Exact Symmetries realized on the Renormalized Group Flow

TL;DR

This paper demonstrates that symmetries, including gauge and chiral symmetries, are exactly preserved along the Wilsonian renormalization group flow through a formalism involving the master equation and antifields, with explicit analysis of Maxwell theory.

Contribution

It introduces a formalism using the master equation in the antifield formalism to preserve symmetries exactly during the renormalization group flow, applicable to various global symmetries.

Findings

Symmetries are preserved exactly along the RG flow.

The renormalized BRS transformation remains off-shell nilpotent.

The formalism reproduces the Ginsparg-Wilson relation and L{" u}scher's symmetry.

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 L{\" u}scher's symmetry.