Topological properties of minimally doubled fermions in two space-time dimensions
Abstract
The two-dimensional Schwinger model is used to explore how lattice fermion operators perceive the global topological charge q ∈ Z of a given background gauge field. We focus on Karsten-Wilczek and Borici-Creutz fermions, which are minimally doubled, and compare them to Wilson, Brillouin, naive, staggered and Adams fermions. For each operator the eigenvalue spectrum in a background with q ≠ 0 is determined along with the chiralities of the eigenmodes, and the spectral flow of the pertinent hermitean operator is worked out. We find that Karsten-Wilczek and Borici-Creutz fermions perceive the global topological charge q in the same way as staggered and naive fermions do.
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