# Exact bosonization in arbitrary dimensions

@article{Chen2019ExactBI,
title={Exact bosonization in arbitrary dimensions},
author={Yu-An Chen},
journal={arXiv: Strongly Correlated Electrons},
year={2019}
}
• Yu-An Chen
• Published 31 October 2019
• Physics
• arXiv: Strongly Correlated Electrons
We extend the previous results of exact bosonization, mapping from fermionic operators to Pauli matrices, in 2d and 3d to arbitrary dimensions. This bosonization map gives a duality between any fermionic system in arbitrary $n$ spatial dimensions and a new class of $(n-1)$-form $\mathbb{Z}_2$ gauge theories in $n$ dimensions with a modified Gauss's law. This map preserves locality and has an explicit dependence on the second Stiefel-Whitney class and a choice of spin structure on the manifold…

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