Lorentz symmetry fractionalization and dualities in (2+1)d
Abstract
We discuss symmetry fractionalization of the Lorentz group in (2+1) d $d$ nonspin quantum field theory (QFT), and its implications for dualities. We prove that two inequivalent nonspin QFTs are dual as spin QFTs if and only if they are related by a Lorentz symmetry fractionalization with respect to an anomalous \mathbb{Z}_2 ${\mathbb{Z}}_{2}$ oneform symmetry. Moreover, if the framing anomalies of two nonspin QFTs differ by a multiple of 8, then they are dual as spin QFTs if and only if they are also dual as nonspin QFTs. Applications to summing over the spin structures, timereversal symmetry, and level/rank dualities are explored. The Lorentz symmetry fractionalization naturally arises in ChernSimons matter dualities that obey certain spin/charge relations, and is instrumental for the dualities to hold when viewed as nonspin theories.
 Authors:

 Walter Burke Institute for Theoretical Physics
 Institute for Advanced Study, Princeton University
 Publication Date:
 Research Org.:
 California Institute of Technology (CalTech), Pasadena, CA (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC)
 OSTI Identifier:
 1597129
 Alternate Identifier(s):
 OSTI ID: 1802226
 Grant/Contract Number:
 SC0011632
 Resource Type:
 Published Article
 Journal Name:
 SciPost Physics Proceedings
 Additional Journal Information:
 Journal Name: SciPost Physics Proceedings Journal Volume: 8 Journal Issue: 2; Journal ID: ISSN 25424653
 Publisher:
 Stichting SciPost
 Country of Publication:
 Netherlands
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Physics
Citation Formats
Hsin, PoShen, and Shao, ShuHeng. Lorentz symmetry fractionalization and dualities in (2+1)d. Netherlands: N. p., 2020.
Web. doi:10.21468/SciPostPhys.8.2.018.
Hsin, PoShen, & Shao, ShuHeng. Lorentz symmetry fractionalization and dualities in (2+1)d. Netherlands. https://doi.org/10.21468/SciPostPhys.8.2.018
Hsin, PoShen, and Shao, ShuHeng. Tue .
"Lorentz symmetry fractionalization and dualities in (2+1)d". Netherlands. https://doi.org/10.21468/SciPostPhys.8.2.018.
@article{osti_1597129,
title = {Lorentz symmetry fractionalization and dualities in (2+1)d},
author = {Hsin, PoShen and Shao, ShuHeng},
abstractNote = {We discuss symmetry fractionalization of the Lorentz group in (2+1) d d nonspin quantum field theory (QFT), and its implications for dualities. We prove that two inequivalent nonspin QFTs are dual as spin QFTs if and only if they are related by a Lorentz symmetry fractionalization with respect to an anomalous \mathbb{Z}_2 ℤ 2 oneform symmetry. Moreover, if the framing anomalies of two nonspin QFTs differ by a multiple of 8, then they are dual as spin QFTs if and only if they are also dual as nonspin QFTs. Applications to summing over the spin structures, timereversal symmetry, and level/rank dualities are explored. The Lorentz symmetry fractionalization naturally arises in ChernSimons matter dualities that obey certain spin/charge relations, and is instrumental for the dualities to hold when viewed as nonspin theories.},
doi = {10.21468/SciPostPhys.8.2.018},
journal = {SciPost Physics Proceedings},
number = 2,
volume = 8,
place = {Netherlands},
year = {2020},
month = {2}
}
https://doi.org/10.21468/SciPostPhys.8.2.018
Web of Science
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