The BV Master Equation for the Wilson Action in general Yang-Mills Gauge Theory
Takeshi Higashi, Etsuko Itou, Taichiro Kugo
TL;DR
This paper demonstrates that the Wilson effective action in general Yang-Mills gauge theories satisfies the BV master equation, maintaining gauge consistency despite a momentum cutoff, and connects to the Ward-Takahashi identity in Abelian cases.
Contribution
It shows the Wilson effective action obeys the BV master equation in gauge theories with a cutoff, extending the understanding of gauge invariance in effective actions.
Findings
Wilson effective action satisfies BV master equation
Gauge invariance is preserved despite momentum cutoff
Derives Ward-Takahashi identity for Abelian gauge theory
Abstract
The Wilson effective action for general Yang-Mills gauge theory is shown to satisfy the usual form of Batalin-Vilkovisky (BV) master equation, despite that a momentum cutoff apparently breaks the gauge invariance. In the case of Abelian gauge theory, in particular, it actually deduces the Ward-Takahashi identity for Wilson action recently derived by Sonoda.
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