Abstract
Using the background field method for the functional renormalization group approach in the case of a generic gauge theory, we study the background field symmetry and gauge dependence of the background average effective action, when the regulator action depends on external fields. The final result is that the symmetry of the average effective action can be maintained for a wide class of regulator functions, but in all cases the dependence of the gauge fixing remains on-shell. The Yang–Mills theory is considered as the main particular example.
Highlights
One of the most prospective non-perturbative approaches in quantum field theory (QFT) is the functional renormalization group (FRG), which is based on the Wetterich equation for the average effective action [1,2,3]
The main problem of functional (or exact) renormalization group (FRG) applied to the gauge theories is that the dependence on the choice of the gauge fixing condition does not disappear on-shell [16], as it is the case in the usual perturbative QFT
One can expect that the renormalization group flow in the Yang–Mills theory will manifest a fundamental gauge dependence, and this certainly shadows the interpretation of the results obtained within the FRG approach in the gauge theories
Summary
One of the most prospective non-perturbative approaches in quantum field theory (QFT) is the functional (or exact) renormalization group (FRG), which is based on the Wetterich equation for the average effective action [1,2,3] (see the reviews [4,5,6,7] and textbook [8] for an introduction to the subject). The considerations in the last and many other papers are based on the background field method, which enables one to maintain the gauge invariance for the Yang–Mills (or gravitational) field explicitly in the effective action. In what follows we consider both gauge invariance and gauge fixing dependence for the effective average action. 4 we present a solution to the background field symmetry of background average effective action with regulator functions which are invariant under gauge transformations of the external field. The Grassmann parity of a quantity A is denoted ε( A)
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