On 2-group global symmetries and their anomalies

Benini, Francesco; Córdova, Clay; Hsin, Po-Shen

doi:10.1007/JHEP03(2019)118

Title: On 2-group global symmetries and their anomalies

Abstract

In general quantum field theories (QFTs), ordinary (0-form) global symmetries and 1-form symmetries can combine into 2-group global symmetries. We describe this phenomenon in detail using the language of symmetry defects. We exhibit a simple procedure to determine the (possible) 2-group global symmetry of a given QFT, and provide a classification of the related ’t Hooft anomalies (for symmetries not acting on spacetime). We also describe how QFTs can be coupled to extrinsic backgrounds for symmetry groups that differ from the intrinsic symmetry acting faithfully on the theory. Finally, we provide a variety of examples, ranging from TQFTs (gapped systems) to gapless QFTs. Along the way, we stress that the “obstruction to symmetry fractionalization” discussed in some condensed matter literature is really an instance of 2-group global symmetry.

Authors:

^[1]; Córdova, Clay ^[2]; Hsin, Po-Shen ^[3]

International School for Advanced Studies (SISSA), Trieste (Italy); Istituto Nazionale di Fisica Nucleare (INFN), Trieste (Italy); Inst. for Advanced Study, Princeton, NJ (United States). School of Natural Sciences
Inst. for Advanced Study, Princeton, NJ (United States). School of Natural Sciences
Princeton Univ., NJ (United States). Dept. of Physics

Publication Date:: Thu Mar 21 00:00:00 EDT 2019

Research Org.:: Institute for Advanced Study, Princeton, NJ (United States)

Sponsoring Org.:: USDOE Office of Science (SC), High Energy Physics (HEP)

OSTI Identifier:: 1598259

Grant/Contract Number:: SC0009988

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: 2019; Journal Issue: 3; Journal ID: ISSN 1029-8479

Publisher:: Springer Berlin

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Global Symmetries; Anomalies in Field and String Theories; Chern-Simons Theories; Topological Field Theories

Citation Formats


                    Benini, Francesco, Córdova, Clay, and Hsin, Po-Shen. On 2-group global symmetries and their anomalies.  United States: N. p., 2019. 
Web.  doi:10.1007/JHEP03(2019)118.

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                    Benini, Francesco, Córdova, Clay, & Hsin, Po-Shen. On 2-group global symmetries and their anomalies.  United States.  https://doi.org/10.1007/JHEP03(2019)118

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                    Benini, Francesco, Córdova, Clay, and Hsin, Po-Shen. Thu .  
"On 2-group global symmetries and their anomalies".  United States.  https://doi.org/10.1007/JHEP03(2019)118.  https://www.osti.gov/servlets/purl/1598259.

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@article{osti_1598259,

  title        = {On 2-group global symmetries and their anomalies},

  author       = {Benini, Francesco and Córdova, Clay and Hsin, Po-Shen},

  abstractNote = {In general quantum field theories (QFTs), ordinary (0-form) global symmetries and 1-form symmetries can combine into 2-group global symmetries. We describe this phenomenon in detail using the language of symmetry defects. We exhibit a simple procedure to determine the (possible) 2-group global symmetry of a given QFT, and provide a classification of the related ’t Hooft anomalies (for symmetries not acting on spacetime). We also describe how QFTs can be coupled to extrinsic backgrounds for symmetry groups that differ from the intrinsic symmetry acting faithfully on the theory. Finally, we provide a variety of examples, ranging from TQFTs (gapped systems) to gapless QFTs. Along the way, we stress that the “obstruction to symmetry fractionalization” discussed in some condensed matter literature is really an instance of 2-group global symmetry.},

  doi          = {10.1007/JHEP03(2019)118},

  journal      = {Journal of High Energy Physics (Online)},

  number       = 3,

  volume       = 2019,

  place        = {United States},

  year         = {Thu Mar 21 00:00:00 EDT 2019},

  month        = {Thu Mar 21 00:00:00 EDT 2019}

}

Copy to clipboard

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Title: On 2-group global symmetries and their anomalies

Abstract

Citation Formats

Polynomial equations for rational conformal field theories journal, October 1988

Toward classification of conformal theories journal, May 1988

From gauge to higher gauge models of topological phases journal, October 2018

Anomaly Indicators for Time-Reversal Symmetric Topological Orders journal, September 2017

Anomalies and fermion zero modes on strings and domain walls journal, January 1985

D-brane charges in five-brane backgrounds journal, October 2001

On the Groups H(Π, n), II: Methods of Computation journal, July 1954

Generalized global symmetries journal, February 2015

On the Groups H(Π, n), I journal, July 1953

Topological field theory on a lattice, discrete theta-angles and confinement journal, January 2014

On simply connected, 4-dimensional polyhedra journal, December 1949

A class of topological actions journal, August 2005

Coupling a QFT to a TQFT and duality journal, April 2014

On simply connected, 4-dimensional polyhedra. text, January 1949

Symmetry fractionalization and twist defects journal, March 2016

Fusion categories and homotopy theory journal, January 2010

Anyons in an exactly solved model and beyond journal, January 2006

Products of Cocycles and Extensions of Mappings journal, April 1947

Comments on abelian Higgs models and persistent order journal, January 2019

Comments on global symmetries, anomalies, and duality in (2 + 1)d journal, April 2017

Combination of saliency histogram equalisation and seam carving for image resizing journal, July 2017

Construction of Universal Bundles, II journal, May 1956

State sum constructions of spin-TFTs and string net constructions of fermionic phases of matter journal, April 2017

Theory of twist liquids: Gauging an anyonic symmetry journal, September 2015

Global Symmetries, Counterterms, and Duality in Chern-Simons Matter Theories with Orthogonal Gauge Groups journal, January 2018

Notes on generalized global symmetries in QFT: Notes on generalized global symmetries in QFT journal, September 2015

Shortening anomalies in supersymmetric theories journal, January 2017

A Certain Exact Sequence journal, July 1950

Chern-Simons-matter dualities with SO and USp gauge groups journal, February 2017

Exploring 2-group global symmetries journal, February 2019

Anomaly cancellations in supersymmetric D = 10 gauge theory and superstring theory journal, December 1984

Naturalness, Chiral Symmetry, and Spontaneous Chiral Symmetry Breaking book, January 1980

Anomalous Discrete Symmetries in Three Dimensions and Group Cohomology journal, June 2014

Time-reversal and spatial-reflection symmetry localization anomalies in (2+1)-dimensional topological phases of matter journal, September 2018

Anomalous Symmetry Fractionalization and Surface Topological Order journal, October 2015

Classifying fractionalization: Symmetry classification of gapped Z 2 spin liquids in two dimensions journal, March 2013

Symmetries and strings in field theory and gravity journal, April 2011

A symmetry breaking scenario for QCD3 journal, January 2018

Time-reversal symmetry, anomalies, and dualities in (2+1)$d$ journal, January 2018

Gapped boundary phases of topological insulators via weak coupling journal, November 2016

Physics of Three-Dimensional Bosonic Topological Insulators: Surface-Deconfined Criticality and Quantized Magnetoelectric Effect journal, February 2013

Framed Wilson operators, fermionic strings, and gravitational anomaly in 4d journal, February 2015

Contact Terms, Unitarity, and F-Maximization in Three-Dimensional Superconformal Theories text, January 2012

Physics of three dimensional bosonic topological insulators: Surface Deconfined Criticality and Quantized Magnetoelectric Effect text, January 2012

Topological Field Theory on a Lattice, Discrete Theta-Angles and Confinement preprint, January 2013

State sum constructions of spin-TFTs and string net constructions of fermionic phases of matter text, January 2016

Chern-Simons-matter dualities with $SO$ and $USp$ gauge groups text, January 2016

Comments on Abelian Higgs Models and Persistent Order text, January 2017

Time-reversal and spatial reflection symmetry localization anomalies in (2+1)D topological phases of matter text, January 2017

Global Symmetries, Counterterms, and Duality in Chern-Simons Matter Theories with Orthogonal Gauge Groups text, January 2017

Three-dimensional dualities with bosons and fermions text, January 2017

Exploring 2-Group Global Symmetries text, January 2018

From gauge to higher gauge models of topological phases text, January 2018

Anyons in an exactly solved model and beyond text, January 2005

A Class of Topological Actions text, January 2004

Exceptional Chern-Simons-Matter dualities journal, January 2019

On 2-form gauge models of topological phases journal, May 2019

Dihedral symmetry in S U ( N ) Yang-Mills theory journal, October 2019

Domain walls in high-T SU(N) super Yang-Mills theory and QCD(adj) journal, May 2019

Self-conjugate QCD journal, October 2019

On 2-form gauge models of topological phases text, January 2019

On gauging finite subgroups text, January 2017

Dai-Freed anomalies in particle physics text, January 2018

Domain walls in high-T SU(N) super Yang-Mills theory and QCD(adj) text, January 2018

Emergent (anomalous) higher symmetries from topological orders and from dynamical electromagnetic field in condensed matter systems text, January 2018

Comments on One-Form Global Symmetries and Their Gauging in 3d and 4d text, January 2018

Exceptional Chern-Simons-Matter Dualities text, January 2018

On 2-form gauge models of topological phases text, January 2019

Anomalies in the Space of Coupling Constants and Their Dynamical Applications I text, January 2019

Anomalies in the Space of Coupling Constants and Their Dynamical Applications II text, January 2019

Polynomial equations for rational conformal field theories
journal, October 1988

Toward classification of conformal theories
journal, May 1988

From gauge to higher gauge models of topological phases
journal, October 2018

Anomaly Indicators for Time-Reversal Symmetric Topological Orders
journal, September 2017

Anomalies and fermion zero modes on strings and domain walls
journal, January 1985

D-brane charges in five-brane backgrounds
journal, October 2001

On the Groups H(Π, n), II: Methods of Computation
journal, July 1954

Generalized global symmetries
journal, February 2015

On the Groups H(Π, n), I
journal, July 1953

Topological field theory on a lattice, discrete theta-angles and confinement
journal, January 2014

On simply connected, 4-dimensional polyhedra
journal, December 1949

A class of topological actions
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Anyons in an exactly solved model and beyond
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Comments on abelian Higgs models and persistent order
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Combination of saliency histogram equalisation and seam carving for image resizing
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State sum constructions of spin-TFTs and string net constructions of fermionic phases of matter
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Global Symmetries, Counterterms, and Duality in Chern-Simons Matter Theories with Orthogonal Gauge Groups
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Shortening anomalies in supersymmetric theories
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A Certain Exact Sequence
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Exploring 2-group global symmetries
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Naturalness, Chiral Symmetry, and Spontaneous Chiral Symmetry Breaking
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Anomalous Discrete Symmetries in Three Dimensions and Group Cohomology
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Classifying fractionalization: Symmetry classification of gapped $Z_{2}$ spin liquids in two dimensions
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Symmetries and strings in field theory and gravity
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A symmetry breaking scenario for QCD3
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Time-reversal symmetry, anomalies, and dualities in (2+1)$d$
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Physics of Three-Dimensional Bosonic Topological Insulators: Surface-Deconfined Criticality and Quantized Magnetoelectric Effect
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Framed Wilson operators, fermionic strings, and gravitational anomaly in 4d
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Contact Terms, Unitarity, and F-Maximization in Three-Dimensional Superconformal Theories
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Physics of three dimensional bosonic topological insulators: Surface Deconfined Criticality and Quantized Magnetoelectric Effect
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Topological Field Theory on a Lattice, Discrete Theta-Angles and Confinement
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State sum constructions of spin-TFTs and string net constructions of fermionic phases of matter
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Chern-Simons-matter dualities with $SO$ and $USp$ gauge groups
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Comments on Abelian Higgs Models and Persistent Order
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Time-reversal and spatial reflection symmetry localization anomalies in (2+1)D topological phases of matter
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Global Symmetries, Counterterms, and Duality in Chern-Simons Matter Theories with Orthogonal Gauge Groups
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Three-dimensional dualities with bosons and fermions
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Exploring 2-Group Global Symmetries
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From gauge to higher gauge models of topological phases
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Anyons in an exactly solved model and beyond
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A Class of Topological Actions
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Exceptional Chern-Simons-Matter dualities
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On 2-form gauge models of topological phases
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Dihedral symmetry in $S U (N)$ Yang-Mills theory
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Domain walls in high-T SU(N) super Yang-Mills theory and QCD(adj)
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Self-conjugate QCD
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On 2-form gauge models of topological phases
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On gauging finite subgroups
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Dai-Freed anomalies in particle physics
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Domain walls in high-T SU(N) super Yang-Mills theory and QCD(adj)
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Emergent (anomalous) higher symmetries from topological orders and from dynamical electromagnetic field in condensed matter systems
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Comments on One-Form Global Symmetries and Their Gauging in 3d and 4d
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Exceptional Chern-Simons-Matter Dualities
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On 2-form gauge models of topological phases
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Anomalies in the Space of Coupling Constants and Their Dynamical Applications I
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Anomalies in the Space of Coupling Constants and Their Dynamical Applications II
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