  We compute in linearized gravity all the contributions to the gravitational
effective action due to a virtual Dirac fermion, related to the conformal
anomaly. This requires, in perturbation theory, the identification of the
gauge-gauge-graviton vertex off mass shell, involving the correlator of the
energy-momentum tensor and two vector currents ($TJJ$), which is responsible
for the generation of the gauge contributions to the conformal anomaly in
gravity. We also present the anomalous effective action in the inverse mass of
the fermion as in the Euler-Heisenberg case.

High Energy Physics - Phenomenology;General Relativity and Quantum Cosmology;High Energy Physics - Theory