Abstract
We show that symmetries are preserved exactly along the (Wilsonian) renormalization group flow, though the IR cutoff deforms concrete forms of the transformations. For a gauge theory the cutoff dependent Ward–Takahashi identity is written as the master equation in the antifield formalism: one may read off the renormalized BRS transformation from the master equation. The Maxwell theory is studied explicitly to see how it works. The renormalized BRS transformation becomes non-local but keeps off-shell nilpotency. Our formalism is applicable for a generic global symmetry. The master equation considered for the chiral symmetry provides us with the continuum analog of the Ginsparg–Wilson relation and the Lüscher's symmetry.
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