Imaginary Rotation Breaks Charge Conjugation in Hot QCD

Starting from the identity $e^{2πi J_z}=(-1)^{F}=e^{iπQ}$ on the color-singlet physical state space, we derive a density-operator identity that ties imaginary rotation to an imaginary quark chemical potential, $ρ(Ω_I+2π,θ_q)=ρ(Ω_I,θ_q+π)$. Hence imaginarily rotating $SU(3)$ QCD at $(Ω_I,θ_q)=(2π,0)$