equations as,
[Qαa,Bi]=−12(τi)baQαb and [ˉQa˙α,Bi]=12ˉQb˙α(τi)ab
- But it is not clear to me as to why over and above the aforementioned equations there should be yet another charge R (called the U(1)R charge) with the defining equations,
[Qαa,R]=Qαa and [ˉQ˙αa,R]=−ˉQ˙αa
I would like to know why the above charge should exist in N=2 supersymetry separate from the R-symmetry.
Is there an analogue for this R for other values of N ?
- Typically this R-charge as defined above is anomalous. How does one see that? Also what is the analogous statement for R-symmetry?
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