CFT Correlators and CP-Violating Trace Anomalies

TL;DR

This paper investigates how parity-odd trace anomalies influence conformal field theory correlators involving currents and stress tensors, revealing conditions under which these correlators are nonzero and constrained by anomalies.

Contribution

It extends the analysis of parity-odd correlators in CFTs to include effects of trace anomalies, providing explicit conditions for nonzero correlators and their anomaly-induced structures.

Findings

Certain parity-odd correlators are nonzero when scalar operator dimension is 4.

Parity-odd trace anomalies induce nonzero JJT and TTT correlators.

The JJT correlator's transverse-traceless part vanishes, with the trace part determined by the anomaly pole.

Abstract

We analyze the parity-odd correlators $\langle JJO\rangle_{odd}$, $\langle JJT\rangle_{odd}$, $\langle TTO\rangle_{odd}$ and $\langle TTT\rangle_{odd}$ 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 $\langle JJO\rangle_{odd}$ and $\langle TTO\rangle_{odd}$ 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 $\langle JJT\rangle_{odd}$ and $\langle TTT\rangle_{odd}$ are nonzero. In particular, in the case of $\langle JJT\rangle_{odd}$ the transverse-traceless component is constrained to vanish, and the correlator is determined only by the trace part with the anomaly pole.