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 conformalWard 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) 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 Delta(3) = 4, as in the case of O = T-mu(mu). 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.