The relationship between the conformal and gravitational anomalies

It is shown that the vectorial part of the general coordinate transformation (GCT) anomaly cannot be eliminated by local counterterms without generating the conformal anomaly for the system with classical GCT and conformal symmetries. The vectorial part of the GCT anomaly is equivalent to the non-topological conformal anomaly similarly as the chiral part of the GCT anomaly is equivalent to the topological Lorentz anomaly. In two dimensions, the conformal anomaly is topological, and equivalent to the Lorentz anomaly up to the factor i for the left (or right) part contribution only.