Abstract
We investigate some properties of Karsten-Wilczek and Borici-Creutz fermions, which are the best known varieties in the class of minimally doubled lattice fermion actions. Our focus is on the dispersion relation and the distribution of eigenvalues in the free-field theory. We consider the situation in two and four space-time dimensions, and we discuss how properties vary as a function of the Wilson-like lifting parameter $r$.
Highlights
The choice of any lattice fermion action is a bit of a compromise
Staggered fermions put a focus on ultralocality and chiral symmetry, at the expense of having four species in the continuum [3]
It is based on adding an extra term to the naive action which lifts 14 of the 16 species in d 1⁄4 4 dimensions, albeit with the important difference to the Wilson term that it does not break chiral symmetry
Summary
The choice of any lattice fermion action is a bit of a compromise. Ideally, one would want to realize ultralocality, chiral symmetry, and the absence of doublers (in addition to a correct continuum limit, ). It is based on adding an extra term (of mass-dimension five) to the naive action which lifts 14 of the 16 species in d 1⁄4 4 dimensions, albeit with the important difference to the Wilson term that it does not break chiral symmetry Such “minimally doubled fermions” have been proposed by Karsten [27] and Wilczek [28], and later by Creutz [29] and Borici [30]. V, and more lengthy calculations are arranged in Appendixes A–E
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