Index Theorem and Overlap Formalism with Naive and Minimally Doubled Fermions

TL;DR

This paper establishes a theoretical foundation for the Index theorem using naive and minimally doubled lattice fermions, introducing flavored mass terms and new overlap fermions that preserve symmetries and detect gauge field topology.

Contribution

It develops a spectral flow approach for naive and minimally doubled fermions, introducing flavored mass terms to construct new overlap fermions with desired properties.

Findings

Spectral flow correctly detects zero mode index linked to gauge topology

New single-flavor naive overlap fermion maintains hypercubic symmetry

Flavored mass terms enable construction of overlap fermions with variable flavor numbers

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. 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. We succeed to obtain a single-flavor naive overlap fermion which maintains hypercubic symmetry.