= CP parity of the Yang-Mills theta density
{c}
{title2=$\epsilon^{\mu\nu\rho\sigma}F^a_{\mu\nu}F^a_{\rho\sigma}$}
The color-contracted density $\epsilon^{\mu\nu\rho\sigma}F^a_{\mu\nu}F^a_{\rho\sigma}$ is even under <charge conjugation> and odd under <parity>. In matrix form the two charge-conjugation signs cancel and transposition leaves the <trace> of the product unchanged. <Parity> contributes its orientation-reversing determinant to the four-index <Levi-Civita symbol>. Thus the density is <CP> odd. A generic fixed coefficient violates <CP symmetry>; being a local total derivative does not eliminate effects from nontrivial gauge topology.
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