Staggered bosons and Kahler-Dirac bosons

TL;DR

The paper introduces a novel lattice bosonic theory with half degrees of freedom per site, featuring non-trivial Poisson brackets, and extends Kahler-Dirac fermions to bosons, enabling supersymmetry on arbitrary triangulations.

Contribution

It presents a new approach to bosonic lattice theories with half degrees of freedom and introduces Kahler-Dirac bosons, facilitating lattice supersymmetry and Dirac equation derivation.

Findings

Constructed gapless theories with non-invertible symmetries.

Developed a bosonic version of Kahler-Dirac fermions applicable to any triangulation.

Enabled straightforward implementation of supersymmetry on the lattice.

Abstract

We describe a novel way to think about bosonic lattice theories in Hamiltonian form where each lattice site has only a half boson degree of freedom. The construction requires a non-trivial Poisson bracket between neighboring sites and leads to gapless theories with non-invertible symmetries. We also describe a bosonic version of Kahler-Dirac fermions, dubbed Kahler-Dirac bosons that can be performed on any triangulation of a manifold. This also leads to a straightforward implementation of supersymmetry on the lattice and one immediately deduces the Dirac equation of the corresponding Kahler-Dirac fermions.