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This work presents a first study of a radiative calculation for thegravitational axial anomaly in the massless Abelian Higgs model. The two loopcontribution to the anomalous correlation function of one axial current and twoenergy-momentum tensors, <A_alpha(z) T_\mu\nu(y) T_\rho\sigma(x)>, is computedat an order that involves only internal matter fields. Conformal properties ofmassless field theories are used in order to perform the Feynman diagramcalculations in the coordinate space representation. The two loop contributionis found not to vanish, due to the presence of two independent tensorstructures in the anomalous correlator.Comment: 34 pages, 5 figures, RevTex, Minor changes, Final version for Phys.  Rev.

Conformal symmetry and the three point function for the gravitational axial anomaly