Index Theorem and Overlap Formalism with Naive and Minimally Doubled Fermions

TL;DR

This paper establishes a theoretical foundation for the index theorem in naive and minimally doubled lattice fermions using spectral flow analysis of Hermitean Dirac operators, introducing flavored mass terms for constructing new overlap fermions.

Contribution

It develops a spectral flow approach for index theorem in naive and minimally doubled fermions and introduces flavored mass terms to create new overlap fermions with variable flavor numbers.

Findings

Spectral flow correctly detects zero mode index related to gauge topology.

Flavored mass terms enable construction of new overlap fermions from naive kernels.

Number of flavors in overlap fermions depends on mass term choices.

Abstract

We present a theoretical foundation for the index theorem in naive and minimally doubled lattice fermions by studying the spectral flow of a Hermitean version of Dirac operators. We utilize the point splitting method to implement flavored mass terms, which play an important role in constructing proper Hermitean operators. We show the spectral flow correctly detects the index of the would-be zero modes which is determined by gauge field topology and the number of species doublers. Using the flavored mass terms, we present new types of overlap fermions from the naive fermion kernels, with a number of flavors that depends on the choice of the mass terms.