Eigenspectra of Minimally Doubled Fermions

TL;DR

This paper investigates the eigenspectra of minimally doubled fermions in lattice gauge theory, demonstrating the spectral flow and the Index theorem for different realizations, providing insights into their topological properties.

Contribution

It compares the eigenspectra of Karsten-Wilczek and Borici-Creutz fermions, showing how spectral flow reveals topological features and supports the Index theorem.

Findings

Spectral flow confirms the Index theorem for both fermion types.

Eigenmode chiralities correlate with topological charge.

Differences observed between KW and BC fermion spectra.

Abstract

In this work, we explored the eigenspectra of minimally doubled fermions, in both Karsten-Wilczek and Borici-Creutz realizations. We generated 4-dim $SU(3)$ gauge fields with a definite topological charge and calculated the chiralities of the eigenmodes for KW and BC fermions. We used the spectral flow of the eigenvalues for this purpose and demonstrated the Index theorem.