Global Symmetries of Naive and Staggered Fermions in Arbitrary Dimensions
It is well-known that the continuum Dirac operator and the lattice Dirac operator of staggered fermions do not necessarily share the same global symmetries. For example in three dimensions the continuum Dirac operator satisfies no chiral symmetry while the staggered Dirac operator does. This change of symmetries has a crucial impact on the number and the kind of the lightest pseudo-scalar mesons showing in the infra-red limit. The reason for this is that the spontaneous symmetry breaking pattern has changed. A few years ago, the origin of this change of symmetries in this discretization scheme was analyzed for two dimensional lattices. A surprisingly rich classification was found where eight of the ten symmetry classes of the Cartan classification exist depending on the number of directions with an even partition of lattice sites. Very recently, we extended this investigation to an arbitrary space-time dimension. We confirmed our predictions by comparing lattice simulations with random matrix theory results. I will report on this project in the talk.
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