Anomalies in the stress tensor of a chiral fermion in a gauge background

In this thesis we study the anomalies of a chiral fermion in a gauge background, using a different regularization from those already present in literature. The aim here is to study all the anomalies involving the stress tensor. The final motivation is to eventually focus on the trace anomaly, which has been of some interest recently. Thus, after a brief introduction to the issue of anomalies in QFT, we proceed by studying the symmetries of a massless left-handed Weyl fermion coupled to an abelian gauge background and to gravity as well (used as an external source for the stress tensor). The regularization of the corresponding QFT is then implemented through Pauli-Villars (PV) fields having a Dirac mass. Particular emphasis is put on the unusual mass term used at this stage, consisting of a customary Dirac mass multiplied by the vierbein determinant e raised to the generic power a. After devoting a chapter to the mathematical tool of the heat kernel, we restrict ourselves to flat space, present the regulators of the model, the "jacobians" associated to each of its symmetries, and all the useful heat kernel coefficients needed for the anomaly calculations. Finally, we evaluate all the anomalies of our model: the usual chiral anomaly and the anomalies in the stress tensor, namely the trace anomaly, the anomaly in the symmetry of the stress tensor (the local Lorentz anomaly), and the anomaly in the conservation of the stress tensor (the gravitational anomaly). The latter is the most demanding task, as it requires the use of particular heat kernel coefficients which have been rarely treated in literature. The calculation of all these anomalies is the leading task accomplished in this thesis. Of course, one does not expect all these anomalies to be genuine, as some are expected to be canceled by the variation of local counterterms, leaving at the end only the chiral and trace anomalies with their known expression. That this is the case is left for future research.