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These notes are intended to be a pedagogical introduction to higher-form symmetries, which are symmetries whose charged objects are extended operators supported on lines, surfaces, and etc.
1904
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C. Turner, Dualities in 2+1 Dimensions, PoS Modave2018
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N. Seiberg, Field Theories With a Vector Global Symmetry, SciPost Phys. 8
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A. M. Polyakov, Quark Confinement and Topology of Gauge Groups, Nucl. Phys. B 120
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A. M. Polyakov, Gauge Fields and Strings , Vol. 3 (1987)
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R. Floreanini and R. Jackiw, Selfdual Fields as Charge Density Solitons, Phys. Rev. Lett. 59
1987
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M. G. Alford and J. March-Russell, Discrete gauge theories, Int. J. Mod. Phys. B 5
1991
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1992
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1992
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1992
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X.-G. Wen, Theory of the Edge States in Fractional Quantum Hall Effects, International Journal of Modern Physics B 6
1992
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1995
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P. Di Francesco, P. Mathieu, and D. Senechal, Conformal Field Theory , Graduate Texts in Contemporary Physics (Springer-Verlag, New York, 1997)
1997
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J. von Delft and H. Schoeller, Bosonization for beginners: Refermionization for experts, Annalen Phys. 7
1998
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D. Senechal, An Introduction to bosonization, in CRM Workshop on Theoretical Methods for Strongly Correlated Fermions (1999) arXiv:cond-mat/9908262
1999
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H. Georgi, Lie algebras in particle physics , 2nd ed., Vol. 54 (Perseus Books, Reading, MA, 1999)
1999
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R. A. Bertlmann, Anomalies in quantum field theory , Vol. 91 (Oxford university press, 2000)
2000
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M. Pretko, X. Chen, and Y. You, Fracton Phases of Matter, Int. J. Mod. Phys. A 35
2001
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2003
Cited alongside, same era.
J. Frohlich, J. Fuchs, I. Runkel, and C. Schweigert, Kramers-Wannier duality from conformal defects, Phys. Rev. Lett. 93
2004
Cited alongside, same era.
2004
Cited alongside, same era.
T. Pantev and E. Sharpe, Notes on gauging noneffective group actions, (2005), arXiv:hep-th/0502027
2005
Cited alongside, same era.
C. Chamon, Quantum glassiness in strongly correlated clean systems: An example of topological overprotection, Physical Review Letters 94
2005
2016
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2017
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E. Lake, Higher-form symmetries and spontaneous symmetry breaking, (2018), arXiv:1802.07747 [hep-th]
2018
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D. Tong, Gauge Theory, (2018)
2018
Later among the works it cites.
2018
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Cited alongside, same era.
S. Weinberg, The Quantum theory of fields. Vol. 1: Foundations (Cambridge University Press, 2005)
2005
Cited alongside, same era.
V. P. Nair, Quantum field theory: A modern perspective (Springer Science & Business Media, 2005)
2005
Cited alongside, same era.
2006
Cited alongside, same era.
S. Hellerman, A. Henriques, T. Pantev, E. Sharpe, and M. Ando, Cluster decomposition, T-duality, and gerby CFT’s, Adv. Theor. Math. Phys. 11
2007
Cited alongside, same era.
M. Srednicki, Quantum field theory (Cambridge University Press, 2007)
2007
Cited alongside, same era.
K. Slagle, Foliated Quantum Field Theory of Fracton Order, Phys. Rev. Lett. 126
2008
Cited alongside, same era.
Z. Nussinov and G. Ortiz, A symmetry principle for topological quantum order, Annals of Physics 324
2009
Cited alongside, same era.
Later among the works it cites.
M. Pretko, The Fracton Gauge Principle, Phys. Rev. B 98
2018
Later among the works it cites.
M. Nakahara, Geometry, topology and physics (CRC press, 2018)
2018
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R. M. Nandkishore and M. Hermele, Fractons, Ann. Rev. Condensed Matter Phys. 10
2019
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2019
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A. Gromov, Towards classification of Fracton phases: the multipole algebra, Phys. Rev. X 9
2019
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2019
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R. Yokokura, An introduction to higher-form symmetries, 2020, Seminar @ IBS, online
2020
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J. McGreevy, Generalized Symmetries in Condensed Matter, (2022), arXiv:2204.03045 [cond-mat.str-el]
2022
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2022
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2022
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2022
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2022
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2022
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2023
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2023
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