Chiral Invariance and Species Doublers in Generic Fermion Models on the Lattice

TL;DR

This paper investigates the fundamental limitations of constructing chirally invariant lattice fermion models, demonstrating that species doublers are unavoidable in well-regularized models, and explores examples of improved models with fewer doublers.

Contribution

It provides a general proof that species doublers are inevitable in chirally invariant lattice models under certain regularization conditions.

Findings

Species doublers are unavoidable in well-regularized chirally invariant lattice models.

The Ward-Takahashi identity is used to derive the general conclusion.

Examples of models with fewer species doublers than naive Dirac action are discussed.

Abstract

Discussions are made on the structures of chirally invariant lattice actions without any restriction of hermiticity. With the help of the Ward-Takahashi identity a general conclusion can be derived that there must be species doublers in any chirally invariant model provided that the model is chosen as well-regularized, that is, there is no singularity in the propagator after introducing fermion mass on the lattice. Various examples are discussed to pick up better models defined in the sense that the number of species doubler is smaller than that of the naive Dirac action.