Gauging staggered fermion shift symmetries

Abstract

Staggered fermion shift symmetries correspond to translations of the fermion field within the unit cell of a hypercubic lattice. They satisfy an algebra and in four Euclidean dimensions can be related to a discrete subgroup of an SU(4) flavor symmetry which plays a crucial role in showing that staggered fermions lead to a theory of four degenerate Dirac fermions in the continuum limit. They are associated with the appearance of certain Z2 valued global parameters. We propose a strategy to try to partially gauge these translation symmetries by allowing these parameters to vary locally in the lattice. To maintain invariance of the action requires the addition of Z2 valued higher form lattice gauge fields. An analogous procedure can be carried out for reduced staggered fermions where the shifts correspond to a discrete subgroup of an SO(4) flavor symmetry. Published by the American Physical Society 2024