Abstract
It is well-known that staggered fermions do not necessarily satisfy the same global symmetries as the continuum theory. We analyze the mechanism behind this phenomenon for arbitrary dimension and gauge group representation. For this purpose we vary the number of lattice sites between even and odd parity in each single direction. Since the global symmetries are manifest in the lowest eigenvalues of the Dirac operator, the spectral statistics and also the symmetry breaking pattern will be affected. We analyze these effects and compare our predictions with Monte-Carlo simulations of naive Dirac operators in the strong coupling limit. This proceeding is a summary of our work [1].
Highlights
The global symmetries of QCD-Dirac operators determine the number and the properties of the lightest pseudo-scalar mesons
In the continuum a symmetry analysis was already done in [9] resulting in ten different symmetry breaking patterns, which correspond to the Altland-Zirnbauer tenfold classification of random matrix theory (RMT) [10], [11],[12]
The classification holds for real, complex and quaternion representations of the gauge group SU (Nc) and matches with the continuum theory in d − Nev dimensions, where Nev denotes the number of lattice directions with even partition of lattice sites
Summary
The global symmetries of QCD-Dirac operators determine the number and the properties of the lightest pseudo-scalar mesons. It is tremendously important that the discretized theory yields the same global symmetries in the continuum limit For staggered fermions this in not necessarily guaranteed as found in [2],[3], at least at a finite lattice spacing. The kind of change depends on the choice of the gauge group representation and the space-time dimension. It is well-known that the global symmetries of the Dirac operator are manifested in the statistical properties of its smallest eigenvalues [6],[7].
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