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Bosonization in three spatial dimensions and a 2-form gauge theory

Chen, Yu-An and Kapustin, Anton (2019) Bosonization in three spatial dimensions and a 2-form gauge theory. Physical Review B, 100 (24). Art. No. 245127. ISSN 2469-9950.

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We describe a 3d analog of the Jordan-Wigner transformation which maps an arbitrary fermionic system on a 3d spatial lattice to a 2-form Z₂ gauge theory with an unusual Gauss law. An important property of this map is that it preserves the locality of the Hamiltonian. The map depends explicitly on the choice of a spin structure of the spatial manifold. We give examples of 3d bosonic systems dual to free fermions. We also describe the corresponding Euclidean lattice models, which is analogous to the Steenrod square term in (3+1)D [compared to the Chern-Simon term in (2+1)D].

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Chen, Yu-An0000-0002-8810-9355
Kapustin, Anton0000-0003-3903-5158
Additional Information:© 2019 American Physical Society. Received 7 September 2019; revised manuscript received 21 November 2019; published 16 December 2019. Y.-A.C. thanks Djordje Radicevic for many very helpful discussions. This research was supported in part by the US Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0011632. A.K. was also supported by the Simons Investigator Award.
Funding AgencyGrant Number
Department of Energy (DOE)DE-SC0011632
Simons FoundationUNSPECIFIED
Issue or Number:24
Record Number:CaltechAUTHORS:20181022-110515479
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:90324
Deposited By: Tony Diaz
Deposited On:22 Oct 2018 20:49
Last Modified:16 Dec 2019 17:40

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