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We consider a Dirac fermion in a metric-axial-tensor (MAT) background. Byregulating it with Pauli-Villars fields we analyze and compute its full anomalystructure. Appropriate limits of the MAT background allows to recover theanomalies of Dirac and Weyl fermions in the usual curved spacetime, obtainingin particular the trace anomaly of a chiral fermion, which has been the objectof recent analyses.

Axial gravity and anomalies of fermions