On the trace anomaly of a Weyl fermion in a gauge background

Broccoli, Matteo (2018) On the trace anomaly of a Weyl fermion in a gauge background. [Laurea magistrale], Università di Bologna, Corso di Studio in Fisica [LM-DM270]
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In this thesis we study the trace anomaly of a Weyl fermion in an abelian gauge background. We first introduce the topic of anomaly in Quantum Fields Theory and provide case studies of a global and a gauge anomaly. Then, we review the lagrangians of the Weyl fermion and Dirac fermion, the models that are the focus of our chiral and trace anomaly computations. Since we evaluate the anomalies using Pauli-Villars (PV) regularization, we present different PV masses and discuss the classical symmetries they break. We identify the differential operators that enter our regularization schemes and we review the method that we use to evaluate anomalies: we read them from the path integral à la Fujikawa and compute them with heat kernel formulas. Then, we evaluate the chiral and trace anomaly of the models we are interested in. The chiral anomaly is well studied in the literature and we reproduce the standard result. The trace anomaly is our original result and, although the presence of the chiral anomaly implies a breakdown of gauge invariance, we find that the trace anomaly can be cast in a gauge invariant form. The issue is analogous to the one recently discussed in the literature about a conjectured contribution of an odd-parity term to the trace anomaly of a Weyl fermion in curved backgrounds. With an abelian gauge background, this odd-parity term would be a Chern-Pontryagin density, that does not appear in our final results.

Tipologia del documento
Tesi di laurea (Laurea magistrale)
Autore della tesi
Broccoli, Matteo
Relatore della tesi
Correlatore della tesi
Corso di studio
Curriculum A: Teorico generale
Ordinamento Cds
Parole chiave
Conformal Fiel Theory,Anomalies in Field and String Theories,Weyl fermion,abelian gauge,gauge invariance,Pauli-Villars regularization,chiral anomaly,trace anomaly,heat kernel,Dirac fermion,path integral
Data di discussione della Tesi
28 Settembre 2018

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