Non-perturbative aspects of chiral anomalies

We investigate the properties of chiral anomalies in d = 2 in the framework of constructive quantum field theory. The condition that the gauge propagator is sufficiently soft in the ultraviolet is essential for the anomaly non-renormalization; when it is violated, as for contact current-current interactions, the anomaly is renormalized by higher order corrections. The same conditions are also essential for the validity, in the massless case of the closed equation obtained combining Ward identities and Schwinger-Dyson equations; this solves the apparent contradiction between perturbative computations and exact analysis