Abstract
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.
Highlights
One can suspect that at some stage differences might emerge between fermions with opposite chiralities in their interaction with gravity
A suitable collapsing limit of this model corresponds to a theory of chiral fermions coupled to 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
The situation appropriate for Weyl fermions is recovered in a specific limit, the collapsing limit
Summary
One can suspect that at some stage differences might emerge between fermions with opposite chiralities in their interaction with gravity. A privileged place where such differences may show up are the anomalies In this case the candidate is the trace anomaly, because it involves precisely the coupling between the metric and the energymomentum tensor. There is no direct way to do it, basically because the Dirac operator for a Weyl fermion contains a chiral projector. The metric-axialtensor (MAT) gravity is designed to do this It is formulated for Dirac fermions coupled to the usual metric and to an axial symmetric tensor. In this case the operator involved is the usual Dirac operator. But more detailed, presentation of both the problem we wish to solve and the method we use
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