Gauging staggered fermion shift symmetries

TL;DR

This paper explores the shift symmetries of staggered fermions on a lattice, relating them to flavor symmetries and proposing a method to gauge these symmetries locally using higher form lattice gauge fields.

Contribution

It introduces a strategy to partially gauge staggered fermion shift symmetries by local variation of global parameters and incorporates $Z_2$ valued higher form gauge fields.

Findings

Relates shift symmetries to $SU(4)$ flavor symmetry in four dimensions.

Proposes a method to gauge these symmetries locally on the lattice.

Extends the approach to reduced staggered fermions with $SO(4)$ symmetry.

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 $Z_2$ 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 $Z_2$ 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.