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Lorentz Symmetry Fractionalization and Dualities in (2+1)d

Hsin, Po-Shen and Shao, Shu-Heng (2020) Lorentz Symmetry Fractionalization and Dualities in (2+1)d. SciPost Physics, 8 . Art. No. 018. ISSN 2542-4653. https://resolver.caltech.edu/CaltechAUTHORS:20191028-150340941

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Abstract

We discuss symmetry fractionalization of the Lorentz group in (2+1)d non-spin quantum field theory (QFT), and its implications for dualities. We prove that two inequivalent non-spin QFTs are dual as spin QFTs if and only if they are related by a Lorentz symmetry fractionalization with respect to an anomalous Z₂ one-form symmetry. Moreover, if the framing anomalies of two non-spin QFTs differ by a multiple of 8, then they are dual as spin QFTs if and only if they are also dual as non-spin QFTs. Applications to summing over the spin structures, time-reversal symmetry, and level/rank dualities are explored. The Lorentz symmetry fractionalization naturally arises in Chern-Simons matter dualities that obey certain spin/charge relations, and is instrumental for the dualities to hold when viewed as non-spin theories.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.21468/SciPostPhys.8.2.018DOIArticle
https://arxiv.org/abs/1909.07383arXivDiscussion Paper
ORCID:
AuthorORCID
Shao, Shu-Heng0000-0003-1294-2786
Additional Information:© 2020 P.-S. Hsin and S.-H. Shao. This work is licensed under the Creative Commons Attribution 4.0 International License. Published by the SciPost Foundation. Received 18-10-2019; Accepted 29-01-2020; Published 04-02-2020. We thank Thomas Dumitrescu, Anton Kapustin, Zohar Komargodski, Nathan Seiberg, and Ryan Thorngren for discussions. We thank Maissam Barkeshli, Nathan Seiberg, and Zhenghan Wang for comments on a draft. S.H.S. would like to thank Nathan Seiberg for enlightening conversations on spin and non-spin TQFTs that inspired part of this work. The work of P.-S. H. is supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0011632, and by the Simons Foundation through the Simons Investigator Award. The work of S.H.S. is supported by the National Science Foundation grant PHY-1606531, the Roger Dashen Membership, and a grant from the Simons Foundation/SFARI (651444, NS). This work was performed in part at Aspen Center for Physics, which is supported by National Science Foundation grant PHY-1607611.
Group:Walter Burke Institute for Theoretical Physics
Funders:
Funding AgencyGrant Number
Department of Energy (DOE)DE-SC0011632
Simons Foundation651444
NSFPHY-1606531
Roger Dashen MembershipUNSPECIFIED
NSFPHY-1607611
Other Numbering System:
Other Numbering System NameOther Numbering System ID
CALT-TH2019-035
Record Number:CaltechAUTHORS:20191028-150340941
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20191028-150340941
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:99500
Collection:CaltechAUTHORS
Deposited By: Joy Painter
Deposited On:28 Oct 2019 23:13
Last Modified:27 Mar 2020 15:56

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