Overlap-Dirac fermions preserve the parity-doubling of the spectrum in a singular monopole background, while naive and Wilson-Dirac fermions break the degeneracy of the Q lowest modes even in the continuum limit.
Comments on staggered fermions / Panel discussion
1 Pith paper cite this work. Polarity classification is still indexing.
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Pith paper citing it
abstract
The rooting procedure commonly used with staggered fermions does not correctly treat non-perturbative effects associated with gauge field topology. In practice these effects are small for the physics of flavor non-singlet particles. However large uncontrolled systematic errors are expected for flavor singlet issues, such as the mass of the eta prime meson. While the relative speed of the algorithm in large scale simulations may justify its use, the method is an approximation and should not be promoted as a first principles approach to the strong interactions.
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A curious behavior of three-dimensional lattice Dirac operators coupled to monopole background
Overlap-Dirac fermions preserve the parity-doubling of the spectrum in a singular monopole background, while naive and Wilson-Dirac fermions break the degeneracy of the Q lowest modes even in the continuum limit.