The bosonic state is of course based on the Polyakov Action. Now, what if we had another state (I'll call it the k-heterotic state) which is formed by tensoring the fermionic string theory state and the type II state. $$|\psi_{\operatorname{H}}\rangle=|\psi_{\operatorname{F}}\rangle\otimes|\psi_{\operatorname {II}}\rangle$$ The fermionic string theory state is based on the Dirac Action: $$S_F=S_{RNS}-S_B$$ Why is this theory not consistent? Whether the bosonic state is chosen or the fermionic state, how does that matter? Is it because the Dirac Action is imaginary (since it has an i outside the integral if one expands out the Dirac matrix fermionic field product)? Does it have anything to do with that?