Friday, 30 August 2019

quantum field theory - Regarding R-symmetry in SUSY algebra


In John Terning, Modern Supersymmetry, $R$-symmetry is introduced as below: "The SUSY algebra is invariant under a multiplication of the supercharges by a phase, so in general there is a linear combination of U(1) charges called $R$-charge, that doesn't commute with the supercharges."


He the proceeds to write down the following commutator relations: $$[Q_{\alpha}, R] = Q_{\alpha}, $$ $$[Q_{\alpha}^{\dagger}, R] = - Q_{\alpha}^{\dagger}$$


How are the above relations derived?




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