Built on

Y.-H. Lin and S.-H. Shao, “Anomalies and Bounds on Charged Operators,” Phys. Rev. D
Original
1904
Earlier work this paper cites.
D. Delmastro and J. Gomis, “Symmetries of Abelian Chern-Simons Theories and Arithmetic,” JHEP
Original
1904
Earlier work this paper cites.
D. Gaiotto and T. Johnson-Freyd, “Condensations in higher categories,” arXiv:1905.09566 [math.CT]
Original
1905
Earlier work this paper cites.
I. n. García Etxebarria, B. Heidenreich, and D. Regalado, “IIB flux non-commutativity and the global structure of field theories,” JHEP
Original
1908
Earlier work this paper cites.
J. Eckhard, H. Kim, S. Schafer-Nameki, and B. Willett, “Higher-Form Symmetries, Bethe Vacua, and the 3d-3d Correspondence,” JHEP
Original
1910
Earlier work this paper cites.
I. Hason, Z. Komargodski, and R. Thorngren, “Anomaly Matching in the Symmetry Broken Phase: Domain Walls, CPT, and the Smith Isomorphism,” SciPost Phys
Original
1910
Earlier work this paper cites.
C. Córdova, K. Ohmori, S.-H. Shao, and F. Yan, “Decorated ℤ 2 \mathbb{Z}_{2} Symmetry Defects and Their Time-Reversal Anomalies,” arXiv:1910.14046 [hep-th]
Original
1910
Earlier work this paper cites.
R. Thorngren and Y. Wang, “Fusion Category Symmetry I: Anomaly In-Flow and Gapped Phases,” arXiv:1912.02817 [hep-th]
Original
1912
Earlier work this paper cites.
Z. Wan, J. Wang, and Y. Zheng, “Higher anomalies, higher symmetries, and cobordisms II: Lorentz symmetry extension and enriched bosonic / fermionic quantum gauge theory,” Ann. Math. Sci. Appl
Original
1912
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E. P. Verlinde, “Fusion Rules and Modular Transformations in 2D Conformal Field Theory,” Nucl. Phys. B
1988
Earlier work this paper cites.
G. W. Moore and N. Seiberg, “Classical and Quantum Conformal Field Theory,” Commun. Math. Phys
1989
Earlier work this paper cites.
T. Senthil and M. P. A. Fisher, “ Z 2 {Z}_{2} gauge theory of electron fractionalization in strongly correlated systems,” Phys. Rev. B
2000
Earlier work this paper cites.
V. B. Petkova and J. B. Zuber, “Generalized twisted partition functions,” Phys. Lett. B
2001
Earlier work this paper cites.
R. Thorngren, “Topological quantum field theory, symmetry breaking, and finite gauge theory in 3+1D,” Phys. Rev. B
Original
2001
Earlier work this paper cites.
J. Fuchs, I. Runkel, and C. Schweigert, “TFT construction of RCFT correlators 1. Partition functions,” Nucl. Phys. B
2002
Earlier work this paper cites.
T. Johnson-Freyd, “On the Classification of Topological Orders,” Commun. Math. Phys
Original
2003
Earlier work this paper cites.
O. Bergman, Y. Tachikawa, and G. Zafrir, “Generalized symmetries and holography in ABJM-type theories,” JHEP
Original
2004
Earlier work this paper cites.
D. R. Morrison, S. Schafer-Nameki, and B. Willett, “Higher-Form Symmetries in 5d,” JHEP
Original
2005
Earlier work this paper cites.
F. Albertini, M. Del Zotto, I. García Etxebarria, and S. S. Hosseini, “Higher Form Symmetries and M-theory,” arXiv:2005.12831 [hep-th]
Original
2005
Earlier work this paper cites.
L. Kong, T. Lan, X.-G. Wen, Z.-H. Zhang, and H. Zheng, “Algebraic higher symmetry and categorical symmetry – a holographic and entanglement view of symmetry,” Phys. Rev. Res
Original
2005
Earlier work this paper cites.
A. Kitaev, “Anyons in an exactly solved model and beyond,” Annals Phys
2006
Earlier work this paper cites.
A. Kapustin, “Wilson-’t Hooft operators in four-dimensional gauge theories and S-duality,” Phys. Rev. D
2006
Earlier work this paper cites.
P.-S. Hsin and H. T. Lam, “Discrete theta angles, symmetries and anomalies,” SciPost Phys
Original
2007
Earlier work this paper cites.
I. Bah, F. Bonetti, and R. Minasian, “Discrete and higher-form symmetries in SCFTs from wrapped M5-branes,” JHEP
Original
2007
Earlier work this paper cites.
M. Del Zotto, I. Garcia Etxebarria, and S. S. Hosseini, “Higher form symmetries of Argyres-Douglas theories,” JHEP
Original
2007
Earlier work this paper cites.
C. Closset, S. Schafer-Nameki, and Y.-N. Wang, “Coulomb and Higgs Branches from Canonical Singularities: Part 0,” arXiv:2007.15600 [hep-th]
Original
2007
Earlier work this paper cites.
Z. Komargodski, K. Ohmori, K. Roumpedakis, and S. Seifnashri, “Symmetries and strings of adjoint QCD 2
Original
2008
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D. Aasen, P. Fendley, and R. S. K. Mong, “Topological Defects on the Lattice: Dualities and Degeneracies,” arXiv:2008.08598 [cond-mat.stat-mech]
Original
2008
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L. Bhardwaj and S. Schäfer-Nameki, “Higher-form symmetries of 6d and 5d theories,” JHEP
Original
2008
Earlier work this paper cites.
F. Apruzzi, M. Dierigl, and L. Lin, “The fate of discrete 1-form symmetries in 6d,” SciPost Phys
Original
2008
Earlier work this paper cites.
D. Gaiotto and J. Kulp, “Orbifold groupoids,” JHEP
Original
2008
Earlier work this paper cites.
C. Cordova, T. T. Dumitrescu, and K. Intriligator, “2-Group Global Symmetries and Anomalies in Six-Dimensional Quantum Field Theories,” JHEP
Original
2009
Earlier work this paper cites.
M. Del Zotto and K. Ohmori, “2-Group Symmetries of 6D Little String Theories and T-Duality,” Annales Henri Poincare
Original
2009
Earlier work this paper cites.
P. Benetti Genolini and L. Tizzano, “Instantons, symmetries and anomalies in five dimensions,” JHEP
Original
2009
Earlier work this paper cites.
L. Bhardwaj, Y. Lee, and Y. Tachikawa, “ S L ( 2 , ℤ ) SL(2,\mathbb{Z}) action on QFTs with ℤ 2 \mathbb{Z}_{2} symmetry and the Brown-Kervaire invariants,” JHEP
Original
2009
Earlier work this paper cites.
Y. Hidaka, M. Nitta, and R. Yokokura, “Global 3-group symmetry and ’t Hooft anomalies in axion electrodynamics,” JHEP
Original
2009
Earlier work this paper cites.

Similar

M. Yu, “Symmetries and anomalies of (1+1)d theories: 2-groups and symmetry fractionalization,” JHEP
Original
2010
Cited alongside, same era.
O. DeWolfe and K. Higginbotham, “Generalized symmetries and 2-groups via electromagnetic duality in A d S / C F T AdS/CFT ,” Phys. Rev. D
Original
2010
Cited alongside, same era.
S. Gukov, P.-S. Hsin, and D. Pei, “Generalized global symmetries of T ⁡ [ M ] T[M] theories. Part I,” JHEP
Original
2010
Cited alongside, same era.
N. Iqbal and N. Poovuttikul, “2-group global symmetries, hydrodynamics and holography,” arXiv:2010.00320 [hep-th]
Original
2010
Cited alongside, same era.
T. D. Brennan and C. Cordova, “Axions, higher-groups, and emergent symmetry,” JHEP

Then

L. Bhardwaj, M. Hubner, and S. Schafer-Nameki, “1-form Symmetries of 4d 𝒩 = 2 \mathcal{N}=2 Class S Theories,” SciPost Phys
Original
2021
Later among the works it cites.
M. Nguyen, Y. Tanizaki, and M. Ünsal, “Noninvertible 1-form symmetry and Casimir scaling in 2D Yang-Mills theory,” Phys. Rev. D
Original
2021
Later among the works it cites.
B. Heidenreich, J. McNamara, M. Montero, M. Reece, T. Rudelius, and I. Valenzuela, “Non-invertible global symmetries and completeness of the spectrum,” JHEP
Original
2021
Later among the works it cites.
F. Apruzzi, M. van Beest, D. S. W. Gould, and S. Schäfer-Nameki, “Holography, 1-form symmetries, and confinement,” Phys. Rev. D
Original
2021
Later among the works it cites.
S. S. Hosseini and R. Moscrop, “Maruyoshi-Song flows and defect groups of D p b {\mathrm{D}}_{\mathrm{p}}^{\mathrm{b}} (G) theories,” JHEP

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2023

Higher Structure of Chiral Symmetry

Copetti, Christian, Del Zotto, Michele, Ohmori, Kantaro et al.

Understand

A recent development in our understanding of the theory of quantum fields is the fact that familiar gauge theories in spacetime dimensions greater than two can have non-invertible symmetries generated by topological defects.

The hallmark of these non-invertible symmetries is that the fusion rule deviates from the usual group-like structure, and in particular the fusion coefficients take values in topological field theories (TFTs) rather than in mere numbers.
In this paper we begin an exploration of the associativity structure of non-invertible symmetries in higher dimensions.
The first layer of associativity is captured by F-symbols, which we find to assume values in TFTs that have one dimension lower than that of the defect.

Built on

Y.-H. Lin and S.-H. Shao, “Anomalies and Bounds on Charged Operators,” Phys. Rev. D
Original
1904
Earlier work this paper cites.
D. Delmastro and J. Gomis, “Symmetries of Abelian Chern-Simons Theories and Arithmetic,” JHEP
Original
1904
Earlier work this paper cites.
D. Gaiotto and T. Johnson-Freyd, “Condensations in higher categories,” arXiv:1905.09566 [math.CT]
Original
1905
Earlier work this paper cites.
I. n. García Etxebarria, B. Heidenreich, and D. Regalado, “IIB flux non-commutativity and the global structure of field theories,” JHEP
Original
1908
Earlier work this paper cites.
J. Eckhard, H. Kim, S. Schafer-Nameki, and B. Willett, “Higher-Form Symmetries, Bethe Vacua, and the 3d-3d Correspondence,” JHEP
Original
1910
Earlier work this paper cites.
I. Hason, Z. Komargodski, and R. Thorngren, “Anomaly Matching in the Symmetry Broken Phase: Domain Walls, CPT, and the Smith Isomorphism,” SciPost Phys
Original
1910
Earlier work this paper cites.
C. Córdova, K. Ohmori, S.-H. Shao, and F. Yan, “Decorated ℤ 2 \mathbb{Z}_{2} Symmetry Defects and Their Time-Reversal Anomalies,” arXiv:1910.14046 [hep-th]
Original
1910
Earlier work this paper cites.
R. Thorngren and Y. Wang, “Fusion Category Symmetry I: Anomaly In-Flow and Gapped Phases,” arXiv:1912.02817 [hep-th]
Original
1912
Earlier work this paper cites.
Z. Wan, J. Wang, and Y. Zheng, “Higher anomalies, higher symmetries, and cobordisms II: Lorentz symmetry extension and enriched bosonic / fermionic quantum gauge theory,” Ann. Math. Sci. Appl
Original
1912
Earlier work this paper cites.
E. P. Verlinde, “Fusion Rules and Modular Transformations in 2D Conformal Field Theory,” Nucl. Phys. B
1988
Earlier work this paper cites.
G. W. Moore and N. Seiberg, “Classical and Quantum Conformal Field Theory,” Commun. Math. Phys
1989
Earlier work this paper cites.
T. Senthil and M. P. A. Fisher, “ Z 2 {Z}_{2} gauge theory of electron fractionalization in strongly correlated systems,” Phys. Rev. B
2000
Earlier work this paper cites.
V. B. Petkova and J. B. Zuber, “Generalized twisted partition functions,” Phys. Lett. B
2001
Earlier work this paper cites.
R. Thorngren, “Topological quantum field theory, symmetry breaking, and finite gauge theory in 3+1D,” Phys. Rev. B
Original
2001
Earlier work this paper cites.
J. Fuchs, I. Runkel, and C. Schweigert, “TFT construction of RCFT correlators 1. Partition functions,” Nucl. Phys. B
2002
Earlier work this paper cites.
T. Johnson-Freyd, “On the Classification of Topological Orders,” Commun. Math. Phys
Original
2003
Earlier work this paper cites.
O. Bergman, Y. Tachikawa, and G. Zafrir, “Generalized symmetries and holography in ABJM-type theories,” JHEP
Original
2004
Earlier work this paper cites.
D. R. Morrison, S. Schafer-Nameki, and B. Willett, “Higher-Form Symmetries in 5d,” JHEP
Original
2005
Earlier work this paper cites.
F. Albertini, M. Del Zotto, I. García Etxebarria, and S. S. Hosseini, “Higher Form Symmetries and M-theory,” arXiv:2005.12831 [hep-th]
Original
2005
Earlier work this paper cites.
L. Kong, T. Lan, X.-G. Wen, Z.-H. Zhang, and H. Zheng, “Algebraic higher symmetry and categorical symmetry – a holographic and entanglement view of symmetry,” Phys. Rev. Res
Original
2005
Earlier work this paper cites.
A. Kitaev, “Anyons in an exactly solved model and beyond,” Annals Phys
2006
Earlier work this paper cites.
A. Kapustin, “Wilson-’t Hooft operators in four-dimensional gauge theories and S-duality,” Phys. Rev. D
2006
Earlier work this paper cites.
P.-S. Hsin and H. T. Lam, “Discrete theta angles, symmetries and anomalies,” SciPost Phys
Original
2007
Earlier work this paper cites.
I. Bah, F. Bonetti, and R. Minasian, “Discrete and higher-form symmetries in SCFTs from wrapped M5-branes,” JHEP
Original
2007
Earlier work this paper cites.
M. Del Zotto, I. Garcia Etxebarria, and S. S. Hosseini, “Higher form symmetries of Argyres-Douglas theories,” JHEP
Original
2007
Earlier work this paper cites.
C. Closset, S. Schafer-Nameki, and Y.-N. Wang, “Coulomb and Higgs Branches from Canonical Singularities: Part 0,” arXiv:2007.15600 [hep-th]
Original
2007
Earlier work this paper cites.
Z. Komargodski, K. Ohmori, K. Roumpedakis, and S. Seifnashri, “Symmetries and strings of adjoint QCD 2
Original
2008
Earlier work this paper cites.
D. Aasen, P. Fendley, and R. S. K. Mong, “Topological Defects on the Lattice: Dualities and Degeneracies,” arXiv:2008.08598 [cond-mat.stat-mech]
Original
2008
Earlier work this paper cites.
L. Bhardwaj and S. Schäfer-Nameki, “Higher-form symmetries of 6d and 5d theories,” JHEP
Original
2008
Earlier work this paper cites.
F. Apruzzi, M. Dierigl, and L. Lin, “The fate of discrete 1-form symmetries in 6d,” SciPost Phys
Original
2008
Earlier work this paper cites.
D. Gaiotto and J. Kulp, “Orbifold groupoids,” JHEP
Original
2008
Earlier work this paper cites.
C. Cordova, T. T. Dumitrescu, and K. Intriligator, “2-Group Global Symmetries and Anomalies in Six-Dimensional Quantum Field Theories,” JHEP
Original
2009
Earlier work this paper cites.
M. Del Zotto and K. Ohmori, “2-Group Symmetries of 6D Little String Theories and T-Duality,” Annales Henri Poincare
Original
2009
Earlier work this paper cites.
P. Benetti Genolini and L. Tizzano, “Instantons, symmetries and anomalies in five dimensions,” JHEP
Original
2009
Earlier work this paper cites.
L. Bhardwaj, Y. Lee, and Y. Tachikawa, “ S L ( 2 , ℤ ) SL(2,\mathbb{Z}) action on QFTs with ℤ 2 \mathbb{Z}_{2} symmetry and the Brown-Kervaire invariants,” JHEP
Original
2009
Earlier work this paper cites.
Y. Hidaka, M. Nitta, and R. Yokokura, “Global 3-group symmetry and ’t Hooft anomalies in axion electrodynamics,” JHEP
Original
2009
Earlier work this paper cites.

Similar

M. Yu, “Symmetries and anomalies of (1+1)d theories: 2-groups and symmetry fractionalization,” JHEP
Original
2010
Cited alongside, same era.
O. DeWolfe and K. Higginbotham, “Generalized symmetries and 2-groups via electromagnetic duality in A d S / C F T AdS/CFT ,” Phys. Rev. D
Original
2010
Cited alongside, same era.
S. Gukov, P.-S. Hsin, and D. Pei, “Generalized global symmetries of T ⁡ [ M ] T[M] theories. Part I,” JHEP
Original
2010
Cited alongside, same era.
N. Iqbal and N. Poovuttikul, “2-group global symmetries, hydrodynamics and holography,” arXiv:2010.00320 [hep-th]
Original
2010
Cited alongside, same era.
T. D. Brennan and C. Cordova, “Axions, higher-groups, and emergent symmetry,” JHEP

Then

L. Bhardwaj, M. Hubner, and S. Schafer-Nameki, “1-form Symmetries of 4d 𝒩 = 2 \mathcal{N}=2 Class S Theories,” SciPost Phys
Original
2021
Later among the works it cites.
M. Nguyen, Y. Tanizaki, and M. Ünsal, “Noninvertible 1-form symmetry and Casimir scaling in 2D Yang-Mills theory,” Phys. Rev. D
Original
2021
Later among the works it cites.
B. Heidenreich, J. McNamara, M. Montero, M. Reece, T. Rudelius, and I. Valenzuela, “Non-invertible global symmetries and completeness of the spectrum,” JHEP
Original
2021
Later among the works it cites.
F. Apruzzi, M. van Beest, D. S. W. Gould, and S. Schäfer-Nameki, “Holography, 1-form symmetries, and confinement,” Phys. Rev. D
Original
2021
Later among the works it cites.
S. S. Hosseini and R. Moscrop, “Maruyoshi-Song flows and defect groups of D p b {\mathrm{D}}_{\mathrm{p}}^{\mathrm{b}} (G) theories,” JHEP

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

Original

2011

Cited alongside, same era.

A. Kapustin and N. Saulina, “Topological boundary conditions in abelian Chern-Simons theory,” Nucl. Phys. B

Original

2011

Cited alongside, same era.

C. Closset, S. Giacomelli, S. Schafer-Nameki, and Y.-N. Wang, “5d and 4d SCFTs: Canonical Singularities, Trinions and S-Dualities,” JHEP

Original

2012

Cited alongside, same era.

R. Thorngren and Y. Wang, “Anomalous symmetries end at the boundary,” JHEP

Original

2012

Cited alongside, same era.

O. Aharony, N. Seiberg, and Y. Tachikawa, “Reading between the lines of four-dimensional gauge theories,” JHEP

Original

2013

Cited alongside, same era.

D. Gaiotto, G. W. Moore, and A. Neitzke, “Framed BPS States,” Adv. Theor. Math. Phys

Original

2013

Cited alongside, same era.

A. M. Essin and M. Hermele, “Classifying fractionalization: Symmetry classification of gapped ℤ 2 \mathbb{Z}_{2} spin liquids in two dimensions,” Phys. Rev. B

Original

2013

Cited alongside, same era.

A. Davydov, M. Müger, D. Nikshych, and V. Ostrik, “The witt group of non-degenerate braided fusion categories,” Journal für die reine und angewandte Mathematik (Crelles Journal)

2013

Cited alongside, same era.

Original

2021

Later among the works it cites.

M. Cvetic, M. Dierigl, L. Lin, and H. Y. Zhang, “Higher-form symmetries and their anomalies in M-/F-theory duality,” Phys. Rev. D

Original

2021

Later among the works it cites.

M. Buican and H. Jiang, “1-form symmetry, isolated 𝒩 \mathcal{N} = 2 SCFTs, and Calabi-Yau threefolds,” JHEP

Original

2021