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Title: Time-reversal symmetry, anomalies, and dualities in (2+1)$d$

Abstract

We study continuum quantum field theories in 2+1 dimensions with time-reversal symmetry \cal T . The standard relation {\cal T}^2=(-1)^F is satisfied on all the “perturbative operators” i.e. polynomials in the fundamental fields and their derivatives. However, we find that it is often the case that acting on more complicated operators {\cal T}^2=(-1)^F {\cal M} with \cal M a non-trivial global symmetry. For example, acting on monopole operators, \cal M could be \pm1 ± 1 depending on the magnetic charge. We study in detail U(1) U ( 1 ) gauge theories with fermions of various charges. Such a modification of the time-reversal algebra happens when the number of odd charge fermions is 2 ~{\rm mod }~4 , e.g. in QED with two fermions. Our work also clarifies the dynamics of QED with fermions of higher charges. In particular, we argue that the long-distance behavior of QED with a single fermion of charge 2 2 is a free theory consisting of a Dirac fermion and a decoupled topological quantum field theory. The extension to an arbitrary even charge is straightforward. The generalization of these abelian theories to SO(N) S O ( N ) gauge theories with fermions in the vector or in two-index tensor representations leads to new results and new consistency conditions on previously suggested scenarios for the dynamics of these theories. Among these new results is a surprising non-abelian symmetry involving time-reversal.

Authors:
 [1];  [2];  [1]
  1. Institute for Advanced Study, Princeton University
  2. Princeton University
Publication Date:
Sponsoring Org.:
USDOE
OSTI Identifier:
1461012
Grant/Contract Number:  
SC0009988
Resource Type:
Published Article
Journal Name:
SciPost Physics Proceedings
Additional Journal Information:
Journal Name: SciPost Physics Proceedings Journal Volume: 5 Journal Issue: 1; Journal ID: ISSN 2542-4653
Publisher:
Stichting SciPost
Country of Publication:
Netherlands
Language:
English

Citation Formats

Cordova, Clay, Hsin, Po-Shen, and Seiberg, Nathan. Time-reversal symmetry, anomalies, and dualities in (2+1)$d$. Netherlands: N. p., 2018. Web. doi:10.21468/SciPostPhys.5.1.006.
Cordova, Clay, Hsin, Po-Shen, & Seiberg, Nathan. Time-reversal symmetry, anomalies, and dualities in (2+1)$d$. Netherlands. doi:10.21468/SciPostPhys.5.1.006.
Cordova, Clay, Hsin, Po-Shen, and Seiberg, Nathan. Fri . "Time-reversal symmetry, anomalies, and dualities in (2+1)$d$". Netherlands. doi:10.21468/SciPostPhys.5.1.006.
@article{osti_1461012,
title = {Time-reversal symmetry, anomalies, and dualities in (2+1)$d$},
author = {Cordova, Clay and Hsin, Po-Shen and Seiberg, Nathan},
abstractNote = {We study continuum quantum field theories in 2+1 dimensions with time-reversal symmetry \cal T . The standard relation {\cal T}^2=(-1)^F is satisfied on all the “perturbative operators” i.e. polynomials in the fundamental fields and their derivatives. However, we find that it is often the case that acting on more complicated operators {\cal T}^2=(-1)^F {\cal M} with \cal M a non-trivial global symmetry. For example, acting on monopole operators, \cal M could be \pm1 ± 1 depending on the magnetic charge. We study in detail U(1) U ( 1 ) gauge theories with fermions of various charges. Such a modification of the time-reversal algebra happens when the number of odd charge fermions is 2 ~{\rm mod }~4 , e.g. in QED with two fermions. Our work also clarifies the dynamics of QED with fermions of higher charges. In particular, we argue that the long-distance behavior of QED with a single fermion of charge 2 2 is a free theory consisting of a Dirac fermion and a decoupled topological quantum field theory. The extension to an arbitrary even charge is straightforward. The generalization of these abelian theories to SO(N) S O ( N ) gauge theories with fermions in the vector or in two-index tensor representations leads to new results and new consistency conditions on previously suggested scenarios for the dynamics of these theories. Among these new results is a surprising non-abelian symmetry involving time-reversal.},
doi = {10.21468/SciPostPhys.5.1.006},
journal = {SciPost Physics Proceedings},
number = 1,
volume = 5,
place = {Netherlands},
year = {2018},
month = {7}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: 10.21468/SciPostPhys.5.1.006

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