CPviolation in gauge theories

We define the $\mathrm{CP}$ transformation properties of scalars, fermions and vectors in a gauge theory and show that only three types of interactions can lead to $\mathrm{CP}$ violation: scalar interactions, fermion-scalar interactions and $F\tilde{F}$ which is associated with the strong $\mathrm{CP}$ problem and which involves only the gauge fields. For technicolor theories this implies the absence of $\mathrm{CP}$ violation within perturbation theory.