Lorentz Symmetry Fractionalization and Dualities in (2+1)d
- Creators
- Hsin, Po-Shen
-
Shao, Shu-Heng
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.
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.Attached Files
Published - SciPostPhys_8_2_018.pdf
Submitted - 1909.07383.pdf
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Additional details
- Eprint ID
- 99500
- Resolver ID
- CaltechAUTHORS:20191028-150340941
- Department of Energy (DOE)
- DE-SC0011632
- Simons Foundation
- 651444
- NSF
- PHY-1606531
- Roger Dashen Membership
- NSF
- PHY-1607611
- Created
-
2019-10-28Created from EPrint's datestamp field
- Updated
-
2021-11-16Created from EPrint's last_modified field
- Caltech groups
- Walter Burke Institute for Theoretical Physics
- Other Numbering System Name
- CALT-TH
- Other Numbering System Identifier
- 2019-035