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

TL;DR

This paper derives a Ginsparg-Wilson relation for lattice chiral symmetry in interacting fermionic theories, providing non-perturbative solutions that enable chiral invariant formulations with auxiliary fields.

Contribution

It introduces a method to incorporate lattice chiral symmetry in interacting fermion theories using auxiliary fields and derives explicit solutions to the Ginsparg-Wilson relation.

Findings

Derived Ginsparg-Wilson relation for interacting fermions.

Obtained explicit non-perturbative solutions.

Constructed chiral invariant partition function.

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.