On the total derivative divergence for a nonminimal vector operator

We report on the calculation of the total derivative □R term in the divergence of the vacuum effective action for the nonminimal vector field operator in a curved space background. This term led to interesting discussions in the literature, in particular because it defines the local part of anomaly-induced effective action in conformal quantum gravity and may be decisive for the renormalizability of this theory. The divergent term of our interest was previously derived several times. One of the main results is that the mentioned local term is gauge-fixing dependent in the case of the electromagnetic field, which contradicts the general theorems about quantum corrections. We perform the derivation by using Riemann's normal coordinates and confirm the previous results. The discussion includes the possible role of the gauge-dependent IR regulators and the related ambiguity.