CFT Constraints on Parity-odd Interactions with Axions and Dilatons

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 $⟨JJO{⟩}_{odd}$ and the $⟨TTO{⟩}_{odd}$ 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.

arXiv comment22 pages, published version