Direct algebraic restoration of Slavnov-Taylor identities in the Abelian Higgs-Kibble model

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. 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 several invariants for the linearized ST operator S0 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. It is suggested that the choice of the basis of counterterms (normalization conditions) and of the linearly independent equations (consistency conditions) can be of great help in actual calculations. An explicit mass term for the gauge field is introduced, in order to study the consistency conditions on general ground and in particular in the case where BRST transformations are not nilpotent.