Lattice Chiral Symmetry in Fermionic Interacting Theories and the Antifield Formalism

TL;DR

This paper explores the realization of exact chiral symmetry in lattice fermionic theories with interactions, utilizing the antifield formalism to derive Ward-Takahashi identities and constructing regular, potentially consistent quantum actions.

Contribution

It introduces a novel application of the antifield formalism to lattice chiral symmetry in interacting fermion theories, providing explicit solutions and regularized actions.

Findings

Quantum master equation generates Ward-Takahashi identities including Ginsparg-Wilson relation.

Explicit solutions to the quantum master equation are obtained, but some are singular.

Two regular actions are identified that may define consistent quantum theories.

Abstract

Recently we have discussed realization of an exact chiral symmetry in theories with self-interacting fermions on the lattice, based upon an auxiliary field method. In this paper we describe construction of the lattice chiral symmetry and discuss its structure in more detail. The antifield formalism is used to make symmetry consideration more transparent. We show that the quantum master equation in the antifield formalism generates all the relevant Ward-Takahashi identities including a Ginsparg-Wilson relation for interacting theories. Solutions of the quantum master equation are obtained in a closed form, but the resulting actions are found to be singular. Canonical transformations are used to obtain four types of regular actions. Two of them may define consistent quantum theories. Their Yukawa couplings are the same as those obtained by using the chiral decomposition in the free field algebra. Inclusion of the complete set of the auxiliary fields is briefly discussed.