Abstract
The program in this chapter is to generalize Bardeen’s setup of non-Abelian gauge theories to general theories in a generalized metric background in \(4\textsf{d}\). That is, beside the usual metric, the model is endowed with an additional symmetric tensor that interacts axially with fermions. This is referred to as the metric-axial-tensor (MAT) gravity. Anomalies in such a background are analyzed with the previously introduced non-perturbative methods, the Schwinger-DeWitt and the Seeley-DeWitt method. The most important results are: the absence of diffeomorphism anomalies, the calculation of the odd (Pontryagin) and even parity trace anomaly and of the KDS anomaly for a Weyl fermion and the ABJ-like trace anomaly for a Dirac fermion.
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Notes
- 1.
One could consider also an axial complex action, but for our purposes this is a useless complication. That is why we use the notation \(\psi (\widehat{x})\) instead of \(\widehat{\psi }(\widehat{x}) \).
- 2.
One could object that the choice of \( \left( i\widehat{\gamma }\!\cdot \!\widehat{\nabla }\right) ^2\) breaks only the axial diffeomorphisms, while eventually we are interested in ordinary diffeomorphisms. This remark, however, is misleading, because in the chiral limit a violation of the axial diffeomorphisms would precisely affect also the ordinary diffeomorphism conservation.
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Bonora, L. (2023). Metric-Axial-Tensor (MAT) Background. In: Fermions and Anomalies in Quantum Field Theories. Theoretical and Mathematical Physics. Springer, Cham. https://doi.org/10.1007/978-3-031-21928-3_10
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