Chiral anomalies in two dimensions

Abstract

Chiral anomalies offer a fundamental probe of the quantum structure of gauge theories and their underlying symmetries. In this paper, we introduce a framework to characterize the chiral anomaly in two dimensions directly at the diagrammatic level. To this end, we establish a consistent prescription for handling $γ^5$ in dimensional regularization at $d=2$. On this basis, we derive an expression for the fully generic chiral anomaly directly from the contributions of the bubble and triangle diagrams, either in the massless or massive case. Then, we show that the different forms of the anomaly can arise from appropriate choices of parameters directly at the level of this master expression. Overall, $d=2$ is shown to provide an excellent environment to investigate chiral anomalies at the amplitude level: Ward identities are demonstrated rigorously and to arbitrary order in the mass expansion without further approximation, resulting in an unprecedented degree of control on the anomaly.