Realization of Global Symmetries in the Wilsonian Renormalization Group

TL;DR

This paper develops a method to solve the master equation for Wilsonian actions within the antifield formalism, enabling the non-perturbative preservation of global symmetries during RG flow.

Contribution

It introduces a representation theory approach for cutoff-dependent global symmetries in the Wilsonian RG, including a continuum Ginsparg-Wilson relation for chiral symmetry.

Findings

Derived a continuum Ginsparg-Wilson relation for free theories.

Constructed chiral invariant operators with fermionic self-interactions.

Presented a realization of SU(2) vector symmetry within the formalism.

Abstract

We present a method to solve the master equation for the Wilsonian action in the antifield formalism. This is based on a representation theory for cutoff dependent global symmetries along the Wilsonian renormalization group (RG) flow. For the chiral symmetry, the master equation for the free theory yields a continuum version of the Ginsparg-Wilson relation. We construct chiral invariant operators describing fermionic self-interactions. The use of canonically transformed variables is shown to simplify the underlying algebraic structure of the symmetry. We also give another non-trivial example, a realization of SU(2) vector symmetry. Our formalism may be used for a non-perturbative truncation of the Wilsonian action preserving global symmetries.