Global Symmetries of Naive and Staggered Fermions in Arbitrary Dimensions

TL;DR

This paper investigates how naive and staggered fermions on a lattice exhibit different global symmetries from the continuum theory across various dimensions, analyzing spectral properties and symmetry breaking patterns.

Contribution

It provides a detailed analysis of the symmetry differences of naive and staggered fermions in arbitrary dimensions, including the impact of lattice parity and spectral statistics.

Findings

Global symmetry differences depend on lattice parity and dimension.

Spectral statistics reveal symmetry breaking patterns.

Monte-Carlo simulations support theoretical predictions.

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.