CFT correlators and CP-violating trace anomalies

We analyze the parity-odd correlators ⟨ J J O ⟩ odd , ⟨ J J T ⟩ odd , ⟨ T T O ⟩ odd and ⟨ T T T ⟩ odd in momentum space, constrained by conformal Ward identities, extending our former investigation of the parity-odd chiral anomaly vertex. We investigate how the presence of parity-odd trace anomalies affect such correlators. Motivations for this study come from holography, early universe cosmology and from a recent debate on the chiral trace anomaly of a Weyl fermion. In the current CFT analysis, O can be either a scalar or a pseudoscalar operator and it can be identified with the trace of the stress–energy tensor. We find that the ⟨ J J O ⟩ odd and ⟨ T T O ⟩ odd can be different from zero in a CFT. This occurs when the conformal dimension of the scalar operator is Δ 3 = 4 , as in the case of O = T μ μ . Moreover, if we assume the existence of parity-odd trace anomalies, the conformal ⟨ J J T ⟩ odd and ⟨ T T T ⟩ odd are nonzero. In particular, in the case of ⟨ J J T ⟩ odd the transverse–traceless component is constrained to vanish, and the correlator is determined only by the trace part with the anomaly pole.