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E. Palti, “The Swampland: Introduction and Review,” Fortsch. Phys
Original
1903
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.
L. Kong, Y. Tian, and S. Zhou, “The center of monoidal 2-categories in 3+1D Dijkgraaf-Witten theory,” Adv. Math
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.
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.
W. Ji and X.-G. Wen, “Categorical symmetry and noninvertible anomaly in symmetry-breaking and topological phase transitions,” Phys. Rev. Res
Original
1912
Earlier work this paper cites.
T. Banchoff, “Triple points and singularities of projections of smoothly immersed surfaces,” Proceedings of the American Mathematical Society
1974
Earlier work this paper cites.
P. Goddard, J. Nuyts, and D. I. Olive, “Gauge Theories and Magnetic Charge,” Nucl. Phys. B
1977
Earlier work this paper cites.
E. Witten, “Dyons of Charge e theta/2 pi,” Phys. Lett. B
1979
Earlier work this paper cites.
G. T. Horowitz and M. Srednicki, “A quantum field theoretic description of linking numbers and their generalization,” Communications in Mathematical Physics
1990
Earlier work this paper cites.
Springer-Verlag, 1991
W. Fulton and J. Harris, Representation Theory · 1991
Earlier work this paper cites.
E. Witten, “AdS / CFT correspondence and topological field theory,” JHEP
1998
Earlier work this paper cites.
Cambridge Univ. Press, Cambridge, 2000
A. Hatcher, Algebraic topology · 2000
Earlier work this paper cites.
T. Johnson-Freyd, “On the Classification of Topological Orders,” Commun. Math. Phys
Original
2003
Earlier work this paper cites.
L. Kong, T. Lan, X.-G. Wen, Z.-H. Zhang, and H. Zheng, “Classification of topological phases with finite internal symmetries in all dimensions,” JHEP
Original
2003
Earlier work this paper cites.
J. Frohlich, J. Fuchs, I. Runkel, and C. Schweigert, “Kramers-Wannier duality from conformal defects,” Phys. Rev. Lett
2004
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.
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. n. García Etxebarria, and S. S. Hosseini, “Higher Form Symmetries and M-theory,” JHEP
Original
2005
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.
J. Fuchs, M. R. Gaberdiel, I. Runkel, and C. Schweigert, “Topological defects for the free boson CFT,” J. Phys. A
Original
2007
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.
C. Closset, S. Schafer-Nameki, and Y.-N. Wang, “Coulomb and Higgs Branches from Canonical Singularities: Part 0,” JHEP
Original
2007
Earlier work this paper cites.
M. Del Zotto, I. n. García Etxebarria, and S. S. Hosseini, “Higher form symmetries of Argyres-Douglas theories,” JHEP
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. Gaiotto and J. Kulp, “Orbifold groupoids,” 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.
L. Bhardwaj and S. Schäfer-Nameki, “Higher-form symmetries of 6d and 5d theories,” JHEP
Original
2008
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.
T. Johnson-Freyd and M. Yu, “Fusion 2-categories With no Line Operators are Grouplike,” Bull. Austral. Math. Soc
Original
2010
Earlier work this paper cites.
S. Gukov, P.-S. Hsin, and D. Pei, “Generalized global symmetries of T ⁡ [ M ] T[M] theories. Part I,” JHEP
Original
2010
Earlier work this paper cites.

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2023

ICTP Lectures on (Non-)Invertible Generalized Symmetries

Schafer-Nameki, Sakura

Understand

What comprises a global symmetry of a Quantum Field Theory (QFT) has been vastly expanded in the past 10 years to include not only symmetries acting on higher-dimensional defects, but also most recently symmetries which do not have an inverse.

The principle that enables this generalization is the identification of symmetries with topological defects in the QFT.
In these lectures, we provide an introduction to generalized symmetries, with a focus on non-invertible symmetries.
We begin with a brief overview of invertible generalized symmetries, including higher-form and higher-group symmetries, and then move on to non-invertible symmetries.