# Scalar-Scalar-Spin(l+1/2) correlator in CFT

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.

• 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. – Peter Kravchuk Jan 24 '19 at 5:49