Built on

D. Gaiotto and T. Johnson-Freyd, “Condensations in higher categories,” arXiv:1905.09566 [math.CT]
Original
1905
Earlier work this paper cites.
Dover Publications, Inc., New York, 1955
W. Burnside, Theory of groups of finite order · 1955
Earlier work this paper cites.
North-Holland, Jan., 2000
S. Bouc, “Burnside rings,” in Handbook of Algebra · 2000
Earlier work this paper cites.
T. Johnson-Freyd, “On the classification of topological orders,” arXiv:2003.06663 [math.CT]
Original
2003
Earlier work this paper cites.
http://arxiv.org/abs/math/0605530
D. Naidu, “Categorical Morita equivalence for group-theoretical categories,” Sept., 2006 · 2006
Earlier work this paper cites.
J. Elgueta, “Representation theory of 2-groups on Kapranov and Voevodsky’s 2-vector spaces,” Adv. Math
2007
Earlier work this paper cites.
L. Kong, Y. Tian, and Z.-H. Zhang, “Defects in the 3-dimensional toric code model form a braided fusion 2-category,” JHEP
Original
2009
Earlier work this paper cites.
J. Greenough, “Monoidal 2-structure of bimodule categories,” Journal of Algebra
2010
Earlier work this paper cites.
Cambridge University Press, 2011
C. Simpson, Homotopy Theory of Higher Categories: From Segal Categories to n-Categories and Beyond · 2011
Earlier work this paper cites.

Similar

Springer Science & Business Media, Apr., 2013
A. Kerber, Applied Finite Group Actions · 2013
Cited alongside, same era.
D. Gaiotto, A. Kapustin, N. Seiberg, and B. Willett, “Generalized Global Symmetries,” JHEP
Original
2015
Cited alongside, same era.
E. Sharpe, “Notes on generalized global symmetries in QFT,” Fortsch. Phys
Original
2015
Cited alongside, same era.
American Mathematical Soc., 2016
P. Etingof, S. Gelaki, D. Nikshych, and V. Ostrik, Tensor categories · 2016
Cited alongside, same era.
L. Bhardwaj and Y. Tachikawa, “On finite symmetries and their gauging in two dimensions,” JHEP
Original
2018
Cited alongside, same era.

Then

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,” Physical Review Research
2020
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.
T. D. Décoppet, “Weak fusion 2-categories,” arXiv preprint arXiv:2103.15150
Original
2021
Later among the works it cites.
T. JOHNSON-FREYD and M. YU, “Fusion 2-categories with no line operators are grouplike,” Bulletin of the Australian Mathematical Society
2021
Later among the works it cites.
https://www.gap-system.org,
The GAP Group, GAP – Groups, Algorithms, and Programming, Version 4.11.1 · 2021

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2022

Universal Non-Invertible Symmetries

Bhardwaj, Lakshya, Schafer-Nameki, Sakura, Wu, Jingxiang

Understand

It is well-known that gauging a finite 0-form symmetry in a quantum field theory leads to a dual symmetry generated by topological Wilson line defects.

These are described by the representations of the 0-form symmetry group which form a 1-category.
We argue that for a d-dimensional quantum field theory the full set of dual symmetries one obtains is in fact much larger and is described by a (d-1)-category, which is formed out of lower-dimensional topological quantum field theories with the same 0-form symmetry.
We study in detail a 2-categorical piece of this (d-1)-category described by 2d topological quantum field theories with 0-form symmetry.

Built on

D. Gaiotto and T. Johnson-Freyd, “Condensations in higher categories,” arXiv:1905.09566 [math.CT]
Original
1905
Earlier work this paper cites.
Dover Publications, Inc., New York, 1955
W. Burnside, Theory of groups of finite order · 1955
Earlier work this paper cites.
North-Holland, Jan., 2000
S. Bouc, “Burnside rings,” in Handbook of Algebra · 2000
Earlier work this paper cites.
T. Johnson-Freyd, “On the classification of topological orders,” arXiv:2003.06663 [math.CT]
Original
2003
Earlier work this paper cites.
http://arxiv.org/abs/math/0605530
D. Naidu, “Categorical Morita equivalence for group-theoretical categories,” Sept., 2006 · 2006
Earlier work this paper cites.
J. Elgueta, “Representation theory of 2-groups on Kapranov and Voevodsky’s 2-vector spaces,” Adv. Math
2007
Earlier work this paper cites.
L. Kong, Y. Tian, and Z.-H. Zhang, “Defects in the 3-dimensional toric code model form a braided fusion 2-category,” JHEP
Original
2009
Earlier work this paper cites.
J. Greenough, “Monoidal 2-structure of bimodule categories,” Journal of Algebra
2010
Earlier work this paper cites.
Cambridge University Press, 2011
C. Simpson, Homotopy Theory of Higher Categories: From Segal Categories to n-Categories and Beyond · 2011
Earlier work this paper cites.

Similar

Springer Science & Business Media, Apr., 2013
A. Kerber, Applied Finite Group Actions · 2013
Cited alongside, same era.
D. Gaiotto, A. Kapustin, N. Seiberg, and B. Willett, “Generalized Global Symmetries,” JHEP
Original
2015
Cited alongside, same era.
E. Sharpe, “Notes on generalized global symmetries in QFT,” Fortsch. Phys
Original
2015
Cited alongside, same era.
American Mathematical Soc., 2016
P. Etingof, S. Gelaki, D. Nikshych, and V. Ostrik, Tensor categories · 2016
Cited alongside, same era.
L. Bhardwaj and Y. Tachikawa, “On finite symmetries and their gauging in two dimensions,” JHEP
Original
2018
Cited alongside, same era.

Then

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,” Physical Review Research
2020
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.
T. D. Décoppet, “Weak fusion 2-categories,” arXiv preprint arXiv:2103.15150
Original
2021
Later among the works it cites.
T. JOHNSON-FREYD and M. YU, “Fusion 2-categories with no line operators are grouplike,” Bulletin of the Australian Mathematical Society
2021
Later among the works it cites.
https://www.gap-system.org,
The GAP Group, GAP – Groups, Algorithms, and Programming, Version 4.11.1 · 2021