Exact bosonization in arbitrary dimensions
Abstract
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 class of (n−1)-form Z₂ 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 spatial manifold. A formula for Stiefel-Whitney homology classes on lattices is derived. In the Euclidean path integral, this exact bosonization map is equivalent to introducing a topological Steenrod square term to the space-time action.
Additional Information
© 2020 Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Received 17 June 2020; revised 10 September 2020; accepted 14 September 2020; published 30 September 2020. Y.C. thanks Po-Shen Hsin and his advisor Prof. Anton Kapustin for many very helpful discussions. Y.C. also thanks Tyler Ellison and Nathanan Tantivasadakarn for their useful feedback. This research was supported in part by the US Department of Energy, Office of Science, Office of High Energy Physics, under Award No. de-sc0011632. Anton Kapustin was also supported by the Simons Investigator Award.Attached Files
Published - PhysRevResearch.2.033527.pdf
Submitted - 1911.00017.pdf
Files
1911.00017.pdf
Additional details
Identifiers
- Eprint ID
- 100354
- Resolver ID
- CaltechAUTHORS:20191218-131107627
Related works
- Describes
- https://arxiv.org/abs/1911.00017 (URL)
Funding
- Department of Energy (DOE)
- DE-SC0011632
- Simons Foundation
Dates
- Created
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2019-12-18Created from EPrint's datestamp field
- Updated
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2021-11-16Created from EPrint's last_modified field