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We show that in Yang-Mills theory the Slavnov-Taylor (ST) identity, extendedin the presence of a background gauge connection, allows to fix in a unique waythe dependence of the vertex functional on the background, once the 1-PIamplitudes at zero background are known. The reconstruction of the backgrounddependence is carried out by purely algebraic techniques and therefore can beapplied in a non-perturbative scheme (e.g. on the lattice or in theSchwinger-Dyson approach), provided that the latter preserves the ST identity.The field-antifield redefinition, which replaces the classicalbackground-quantum splitting when quantum corrections are taken into account,is considered on the example of an instanton background in SU(2) Yang-Millstheory.

Background field dependence from the Slavnov-Taylor identity in (non-perturbative) Yang-Mills theory