Staggered bosons and Kahler-Dirac bosons
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.
Cite
@article{arxiv.2405.03758,
title = {Staggered bosons and Kahler-Dirac bosons},
author = {David Berenstein and Simon Catterall and P. N. Thomas Lloyd},
journal= {arXiv preprint arXiv:2405.03758},
year = {2024}
}
Comments
8 pages, Proceedings of the Corfu Summer Institute 2023, Workshop on Noncommutative and Generalized Geometry in String theory, Gauge theory and Related Physical Models