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

TL;DR

This paper demonstrates how the Slavnov-Taylor identity can algebraically determine the background dependence of the vertex functional in non-perturbative Yang-Mills theory, applicable in lattice and Schwinger-Dyson approaches.

Contribution

It introduces a method to fix background dependence algebraically using the Slavnov-Taylor identity, applicable in non-perturbative schemes like lattice and Schwinger-Dyson approaches.

Findings

Background dependence can be uniquely fixed algebraically from zero-background amplitudes.

The method applies to non-perturbative schemes preserving the Slavnov-Taylor identity.

Field-antifield redefinition is exemplified on an SU(2) instanton background.

Abstract

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.