Index theorem with Minimally Doubled Fermions in four space-time dimensions

TL;DR

This paper investigates the zero eigenmode spectrum of Minimally Doubled Fermions in four-dimensional lattice gauge theories, verifying the Atiyah-Singer index theorem using background gauge fields with different topological charges.

Contribution

It demonstrates the spectral flow and topological properties of Minimally Doubled Fermions, confirming the index theorem in various gauge field backgrounds.

Findings

Spectral flow detects gauge field topology.

Zero modes' chiralities match topological charge.

Index theorem verified for different gauge backgrounds.

Abstract

We determine the zero eigenmode spectrum of Minimally Doubled Fermions (MDF), namely in Karsten-Wilczek (KW) and Borici-Creutz (BC) formulations on the 4-dimensional space-time lattice. We employ background gauge fields with integer valued topological charges. The Atiyah-Singer index theorem is verified in the presence of two different background gauge fields, namely Smit-Vink [1] and cooled down MILC asqtad ensembles with $N_f=2+1$ dynamical flavors of quarks [2]. Using flavored mass terms [3,4], we find that the spectral flow of the eigenvalues detects the topology of the background gauge field. With the use of the modified chirality operator, we obtain chiralities of the zero eigenmodes and the fermionic topological charge.