Spin-taste structure of minimally doubled fermions

TL;DR

This paper explores the spin-taste structure of minimally doubled fermions on the lattice, analyzing their symmetries, representations, and implications for constructing hadron operators, with some numerical results supporting the theoretical framework.

Contribution

It provides explicit spin-taste algebra representations for Karsten-Wilczek and Borici-Creutz fermions, clarifies symmetry properties, and discusses counterterm amendments.

Findings

Tasted charge conjugation symmetry identified for KW and BC fermions

Explicit spin-taste algebra representations constructed

Numerical results for KW fermions align with theoretical expectations

Abstract

Minimally doubled fermions realize one degenerate pair of Dirac fermions on the lattice. Similarities to staggered fermions exist, namely, spin and taste degrees of freedom become intertwined, and a remnant, non-singlet chiral symmetry and ultralocality are maintained. However, charge conjugation, isotropy and some space-time reflection symmetries are broken by the cutoff. For two variants, i.e., Karsten-Wilczek (KW) or Borici-Creutz (BC) fermions, a tasted charge conjugation symmetry can be identified, and the respective representations of the spin-taste algebra can be constructed explicitly. In the case of BC fermions, the tasted symmetry indicates that amendments to the published counterterms are necessary. The spin-taste representation on the quark level permits construction of local or extended hadron interpolating operators for any spin-taste combination, albeit with contamination by parity partners and taste-symmetry violation. The few available numerical results for KW fermions are in line with expectations.