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arXiv · 2405.03758

Staggered bosons and Kahler-Dirac bosons

David Berenstein·Simon Catterall·P. N. Thomas Lloyd
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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.

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David Berenstein, Simon Catterall, P. N. Thomas Lloyd. 2024-05-06. Staggered bosons and Kahler-Dirac bosons. https://arxiv.org/abs/2405.03758

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