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In case anyone has the same question, I found the answer. On-shell and off-shell degrees of freedom have to be counted separately. So off-shell means we don't use EOM, thus F fields do not depend on $\phi$, and degrees of freedom are 4, both bosonic and fermionic. But if we are on-shell, Weyl equations reduce fermionic degrees of freedom to 2, and EOM for ...

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