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

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

2011-12-08

arxiv.org/abs/1112.1817v1

Physics

High Energy Physics

High Energy Physics - Theory

12 pages. Prepared for QCD-TNT II, September 5-9, 2011, Trento, Italy

Scientific paper

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

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