Generalized global symmetries

Gaiotto, Davide; Kapustin, Anton; Seiberg, Nathan; Willett, Brian

doi:10.1007/JHEP02(2015)172

Title: Generalized global symmetries

Abstract

A q-form global symmetry is a global symmetry for which the charged operators are of space-time dimension q; e.g. Wilson lines, surface defects, etc., and the charged excitations have q spatial dimensions; e.g. strings, membranes, etc. Many of the properties of ordinary global symmetries (q = 0) apply here. They lead to Ward identities and hence to selection rules on amplitudes. Such global symmetries can be coupled to classical background fields and they can be gauged by summing over these classical fields. These generalized global symmetries can be spontaneously broken (either completely or to a sub-group). They can also have ’t Hooft anomalies, which prevent us from gauging them, but lead to ’t Hooft anomaly matching conditions. Such anomalies can also lead to anomaly inflow on various defects and exotic Symmetry Protected Topological phases. In conclusion, our analysis of these symmetries gives a new unified perspective of many known phenomena and uncovers new results.

Authors:

Gaiotto, Davide ^[1]; Kapustin, Anton ^[2]; Seiberg, Nathan ^[3]; Willett, Brian ^[3]

Perimeter Inst. for Theoretical Physics, Waterloo, ON (Canada)
State Univ. of New York (SUNY), Stony Brook, NY (United States). Simons Center for Geometry and Physics
Inst. for Advanced Study, Princeton, NJ (United States). School of Natural Sciences

Publication Date:: Thu Feb 26 00:00:00 EST 2015

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

Sponsoring Org.:: USDOE; Simons Foundation; United States-Israel Binational Science Foundation (BSF)

OSTI Identifier:: 1440979

Grant/Contract Number:: SC0009988; FG02-92ER40701; 2010/629

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: 2015; Journal Issue: 2; 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; Wilson; ’t Hooft and Polyakov loops; Topological States of Matter; Anomalies in Field and String Theories

Citation Formats


                    Gaiotto, Davide, Kapustin, Anton, Seiberg, Nathan, and Willett, Brian. Generalized global symmetries.  United States: N. p., 2015. 
Web.  doi:10.1007/JHEP02(2015)172.

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                    Gaiotto, Davide, Kapustin, Anton, Seiberg, Nathan, & Willett, Brian. Generalized global symmetries.  United States.  https://doi.org/10.1007/JHEP02(2015)172

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                    Gaiotto, Davide, Kapustin, Anton, Seiberg, Nathan, and Willett, Brian. Thu .  
"Generalized global symmetries".  United States.  https://doi.org/10.1007/JHEP02(2015)172.  https://www.osti.gov/servlets/purl/1440979.

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@article{osti_1440979,

  title        = {Generalized global symmetries},

  author       = {Gaiotto, Davide and Kapustin, Anton and Seiberg, Nathan and Willett, Brian},

  abstractNote = {A q-form global symmetry is a global symmetry for which the charged operators are of space-time dimension q; e.g. Wilson lines, surface defects, etc., and the charged excitations have q spatial dimensions; e.g. strings, membranes, etc. Many of the properties of ordinary global symmetries (q = 0) apply here. They lead to Ward identities and hence to selection rules on amplitudes. Such global symmetries can be coupled to classical background fields and they can be gauged by summing over these classical fields. These generalized global symmetries can be spontaneously broken (either completely or to a sub-group). They can also have ’t Hooft anomalies, which prevent us from gauging them, but lead to ’t Hooft anomaly matching conditions. Such anomalies can also lead to anomaly inflow on various defects and exotic Symmetry Protected Topological phases. In conclusion, our analysis of these symmetries gives a new unified perspective of many known phenomena and uncovers new results.},

  doi          = {10.1007/JHEP02(2015)172},

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

  number       = 2,

  volume       = 2015,

  place        = {United States},

  year         = {Thu Feb 26 00:00:00 EST 2015},

  month        = {Thu Feb 26 00:00:00 EST 2015}

}

Copy to clipboard

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Works referenced in this record:

Modifying the sum over topological sectors and constraints on supergravity
journal, July 2010

Seiberg, Nathan
Journal of High Energy Physics, Vol. 2010, Issue 7
DOI: 10.1007/JHEP07(2010)070

Instantons and disorder in antisymmetric tensor gauge fields
journal, April 1982

Orland, Peter
Nuclear Physics B, Vol. 205, Issue 1
DOI: 10.1016/0550-3213(82)90468-0

Duality, monopoles, dyons, confinement and oblique confinement in supersymmetric SO(nc) gauge theories
journal, June 1995

Intriligator, K.; Seiberg, N.
Nuclear Physics B, Vol. 444, Issue 1-2
DOI: 10.1016/0550-3213(95)00159-P

Higher regulators and values of L-functions
journal, July 1985

Beilinson, A. A.
Journal of Soviet Mathematics, Vol. 30, Issue 2
DOI: 10.1007/BF02105861

Surgery With Coefficients
journal, September 1974

Milgram, R. James
The Annals of Mathematics, Vol. 100, Issue 2
DOI: 10.2307/1971072

Theory of one- and two-dimensional magnets with an easy magnetization plane. II. The planar, classical, two-dimensional magnet
journal, January 1975

Villain, J.
Journal de Physique, Vol. 36, Issue 6
DOI: 10.1051/jphys:01975003606058100

Charge lattices and consistency of 6D supergravity
journal, June 2011

Seiberg, Nathan; Taylor, Washington
Journal of High Energy Physics, Vol. 2011, Issue 6
DOI: 10.1007/JHEP06(2011)001

Monopoles, duality and chiral symmetry breaking in N = 2 supersymmetric QCD
journal, December 1994

Seiberg, N.; Witten, E.
Nuclear Physics B, Vol. 431, Issue 3
DOI: 10.1016/0550-3213(94)90214-3

Supercurrents and brane currents in diverse dimensions
journal, July 2011

Dumitrescu, Thomas T.; Seiberg, Nathan
Journal of High Energy Physics, Vol. 2011, Issue 7
DOI: 10.1007/JHEP07(2011)095

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

Maldacena, Juan; Seiberg, Nathan; Moore, Gregory
Journal of High Energy Physics, Vol. 2001, Issue 10
DOI: 10.1088/1126-6708/2001/10/005

Heisenberg groups and noncommutative fluxes
journal, January 2007

Freed, Daniel S.; Moore, Gregory W.; Segal, Graeme
Annals of Physics, Vol. 322, Issue 1
DOI: 10.1016/j.aop.2006.07.014

Symmetry protected topological orders and the group cohomology of their symmetry group
journal, April 2013

Chen, Xie; Gu, Zheng-Cheng; Liu, Zheng-Xin
Physical Review B, Vol. 87, Issue 15
DOI: 10.1103/PhysRevB.87.155114

Gauge theory generalization of the fermion doubling theorem
journal, October 2013

Kravec, S. M.; McGreevy, John
Physical Review Letters, Vol. 111, Issue 16
DOI: 10.1103/PhysRevLett.111.161603

A dynamical origin for the electromagnetic field
journal, October 1963

Bjorken, J. D.
Annals of Physics, Vol. 24
DOI: 10.1016/0003-4916(63)90069-1

Gauge invariance for extended objects
journal, January 1986

Teitelboim, Claudio
Physics Letters B, Vol. 167, Issue 1
DOI: 10.1016/0370-2693(86)90546-0

Phases of Script N = 1 supersymmetric gauge theories
journal, February 2003

Cachazo, Freddy; Seiberg, Nathan; Witten, Edward
Journal of High Energy Physics, Vol. 2003, Issue 02
DOI: 10.1088/1126-6708/2003/02/042

Monopoles of higher rank
journal, January 1986

Teitelboim, Claudio
Physics Letters B, Vol. 167, Issue 1
DOI: 10.1016/0370-2693(86)90547-2

Modular invariance and discrete torsion on orbifolds
journal, September 1986

Vafa, Cumrun
Nuclear Physics B, Vol. 273, Issue 3-4
DOI: 10.1016/0550-3213(86)90379-2

Comments on the Fayet-Iliopoulos term in field theory and supergravity
journal, June 2009

Komargodski, Zohar; Seiberg, Nathan
Journal of High Energy Physics, Vol. 2009, Issue 06
DOI: 10.1088/1126-6708/2009/06/007

Electric-magnetic duality in supersymmetric non-Abelian gauge theories
journal, February 1995

Seiberg, N.
Nuclear Physics B, Vol. 435, Issue 1-2
DOI: 10.1016/0550-3213(94)00023-8

Orbifolds in Mathematics and Physics
book, January 2002

Adem, Alejandro; Morava, Jack; Ruan, Yongbin
Contemporary Mathematics
DOI: 10.1090/conm/310/05404

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

Kapustin, Anton; Thorngren, Ryan
Advances in Theoretical and Mathematical Physics, Vol. 18, Issue 5
DOI: 10.4310/ATMP.2014.v18.n5.a4

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

Whitehead, J. H. C.
Commentarii Mathematici Helvetici, Vol. 22, Issue 1
DOI: 10.1007/BF02568048

The Uncertainty of Fluxes
journal, January 2007

Freed, Daniel S.; Moore, Gregory W.; Segal, Graeme
Communications in Mathematical Physics, Vol. 271, Issue 1
DOI: 10.1007/s00220-006-0181-3

Duality and defects in rational conformal field theory
journal, February 2007

Fröhlich, Jürg; Fuchs, Jürgen; Runkel, Ingo
Nuclear Physics B, Vol. 763, Issue 3
DOI: 10.1016/j.nuclphysb.2006.11.017

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

Kapustin, Anton; Seiberg, Nathan
Journal of High Energy Physics, Vol. 2014, Issue 4
DOI: 10.1007/JHEP04(2014)001

Finite-temperature behavior of the lattice abelian Higgs model
journal, December 1979

Banks, Thomas; Rabinovici, Eliezer
Nuclear Physics B, Vol. 160, Issue 2
DOI: 10.1016/0550-3213(79)90064-6

Electric-magnetic duality, monopole condensation, and confinement in N=2 supersymmetric Yang-Mills theory
journal, September 1994

Seiberg, N.; Witten, E.
Nuclear Physics B, Vol. 426, Issue 1
DOI: 10.1016/0550-3213(94)90124-4

Quantum field theory and the Jones polynomial
journal, September 1989

Witten, Edward
Communications in Mathematical Physics, Vol. 121, Issue 3
DOI: 10.1007/BF01217730

Framed BPS states
journal, January 2013

Gaiotto, Davide; Moore, Gregory W.; Neitzke, Andrew
Advances in Theoretical and Mathematical Physics, Vol. 17, Issue 2
DOI: 10.4310/ATMP.2013.v17.n2.a1

A symmetry principle for topological quantum order
journal, May 2009

Nussinov, Zohar; Ortiz, Gerardo
Annals of Physics, Vol. 324, Issue 5
DOI: 10.1016/j.aop.2008.11.002

Topological gauge theories and group cohomology
journal, April 1990

Dijkgraaf, Robbert; Witten, Edward
Communications in Mathematical Physics, Vol. 129, Issue 2
DOI: 10.1007/BF02096988

Reading between the lines of four-dimensional gauge theories
journal, August 2013

Aharony, Ofer; Seiberg, Nathan; Tachikawa, Yuji
Journal of High Energy Physics, Vol. 2013, Issue 8
DOI: 10.1007/JHEP08(2013)115

Invertible defects and isomorphisms of rational CFTs
journal, January 2011

Davydov, Alexei; Kong, Liang; Runkel, Ingo
Advances in Theoretical and Mathematical Physics, Vol. 15, Issue 1
DOI: 10.4310/ATMP.2011.v15.n1.a2

Rigid Surface Operators
journal, January 2010

Gukov, Sergei; Witten, Edward
Advances in Theoretical and Mathematical Physics, Vol. 14, Issue 1
DOI: 10.4310/ATMP.2010.v14.n1.a3

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

Whitehead, J. H. C.
Birkhäuser
DOI: 10.5169/seals-19190

Surgery with Coefficients
book, January 1977

Anderson, Gerald A.
Lecture Notes in Mathematics
DOI: 10.1007/bfb0096745

Surgery with coefficients
book, January 1977

Anderson, Gerald A.
Lecture Notes in Mathematics
DOI: 10.1007/bfb0096749

Invertible defects and isomorphisms of rational CFTs
text, January 2010

Davydov, Alexei; Kong, Liang; Runkel, Ingo
arXiv
DOI: 10.48550/arxiv.1004.4725

Symmetry protected topological orders and the group cohomology of their symmetry group
text, January 2011

Chen, Xie; Gu, Zheng-Cheng; Liu, Zheng-Xin
arXiv
DOI: 10.48550/arxiv.1106.4772

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

Kapustin, Anton; Thorngren, Ryan
arXiv
DOI: 10.48550/arxiv.1308.2926

Works referencing / citing this record:

The Swampland: Introduction and Review
journal, April 2019

Palti, Eran
Fortschritte der Physik, Vol. 67, Issue 6
DOI: 10.1002/prop.201900037

Metastable vacua in large-N QCD3
journal, January 2020

Armoni, Adi; Dumitrescu, Thomas T.; Festuccia, Guido
Journal of High Energy Physics, Vol. 2020, Issue 1
DOI: 10.1007/jhep01(2020)004

Excitations in strict 2-group higher gauge models of topological phases
journal, January 2020

Bullivant, Alex; Delcamp, Clement
Journal of High Energy Physics, Vol. 2020, Issue 1
DOI: 10.1007/jhep01(2020)107

Yang-Mills glueballs as closed bosonic strings
journal, February 2017

Dubovsky, Sergei; Hernández-Chifflet, Guzmán
Journal of High Energy Physics, Vol. 2017, Issue 2
DOI: 10.1007/jhep02(2017)022

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

Delcamp, Clement; Tiwari, Apoorv
Journal of High Energy Physics, Vol. 2019, Issue 5
DOI: 10.1007/jhep05(2019)064

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

Anber, Mohamed M.; Poppitz, Erich
Journal of High Energy Physics, Vol. 2019, Issue 5
DOI: 10.1007/jhep05(2019)151

QCD domain walls, Chern-Simons theories and holography
journal, September 2018

Argurio, Riccardo; Bertolini, Matteo; Bigazzi, Francesco
Journal of High Energy Physics, Vol. 2018, Issue 9
DOI: 10.1007/jhep09(2018)090

Seifert fibering operators in 3d N = 2 $$ \mathcal{N}=2 $$ theories
journal, November 2018

Closset, Cyril; Kim, Heeyeon; Willett, Brian
Journal of High Energy Physics, Vol. 2018, Issue 11
DOI: 10.1007/jhep11(2018)004

Chiral 3d SU(3) SQCD and N = 2 $$ \mathcal{N}=2 $$ mirror duality
journal, November 2018

Fazzi, Marco; Lanir, Assaf; Razamat, Shlomo S.
Journal of High Energy Physics, Vol. 2018, Issue 11
DOI: 10.1007/jhep11(2018)025

Secondary Products in Supersymmetric Field Theory
journal, February 2020

Beem, Christopher; Ben-Zvi, David; Bullimore, Mathew
Annales Henri Poincaré, Vol. 21, Issue 4
DOI: 10.1007/s00023-020-00888-3

On the Cobordism Classification of Symmetry Protected Topological Phases
journal, April 2019

Yonekura, Kazuya
Communications in Mathematical Physics, Vol. 368, Issue 3
DOI: 10.1007/s00220-019-03439-y

Fermionic Finite-Group Gauge Theories and Interacting Symmetric/Crystalline Orders via Cobordisms
journal, January 2020

Guo, Meng; Ohmori, Kantaro; Putrov, Pavel
Communications in Mathematical Physics, Vol. 376, Issue 2
DOI: 10.1007/s00220-019-03671-6

Two-dimensional algebra in lattice gauge theory
journal, April 2019

Parzygnat, Arthur J.
Journal of Mathematical Physics, Vol. 60, Issue 4
DOI: 10.1063/1.5078532

A new SU(2) anomaly
journal, May 2019

Wang, Juven; Wen, Xiao-Gang; Witten, Edward
Journal of Mathematical Physics, Vol. 60, Issue 5
DOI: 10.1063/1.5082852

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

Seiberg, Nathan; Witten, Edward
Progress of Theoretical and Experimental Physics, Vol. 2016, Issue 12
DOI: 10.1093/ptep/ptw083

Tunneling topological vacua via extended operators: (Spin-)TQFT spectra and boundary deconfinement in various dimensions
journal, May 2018

Wang, Juven; Ohmori, Kantaro; Putrov, Pavel
Progress of Theoretical and Experimental Physics, Vol. 2018, Issue 5
DOI: 10.1093/ptep/pty051

Landau-Ginzburg theories of non-Abelian quantum Hall states from non-Abelian bosonization
journal, September 2019

Goldman, Hart; Sohal, Ramanjit; Fradkin, Eduardo
Physical Review B, Vol. 100, Issue 11
DOI: 10.1103/physrevb.100.115111

Gapless topological order, gravity, and black holes
journal, April 2018

Rasmussen, Alex; Jermyn, Adam S.
Physical Review B, Vol. 97, Issue 16
DOI: 10.1103/physrevb.97.165141

Lieb-Schultz-Mattis type theorem with higher-form symmetry and the quantum dimer models
journal, January 2019

Kobayashi, Ryohei; Shiozaki, Ken; Kikuchi, Yuta
Physical Review B, Vol. 99, Issue 1
DOI: 10.1103/physrevb.99.014402

Classifying local fractal subsystem symmetry-protected topological phases
journal, June 2019

Devakul, Trithep
Physical Review B, Vol. 99, Issue 23
DOI: 10.1103/physrevb.99.235131

Anomalies and bounds on charged operators
journal, July 2019

Lin, Ying-Hsuan; Shao, Shu-Heng
Physical Review D, Vol. 100, Issue 2
DOI: 10.1103/physrevd.100.025013

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

Aitken, Kyle; Cherman, Aleksey; Ünsal, Mithat
Physical Review D, Vol. 100, Issue 8
DOI: 10.1103/physrevd.100.085004