Ginsparg-Wilson Relation and Lattice Chiral Symmetry in Fermionic Interacting Theories

Abstract

We derive Ginsparg-Wilson relation for a lattice chiral symmetry in theories with self-interacting fermions. Auxiliary scalar and pseudo-scalar fields are introduced on a coarse lattice to give an effective description of the fermionic interactions. We obtain particular solutions to the Ginsparg-Wilson relation and other Ward-Takahashi identities in a closed form. These non-perturbative solutions can be used to construct a chiral invariant action and an invariant path-integral measure on the coarse lattice. The resulting partition function exhibits the exact chiral symmetry in the fermionic system with the auxiliary fields.

References in corpus (8)

• Locality properties of Neuberger's lattice Dirac operator
• Abelian chiral gauge theories on the lattice with exact gauge invariance
• Exact chiral symmetry, topological charge and related topics
• Topology and the axial anomaly in abelian lattice gauge theories
• Ginsparg-Wilson Relation and Ultralocality
• Chiral structure of the solutions of the Ginsparg-Wilson relation
• Realization of Global Symmetries in the Wilsonian Renormalization Group
• Gross-Neveu model with overlap fermions

Cited by in corpus (6)

• Flow Equation for Supersymmetric Quantum Mechanics
• Generalising the Ginsparg-Wilson relation: Lattice Supersymmetry from Blocking Transformations
• Magnetic catalysis in the (2+1)-dimensional Gross-Neveu model
• Formulation of Supersymmetry on a Lattice as a Representation of a Deformed Superalgebra
• Gradient flow exact renormalization group -- inclusion of fermion fields
• Lattice Chiral Symmetry in Fermionic Interacting Theories and the Antifield Formalism