Gravitational axial anomaly for four-dimensional conformal field theories Original Research Article

We construct the three-point function involving an axial vector current and two energy–momentum tensors for four-dimensional conformal field theories. Conformal symmetry determines the form of this three-point function uniquely up to a constant factor if the necessary conservation conditions are imposed. The gravitational axial anomaly present on a curved space background leads to a non-zero contribution for the divergence of the axial current in this three-point function even on flat space. Using techniques related to differential regularisation which guarantee that the energy–momentum tensor is conserved and traceless, we calculate the anomaly in the three-point function directly. In this way we relate the overall coefficient of the three-point function to the scale of the gravitational axial anomaly. We apply our results to the examples of the fermion and photon axial currents.