Higher order anomaly consistency conditions: renormalization and non-locality

We study the Slavnov–Taylor Identities (STI) breaking terms, up to the second order in perturbation theory. We investigate which requirements are needed for the first order Wess–Zumino consistency condition to hold true at the next order in perturbation theory. We find that: (a) If the cohomologically trivial contributions to the first order ST breaking terms are not removed by a suitable choice of the first order normalization conditions, the Wess–Zumino consistency condition is modified at the second order. (b) Moreover, if one fails to remove the cohomologically trivial part of the first order STI breaking local functional, the second order anomaly actually turns out to be a non-local functional of the fields and the external sources. By using the Wess–Zumino consistency condition and the Quantum Action Principle, we show that the cohomological analysis of the first order STI breaking terms can actually be performed also in a model (the massive Abelian Higgs–Kibble one) where the BRST transformations are not nilpotent.