Realization of Global Symmetries in the Wilsonian Renormalization Group

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.

11 pages

References in corpus (4)

• Exact evolution equation for the effective potential
• BRS Symmetry, the Quantum Master Equation, and the Wilsonian Renormalization Group
• Exact Symmetries realized on the Renormalized Group Flow
• Exact BRS Symmetry realized on the Renormalization Group Flow

Cited by in corpus (5)

• The nonperturbative functional renormalization group and its applications
• Quantum gravity: a fluctuating point of view
• Generalising the Ginsparg-Wilson relation: Lattice Supersymmetry from Blocking Transformations
• Ginsparg-Wilson Relation and Lattice Chiral Symmetry in Fermionic Interacting Theories
• Lattice Chiral Symmetry in Fermionic Interacting Theories and the Antifield Formalism