Axial gravity: a non-perturbative approach to split anomalies

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.Comment: 43 pages, some additions in section 6.3 and 6.5 plus minor correction

Axial gravity, massless fermions and trace anomalies

This article deals with two main topics. One is odd parity trace anomalies in Weyl fermion theories in a 4d curved background, the second is the introduction of axial gravity. The motivation for reconsidering the former is to clarify the theoretical background underlying the approach and complete the calculation of the anomaly. The reference is in particular to the difference between Weyl and massless Majorana fermions and to the possible contributions from tadpole and seagull terms in the Feynman diagram approach. A first, basic, result of this paper is that a more thorough treatment, taking account of such additional terms { and using dimensional regularization}, confirms the earlier result. The introduction of an axial symmetric tensor besides the usual gravitational metric is instrumental to a different derivation of the same result using Dirac fermions, which are coupled not only to the usual metric but also to the additional axial tensor. The action of Majorana and Weyl fermions can be obtained in two different limits of such a general configuration. The results obtained in this way confirm the previously obtained ones.Comment: 55 pages, comments added in section 2 and 5. Sections 6.4, 6.6, 7, 7.1, 7.2 and Appendices 5.3, 5.5 partially modifie

Worldline quantization of field theory, effective actions and L ∞ structure

Abstract We formulate the worldline quantization (a.k.a. deformation quantization) of a massive fermion model coupled to external higher spin sources. We use the relations obtained in this way to show that its regularized effective action is endowed with an L ∞ symmetry. The same result holds also for a massive scalar model