Higher Order Anomaly Consistency Conditions: Renormalization and Non-Locality

TL;DR

This paper analyzes the second order breaking terms of Slavnov-Taylor identities in perturbation theory, revealing conditions under which anomalies remain local and consistent, especially in models with non-nilpotent BRST transformations.

Contribution

It extends cohomological analysis of STI breaking terms to second order and non-nilpotent BRST models, clarifying conditions for anomaly locality and consistency.

Findings

Failure to remove trivial first order contributions modifies second order consistency.

Unrecovered trivial parts lead to non-local second order anomalies.

Analysis applies even when BRST nilpotency is broken.

Abstract

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 recover 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.