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Title: Symmetry-enriched quantum spin liquids in (3 + 1)d

Abstract

We use the intrinsic one-form and two-form global symmetries of (3+1)d bosonic field theories to classify quantum phases enriched by ordinary (0-form) global symmetry. Different symmetry-enriched phases correspond to different ways of coupling the theory to the background gauge field of the ordinary symmetry. The input of the classification is the higher-form symmetries and a permutation action of the 0-form symmetry on the lines and surfaces of the theory. From these data we classify the couplings to the background gauge field by the 0-form symmetry defects constructed from the higher-form symmetry defects. For trivial two-form symmetry the classification coincides with the classification for symmetry fractionalizations in (2 + 1)d. We also provide a systematic method to obtain the symmetry protected topological phases that can be absorbed by the coupling, and we give the relative ’t Hooft anomaly for different couplings. We discuss several examples including the gapless pure U(1) gauge theory and the gapped Abelian finite group gauge theory. As an application, we discover a tension with a conjectured duality in (3 + 1)d for SU(2) gauge theory with two adjoint Weyl fermions.

Authors:
 [1]; ORCiD logo [1]
  1. California Institute of Technology (CalTech), Pasadena, CA (United States)
Publication Date:
Research Org.:
California Institute of Technology (CalTech), Pasadena, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP); National Science Foundation (NSF)
OSTI Identifier:
1762780
Grant/Contract Number:  
SC0011632; PHY-1607611
Resource Type:
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2020; Journal Issue: 9; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Anomalies in Field and String Theories; Global Symmetries; Topological Field Theories; Topological States of Matter

Citation Formats

Hsin, Po-Shen, and Turzillo, Alex. Symmetry-enriched quantum spin liquids in (3 + 1)d. United States: N. p., 2020. Web. doi:10.1007/jhep09(2020)022.
Hsin, Po-Shen, & Turzillo, Alex. Symmetry-enriched quantum spin liquids in (3 + 1)d. United States. https://doi.org/10.1007/jhep09(2020)022
Hsin, Po-Shen, and Turzillo, Alex. Wed . "Symmetry-enriched quantum spin liquids in (3 + 1)d". United States. https://doi.org/10.1007/jhep09(2020)022. https://www.osti.gov/servlets/purl/1762780.
@article{osti_1762780,
title = {Symmetry-enriched quantum spin liquids in (3 + 1)d},
author = {Hsin, Po-Shen and Turzillo, Alex},
abstractNote = {We use the intrinsic one-form and two-form global symmetries of (3+1)d bosonic field theories to classify quantum phases enriched by ordinary (0-form) global symmetry. Different symmetry-enriched phases correspond to different ways of coupling the theory to the background gauge field of the ordinary symmetry. The input of the classification is the higher-form symmetries and a permutation action of the 0-form symmetry on the lines and surfaces of the theory. From these data we classify the couplings to the background gauge field by the 0-form symmetry defects constructed from the higher-form symmetry defects. For trivial two-form symmetry the classification coincides with the classification for symmetry fractionalizations in (2 + 1)d. We also provide a systematic method to obtain the symmetry protected topological phases that can be absorbed by the coupling, and we give the relative ’t Hooft anomaly for different couplings. We discuss several examples including the gapless pure U(1) gauge theory and the gapped Abelian finite group gauge theory. As an application, we discover a tension with a conjectured duality in (3 + 1)d for SU(2) gauge theory with two adjoint Weyl fermions.},
doi = {10.1007/jhep09(2020)022},
journal = {Journal of High Energy Physics (Online)},
number = 9,
volume = 2020,
place = {United States},
year = {Wed Sep 02 00:00:00 EDT 2020},
month = {Wed Sep 02 00:00:00 EDT 2020}
}

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