CFT Constraints on Parity-odd Interactions with Axions and Dilatons

TL;DR

This paper uses conformal Ward identities in momentum space to analyze parity-odd three-point correlators involving currents, energy-momentum tensors, and scalars, revealing constraints on axion and dilaton couplings in a conformal early universe.

Contribution

It provides a detailed analysis of how conformal invariance constrains parity-odd correlators and identifies specific non-vanishing correlators related to anomalies, informing axion and dilaton interactions.

Findings

Most parity-odd correlators vanish due to conformal invariance.

Non-zero correlators are protected by anomalies and involve specific scalar operators.

Results constrain axion and dilaton couplings in conformal cosmological models.

Abstract

We illustrate how the conformal Ward identities (CWIs) in momentum space completely determine the structure of a parity-odd 3-point correlator involving currents, energy momentum tensors and at least one scalar operator in $d=4$. Conformal invariance fixes almost all such possible correlators to vanish. The only exceptions are given by the $\langle JJO\rangle_{odd}$ and the $\langle TTO \rangle_{odd}$ which in momentum-space are protected by chiral and conformal anomalies. Specifically, one can obtain a non-vanishing solution by considering scalar operators such as $O=\nabla \cdot J_A$, $O=g_{\mu\nu}T^{\mu\nu}$ or their shadow transforms. We comment on the implications of these results that constrain the coupling of axions and dilatons in a conformal phase of the early universe.