Gauging staggered fermion shift symmetries

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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>S</a:mi><a:mi>U</a:mi><a:mo stretchy="false">(</a:mo><a:mn>4</a:mn><a:mo stretchy="false">)</a:mo></a:math> 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 <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msub><e:mi>Z</e:mi><e:mn>2</e:mn></e:msub></e:math> 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 <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msub><g:mi>Z</g:mi><g:mn>2</g:mn></g:msub></g:math> 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 <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>S</i:mi><i:mi>O</i:mi><i:mo stretchy="false">(</i:mo><i:mn>4</i:mn><i:mo stretchy="false">)</i:mo></i:math> flavor symmetry. Published by the American Physical Society 2024