  In a theory of a Dirac fermion field coupled to a metric-axial-tensor (MAT)
background, using a Schwinger-DeWitt heat kernel technique, we compute
non-perturbatively the two (odd parity) trace anomalies. A suitable collapsing
limit of this model corresponds to a theory of chiral fermions coupled to
(ordinary) gravity. Taking this limit on the two computed trace anomalies we
verify that they tend to the same expression, which coincides with the already
found odd parity trace anomaly, with the identical coefficient. This confirms
our previous results on this issue.
