CFT constraints on parity-odd interactions with axions and dilatons

We illustrate how the conformal Ward identities in momentum space completely determine the structure of a parity-odd three-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 nonvanishing solution by considering scalar operators such as O= ·JA, O=gμνTμν, 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.