We analyze the chiral (Adler) anomaly in abelian gauge theories. With the aid of the renormalization group flow equation, we prove UV and IR bounds on the euclidean perturbative 1-PI functions of massless theories. We then prove the absence of anomalies for a class of chiral abelian gauge theories. At the end, we comment on the standard model.

CPHT, Ecole Polytechnique