CFT Correlators and CP-Violating Trace Anomalies

Abstract

We analyze the parity-odd correlators $⟨JJO{⟩}_{odd}$, $⟨JJT{⟩}_{odd}$, $⟨TTO{⟩}_{odd}$ and $⟨TTT{⟩}_{odd}$ 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 $⟨JJO{⟩}_{odd}$ and $⟨TTO{⟩}_{odd}$ can be different from zero in a CFT. This occurs when the conformal dimension of the scalar operator is $\hat{I}{”}_3=4$, as in the case of $O=T^{\hat{I}}{¼}_{\hat{I}}¼$. Moreover, if we assume the existence of parity-odd trace anomalies, the conformal $⟨JJT{⟩}_{odd}$ and $⟨TTT{⟩}_{odd}$ are nonzero. In particular, in the case of $⟨JJT{⟩}_{odd}$ the transverse-traceless component is constrained to vanish, and the correlator is determined only by the trace part with the anomaly pole.

43 pages, Corrections to Section 7 after publication