Shift of symmetries of naive and staggered fermions in QCD-like lattice theories

Abstract

We study the global symmetries of naive and staggered lattice Dirac operators in QCD-like theories in any dimension larger than two. In particular we investigate how the chosen number of lattice sites in each direction affects the global symmetries of the Dirac operator. These symmetries are important since they determine not only the infrared spectrum of the Dirac operator but also the symmetry breaking pattern and, thus, the lightest pseudoscalar mesons. We perform the symmetry analysis and discuss the possible zero modes and the degree of degeneracy of the lattice Dirac operators. Moreover we explicitly identify a "reduced" lattice Dirac operator which is the naive Dirac operator apart fr..