Consider a $\mathcal{N}=2$ SCFT radially quantized on $R^3 \times S^1$. The Lorentz group is $SU(2)_+ \times SU(2)_-$ and there are 8 independent supercharges $Q_{\alpha}^I,\tilde{Q}_{I \dot \alpha} $ where the $\alpha$ index takes values 1 and 2 as does the $\dot{\alpha}$. The first one transforms in the doublet of the first factor $SU(2)_{+}$ while the dotted one in the doublet of $SU(2)_-$. The $I$ index is the $SU(2)_R$ index. If it is up the it transforms in the $4$ and if it is down in the $\bar{4}$ representation.

In the context of the superconformal index one chooses a specific supercharge, say $Q_{1\dot{1}}$ and its conjugate $Q_{1\dot{1}}^{\dagger}$.

Question. Why is it claimed that $$ \{ Q_{1\dot{1}}, Q_{1\dot{1}}^{\dagger}\} = H -\frac{3}{2}R - 2J_3 := \Delta $$ I saw this in this reference, equation (7).


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