Direct Algebraic Restoration of Slavnov-Taylor Identities in the Abelian Higgs-Kibble Model

TL;DR

This paper introduces an algebraic method to restore Slavnov-Taylor identities in the Abelian Higgs-Kibble model, avoiding explicit breaking term evaluation and ensuring consistency through linear problem solving.

Contribution

It presents a novel algebraic approach for restoring STI in gauge theories, applicable to models with mass terms, and discusses conditions for consistent solutions.

Findings

No anomalies found, STI restoration is equivalent to solving a linear problem.

Multiple solutions exist due to invariants, corresponding to different normalization conditions.

Over-determined system requires consistency conditions for STI restoration.

Abstract

A purely algebraic method is devised in order to recover Slavnov-Taylor identities (STI), broken by intermediate renormalization. The counterterms are evaluated order by order in terms of finite amplitudes computed at zero external momenta. The evaluation of the breaking terms of the STI is avoided and their validity is imposed directly on the vertex functional. The method is applied to the abelian Higgs-Kibble model. An explicit mass term for the gauge field is introduced, in order to check the relevance of nilpotency. We show that, since there are no anomalies, the imposition of the STI turns out to be equivalent to the solution of a linear problem. The presence of ST invariants implies that there are many possible solutions, corresponding to different normalization conditions. Moreover, we find more equations than unknowns (over-determined problem). This leads us to the consideration of consistency conditions, that must be obeyed if the restoration of STI is possible.