CFT correlators and CP-violating trace anomalies

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We analyze the parity-odd correlators langle JJOrangle _{odd},langle JJTrangle _{odd},langle TTOrangle _{odd} and langle TTTrangle _{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 langle JJOrangle _{odd} and langle TTOrangle _{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 langle JJTrangle _{odd} and langle TTTrangle _{odd} are nonzero. In particular, in the case of langle JJTrangle _{odd} the transverse–traceless component is constrained to vanish, and the correlator is determined only by the trace part with the anomaly pole.