The trace anomaly of four-dimensional Weyl fermions in a non-abelian gauge background is (1/48 pi^2) tr F^2 with no parity-odd Chern-Pontryagin contribution, derived via Pauli-Villars regularization.
CP-violating CFT and trace anomaly
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abstract
It is logically possible that the trace anomaly in four dimension 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.
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Weyl fermions in a non-abelian gauge background and trace anomalies
The trace anomaly of four-dimensional Weyl fermions in a non-abelian gauge background is (1/48 pi^2) tr F^2 with no parity-odd Chern-Pontryagin contribution, derived via Pauli-Villars regularization.