Built on

C. Delcamp and A. Tiwari, On 2-form gauge models of topological phases , JHEP 05
Original
1901
Earlier work this paper cites.
D. Gaiotto and T. Johnson-Freyd, Condensations in higher categories , 1905.09566
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 10
Original
1908
Earlier work this paper cites.
Y.-H. Lin and S.-H. Shao, Duality Defect of the Monster CFT , J. Phys. A 54
Original
1911
Earlier work this paper cites.
R. Thorngren and Y. Wang, Fusion Category Symmetry I: Anomaly In-Flow and Gapped Phases , 1912.02817
Original
1912
Earlier work this paper cites.
E. P. Verlinde, Fusion Rules and Modular Transformations in 2D Conformal Field Theory , Nucl. Phys. B 300
1988
Earlier work this paper cites.
J. C. Baez, An introduction to n-categories , in International Conference on Category Theory and Computer Science , pp. 1–33, Springer, 1997
1997
Earlier work this paper cites.
D. Tambara and S. Yamagami, Tensor categories with fusion rules of self-duality for finite abelian groups , J. Algebra 209
1998
Earlier work this paper cites.
V. B. Petkova and J. B. Zuber, Generalized twisted partition functions , Phys. Lett. B 504
2001
Earlier work this paper cites.
J. Fuchs, I. Runkel and C. Schweigert, TFT construction of RCFT correlators 1. Partition functions , Nucl. Phys. B 646
2002
Earlier work this paper cites.
V. Mulevičius and I. Runkel, Constructing modular categories from orbifold data , 2002.00663
Original
2002
Earlier work this paper cites.
D. Gaiotto, J. H. Lee and J. Wu, Integrable Kondo problems , JHEP 04
Original
2003
Earlier work this paper cites.
T. Johnson-Freyd, On the classification of topological orders , 2003.06663
Original
2003
Earlier work this paper cites.
A. Y. Kitaev, Fault tolerant quantum computation by anyons , Annals Phys. 303
2003
Earlier work this paper cites.
C. Bachas and M. Gaberdiel, Loop operators and the Kondo problem , JHEP 11
2004
Earlier work this paper cites.
D. R. Morrison, S. Schafer-Nameki and B. Willett, Higher-Form Symmetries in 5d , JHEP 09
Original
2005
Earlier work this paper cites.
F. Albertini, M. Del Zotto, I. n. García Etxebarria and S. S. Hosseini, Higher Form Symmetries and M-theory , JHEP 12
Original
2005
Earlier work this paper cites.
J. Fuchs, M. R. Gaberdiel, I. Runkel and C. Schweigert, Topological defects for the free boson CFT , J. Phys. A 40
Original
2007
Earlier work this paper cites.

Similar

P.-S. Hsin and H. T. Lam, Discrete theta angles, symmetries and anomalies , SciPost Phys. 10
Original
2007
Cited alongside, same era.
D. S. Freed, G. W. Moore and G. Segal, Heisenberg Groups and Noncommutative Fluxes , Annals Phys. 322
2007
Cited alongside, same era.
Z. Komargodski, K. Ohmori, K. Roumpedakis and S. Seifnashri, Symmetries and strings of adjoint QCD 2
Original
2008
Cited alongside, same era.
D. Gaiotto and J. Kulp, Orbifold groupoids , JHEP 02
Original
2008
Cited alongside, same era.
L. Bhardwaj and S. Schafer-Nameki, Higher-form symmetries of 6d and 5d theories , JHEP 02
Original
2008
Cited alongside, same era.

Then

M. Del Zotto, J. J. Heckman, D. S. Park and T. Rudelius, On the Defect Group of a 6D SCFT , Lett. Math. Phys. 106
Original
2016
Later among the works it cites.
L. Bhardwaj and Y. Tachikawa, On finite symmetries and their gauging in two dimensions , JHEP 03
Original
2018
Later among the works it cites.
C. L. Douglas and D. J. Reutter, Fusion 2-categories and a state-sum invariant for 4-manifolds , arXiv preprint arXiv:1812.11933 (2018)
Original
2018
Later among the works it cites.
C. Delcamp and A. Tiwari, From gauge to higher gauge models of topological phases , JHEP 10
Original
2018
Later among the works it cites.
C.-M. Chang, Y.-H. Lin, S.-H. Shao, Y. Wang and X. Yin, Topological Defect Lines and Renormalization Group Flows in Two Dimensions , JHEP 01

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2022

Non-Invertible Higher-Categorical Symmetries

Bhardwaj, Lakshya, Bottini, Lea E., Schafer-Nameki, Sakura et al.

Understand

We sketch a procedure to capture general non-invertible symmetries of a d-dimensional quantum field theory in the data of a higher-category, which captures the local properties of topological defects associated to the symmetries.

We also discuss fusions of topological defects, which involve condensations/gaugings of higher-categorical symmetries localized on the worldvolumes of topological defects.
Recently some fusions of topological defects were discussed in the literature where the dimension of topological defects seems to jump under fusion.
This is not possible in the standard description of higher-categories.

Built on

C. Delcamp and A. Tiwari, On 2-form gauge models of topological phases , JHEP 05
Original
1901
Earlier work this paper cites.
D. Gaiotto and T. Johnson-Freyd, Condensations in higher categories , 1905.09566
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 10
Original
1908
Earlier work this paper cites.
Y.-H. Lin and S.-H. Shao, Duality Defect of the Monster CFT , J. Phys. A 54
Original
1911
Earlier work this paper cites.
R. Thorngren and Y. Wang, Fusion Category Symmetry I: Anomaly In-Flow and Gapped Phases , 1912.02817
Original
1912
Earlier work this paper cites.
E. P. Verlinde, Fusion Rules and Modular Transformations in 2D Conformal Field Theory , Nucl. Phys. B 300
1988
Earlier work this paper cites.
J. C. Baez, An introduction to n-categories , in International Conference on Category Theory and Computer Science , pp. 1–33, Springer, 1997
1997
Earlier work this paper cites.
D. Tambara and S. Yamagami, Tensor categories with fusion rules of self-duality for finite abelian groups , J. Algebra 209
1998
Earlier work this paper cites.
V. B. Petkova and J. B. Zuber, Generalized twisted partition functions , Phys. Lett. B 504
2001
Earlier work this paper cites.
J. Fuchs, I. Runkel and C. Schweigert, TFT construction of RCFT correlators 1. Partition functions , Nucl. Phys. B 646
2002
Earlier work this paper cites.
V. Mulevičius and I. Runkel, Constructing modular categories from orbifold data , 2002.00663
Original
2002
Earlier work this paper cites.
D. Gaiotto, J. H. Lee and J. Wu, Integrable Kondo problems , JHEP 04
Original
2003
Earlier work this paper cites.
T. Johnson-Freyd, On the classification of topological orders , 2003.06663
Original
2003
Earlier work this paper cites.
A. Y. Kitaev, Fault tolerant quantum computation by anyons , Annals Phys. 303
2003
Earlier work this paper cites.
C. Bachas and M. Gaberdiel, Loop operators and the Kondo problem , JHEP 11
2004
Earlier work this paper cites.
D. R. Morrison, S. Schafer-Nameki and B. Willett, Higher-Form Symmetries in 5d , JHEP 09
Original
2005
Earlier work this paper cites.
F. Albertini, M. Del Zotto, I. n. García Etxebarria and S. S. Hosseini, Higher Form Symmetries and M-theory , JHEP 12
Original
2005
Earlier work this paper cites.
J. Fuchs, M. R. Gaberdiel, I. Runkel and C. Schweigert, Topological defects for the free boson CFT , J. Phys. A 40
Original
2007
Earlier work this paper cites.

Similar

P.-S. Hsin and H. T. Lam, Discrete theta angles, symmetries and anomalies , SciPost Phys. 10
Original
2007
Cited alongside, same era.
D. S. Freed, G. W. Moore and G. Segal, Heisenberg Groups and Noncommutative Fluxes , Annals Phys. 322
2007
Cited alongside, same era.
Z. Komargodski, K. Ohmori, K. Roumpedakis and S. Seifnashri, Symmetries and strings of adjoint QCD 2
Original
2008
Cited alongside, same era.
D. Gaiotto and J. Kulp, Orbifold groupoids , JHEP 02
Original
2008
Cited alongside, same era.
L. Bhardwaj and S. Schafer-Nameki, Higher-form symmetries of 6d and 5d theories , JHEP 02
Original
2008
Cited alongside, same era.

Then

M. Del Zotto, J. J. Heckman, D. S. Park and T. Rudelius, On the Defect Group of a 6D SCFT , Lett. Math. Phys. 106
Original
2016
Later among the works it cites.
L. Bhardwaj and Y. Tachikawa, On finite symmetries and their gauging in two dimensions , JHEP 03
Original
2018
Later among the works it cites.
C. L. Douglas and D. J. Reutter, Fusion 2-categories and a state-sum invariant for 4-manifolds , arXiv preprint arXiv:1812.11933 (2018)
Original
2018
Later among the works it cites.
C. Delcamp and A. Tiwari, From gauge to higher gauge models of topological phases , JHEP 10
Original
2018
Later among the works it cites.
C.-M. Chang, Y.-H. Lin, S.-H. Shao, Y. Wang and X. Yin, Topological Defect Lines and Renormalization Group Flows in Two Dimensions , JHEP 01

Beyond the bibliography

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

Open on alphaXiv

alphaXiv is searching for related work…

L. Kong, Y. Tian and Z.-H. Zhang, Defects in the 3-dimensional toric code model form a braided fusion 2-category , JHEP 12

Original

2009

Cited alongside, same era.

C. Cordova, T. T. Dumitrescu and K. Intriligator, 2-Group Global Symmetries and Anomalies in Six-Dimensional Quantum Field Theories , 2009.00138

Original

2009

Cited alongside, same era.

0909.5013

Original

J. Frohlich, J. Fuchs, I. Runkel and C. Schweigert, Defect lines, dualities, and generalised orbifolds , in 16th International Congress on Mathematical Physics , 9, 2009 · 2009

Cited alongside, same era.

C. Bachas and S. Monnier, Defect loops in gauged Wess-Zumino-Witten models , JHEP 02

Original

2010

Cited alongside, same era.

D. Gaiotto, J. H. Lee, B. Vicedo and J. Wu, Kondo line defects and affine Gaudin models , JHEP 01

Original

2010

Cited alongside, same era.

H. Bombin, Topological order with a twist: Ising anyons from an abelian model , Phys. Rev. Lett. 105

2010

Cited alongside, same era.