We are dealing with two-dimensional gravitational anomalies, specificallywith the Einstein anomaly and the Weyl anomaly, and we show that they are fullydetermined by dispersion relations independent of any renormalization procedure(or ultraviolet regularization). The origin of the anomalies is the existenceof a superconvergence sum rule for the imaginary part of the relevantformfactor. In the zero mass limit the imaginary part of the formfactorapproaches a $\delta$-function singularity at zero momentum squared, exhibitingin this way the infrared feature of the gravitational anomalies. We find anequivalence between the dispersive approach and the dimensional regularizationprocedure. The Schwinger terms appearing in the equal time commutators of theenergy momentum tensors can be calculated by the same dispersive method.Although all computations are performed in two dimensions the method isexpected to work in higher dimensions too.
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