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It is logically possible that the trace anomaly in four dimension includesthe Hirzebruch-Pontryagin density in CP violating theories. Although the termvanishes at free conformal fixed points, we realize such a possibility in theholographic renormalization group and show that it is indeed possible. TheHirzebruch-Pontryagin term in the trace anomaly may serve as a barometer tounderstand how much CP is violated in conformal field theories.

CP-violating CFT and trace anomaly