CP-violating CFT and trace anomaly

It is logically possible that the trace anomaly in four dimensions includes the Hirzebruch-Pontryagin density in CP-violating theories. Although the term vanishes at free conformal fixed points, we realize such a possibility in the holographic renormalization group and show that it is indeed possible. The Hirzebruch-Pontryagin term in the trace anomaly may serve as a barometer to understand how much CP is violated in conformal field theories.