Higher order anomaly consistency conditions: renormalization and non-locality

We study the Slavnov-Taylor Identities (STI) breaking terms, up to the seco nd order in perturbation theory. We investigate which requirements an neede d for the first order Wess-Zumino consistency condition to hold true at the next order in perturbation theory. We find that: (a) If the cohomologicall y trivial contributions to the first order ST breaking terms are not remove d by a suitable choice of the first order normalization conditions, the Wes s-Zumino consistency condition is modified at the second order. (b) Moreove r, if one fails to remove the cohomologically trivial part of the first ord er STI breaking local functional, the second order anomaly actually turns o ut to be a non-local functional of the fields and the external sources. By using the Wess-Zurnino consistency condition and the Quantum Action Princip le, 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. (C) 2001 Els evier Science B.V. All rights reserved.