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Title: Lorentz symmetry fractionalization and dualities in (2+1)d

Abstract

We discuss symmetry fractionalization of the Lorentz group in (2+1) d 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 \mathbb{Z}_2 ℤ 2 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.

Authors:
 [1];  [2]
+ Show Author Affiliations
  1. Walter Burke Institute for Theoretical Physics
  2. 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
Additional Journal Information:
Journal Name: SciPost Physics Journal Volume: 8 Journal Issue: 2; Journal ID: ISSN 2542-4653
Publisher:
Stichting SciPost
Country of Publication:
Netherlands
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Physics

Citation Formats

Hsin, Po-Shen, and Shao, Shu-Heng. Lorentz symmetry fractionalization and dualities in (2+1)d. Netherlands: N. p., 2020. Web. doi:10.21468/SciPostPhys.8.2.018.
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Hsin, Po-Shen, & Shao, Shu-Heng. Lorentz symmetry fractionalization and dualities in (2+1)d. Netherlands. https://doi.org/10.21468/SciPostPhys.8.2.018
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Hsin, Po-Shen, and Shao, Shu-Heng. Tue . "Lorentz symmetry fractionalization and dualities in (2+1)d". Netherlands. https://doi.org/10.21468/SciPostPhys.8.2.018.
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@article{osti_1597129,
title = {Lorentz symmetry fractionalization and dualities in (2+1)d},
author = {Hsin, Po-Shen and Shao, Shu-Heng},
abstractNote = {We discuss symmetry fractionalization of the Lorentz group in (2+1) d 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 \mathbb{Z}_2 ℤ 2 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.},
doi = {10.21468/SciPostPhys.8.2.018},
journal = {SciPost Physics},
number = 2,
volume = 8,
place = {Netherlands},
year = {Tue Feb 04 00:00:00 EST 2020},
month = {Tue Feb 04 00:00:00 EST 2020}
}
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https://doi.org/10.21468/SciPostPhys.8.2.018
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