Slavnov-Taylor parameterization for the quantum restoration of BRST symmetries in anomaly-free gauge theories

It is shown that the problem of the recursive restoration of theSlavnov-Taylor (ST) identities at the quantum level for anomaly-free gaugetheories is equivalent to the problem of parameterizing the local approximationto the quantum effective action in terms of ST functionals, associated with thecohomology classes of the classical linearized ST operator. The ST functionalsof dimension <=4 correspond to the invariant counterterms, those of dimension>4 generate the non-symmetric counterterms upon projection on the action-likesector. At orders higher than one in the loop expansion there are additionalcontributions to the non-invariant counterterms, arising from known lower orderterms. They can also be parameterized by using the ST functionals. We apply themethod to Yang-Mills theory in the Landau gauge with an explicit mass termintroduced in a BRST-invariant way via a BRST doublet. Despite beingnon-unitary, this model provides a good example where the method devised in thepaper can be applied to derive the most general solution for the action-likepart of the quantum effective action, compatible with the fulfillment of the STidentities and the other relevant symmetries of the model, to all orders in theloop expansion. The full dependence of the solution on the normalizationconditions is given.Comment: 23 pages. Final version published in the journa