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Is the $\langle \phi^{(0)} \phi^{(0)} \psi^{(l)} \rangle$ in a CFT zero ? Where $\phi$ and $\psi$ are spin-0 and spin-$(l+1/2)$ fields respectively and $l$ is an integer. If so, please, explain why ? The above fields are primaries.

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    $\begingroup$ A correlation function must contain an even number of fermions in order to be nonzero. One way to prove this is to note that otherwise it will not be invariant under a $2\pi$ rotation. $\endgroup$ – Peter Kravchuk Jan 24 '19 at 5:49

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