Dumbell Fermions and Fermi-Pauli Duality

TL;DR

This paper introduces a duality between fermionic models with $Z_2$ gauge symmetry and bosonic lattice models using a 'dumbbell' fermion representation, expanding understanding of fermion-boson dualities.

Contribution

It presents a novel duality framework linking fermionic and bosonic lattice models via a 'dumbbell' fermion construction, generalizing previous dualities.

Findings

Establishes a duality between local fermionic and bosonic models.

Uses the Kantor-Susskind fermion model as a basis.

Provides a new perspective on fermion-boson dualities in lattice systems.

Abstract

We use the Kantor-Susskind\cite{kantsuss} model of fermions as "dumbbells" connecting points on a cubic lattice to points on its dual, to define a duality between local fermionic models invariant under a $Z_2$ gauge symmetry and models of bosonic variables (generalizations of Pauli matrices) defined on the lattice.