CFT correlators and CP-violating trace anomalies

Abstract

AbstractWe analyze the parity-odd correlators $$\langle JJO\rangle _{odd},$$ ⟨ J J O ⟩ odd , $$\langle JJT\rangle _{odd},$$ ⟨ J J T ⟩ odd , $$\langle TTO\rangle _{odd}$$ ⟨ T T O ⟩ odd and $$\langle TTT\rangle _{odd}$$ ⟨ 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 $$\langle JJO\rangle _{odd}$$ ⟨ J J O ⟩ odd and $$\langle TTO\rangle _{odd}$$ ⟨ T T O ⟩ odd can be different from zero in a CFT. This occurs when the conformal dimension of the scalar operator is $$\Delta _3=4,$$ Δ 3 = 4 , as in the case of $$O=T^{\mu }_{\mu }.$$ O = T μ μ . Moreover, if we assume the existence of parity-odd trace anomalies, the conformal $$\langle JJT\rangle _{odd}$$ ⟨ J J T ⟩ odd and $$\langle TTT\rangle _{odd}$$ ⟨ T T T ⟩ odd are nonzero. In particular, in the case of $$\langle JJT\rangle _{odd}$$ ⟨ 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.