Regular Article - Theoretical Physics
Adler–Bardeen theorem and manifest anomaly cancellation to all orders in gauge theories
Dipartimento di Fisica “Enrico Fermi”, Università di Pisa, and INFN, Sezione di Pisa, Largo B. Pontecorvo 3, 56127, Pisa, Italy
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Accepted: 15 September 2014
Published online: 7 October 2014
We reconsider the Adler–Bardeen theorem for the cancellation of gauge anomalies to all orders, when they vanish at one loop. Using the Batalin–Vilkovisky formalism and combining the dimensional-regularization technique with the higher-derivative gauge invariant regularization, we prove the theorem in the most general perturbatively unitary renormalizable gauge theories coupled to matter in four dimensions, and we identify the subtraction scheme where anomaly cancellation to all orders is manifest, namely no subtractions of finite local counterterms are required from two loops onwards. Our approach is based on an order-by-order analysis of renormalization, and, differently from most derivations existing in the literature, does not make use of arguments based on the properties of the renormalization group. As a consequence, the proof we give also applies to conformal field theories and finite theories.
© SIF and Springer-Verlag Berlin Heidelberg, 2014