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arxiv: 2205.09545 · v1 · pith:7Q2Q2CZRnew · submitted 2022-05-19 · ✦ hep-th · hep-ph

Snowmass White Paper: Generalized Symmetries in Quantum Field Theory and Beyond

Clay Cordova , Thomas T. Dumitrescu , Kenneth Intriligator , Shu-Heng Shao This is my paper

Pith reviewed 2026-05-21 13:16 UTC · model grok-4.3

classification ✦ hep-th hep-ph
keywords generalized symmetriesquantum field theoryanomaliesdefectscategorical symmetriessymmetry constraintsSnowmass white paper
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0 comments X

The pith

Generalized symmetries acting on defects and categorical symmetries introduce new anomalies that constrain quantum field theory dynamics.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This review paper examines how symmetry in quantum field theory extends beyond ordinary group transformations to include actions on defects and subsystems as well as non-group-like categorical structures. These generalized symmetries produce novel anomaly phenomena that were not captured by traditional approaches. The authors survey key examples where these anomalies impose restrictions on allowed dynamics and phase structures. A reader would care because such constraints offer new ways to analyze strongly coupled theories and unify disparate phenomena across high-energy and condensed-matter physics.

Core claim

Symmetries in quantum field theory now encompass actions on defects and other subsystems together with categorical rather than group-like structures; these extensions generate new classes of anomalies that constrain the possible dynamics of the theory, as illustrated by recent transformative applications.

What carries the argument

Generalized symmetries, including defect-acting symmetries and categorical symmetries, which extend ordinary group symmetries to produce additional anomaly structures that limit dynamics.

If this is right

  • New anomaly constraints can rule out certain infrared phases or transitions that would otherwise appear allowed.
  • These symmetries provide additional selection rules for correlation functions involving defects.
  • Categorical symmetries organize fusion rules and modular data in two-dimensional theories more systematically.
  • Applications appear in classifying gapped phases and in constraining effective descriptions of strongly coupled systems.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same generalized-symmetry language may eventually classify anomalies in gravitational theories or in holographic duals.
  • Lattice simulations could test whether the predicted anomaly cancellations survive discretization.
  • Connections to topological order in condensed matter suggest a route to experimental probes via anyonic defects.

Load-bearing premise

The reviewed literature accurately identifies the generalized symmetries and correctly derives their anomaly implications without overlooked inconsistencies in the underlying constructions.

What would settle it

Discovery of a concrete dynamical model or lattice realization where a claimed anomaly from a defect or categorical symmetry fails to constrain the physics as predicted.

read the original abstract

Symmetry plays a central role in quantum field theory. Recent developments include symmetries that act on defects and other subsystems, and symmetries that are categorical rather than group-like. These generalized notions of symmetry allow for new kinds of anomalies that constrain dynamics. We review some transformative instances of these novel aspects of symmetry in quantum field theory, and give a broad-brush overview of recent applications.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 2 minor

Summary. The manuscript is a Snowmass white paper reviewing generalized symmetries in quantum field theory, with emphasis on symmetries that act on defects and other subsystems as well as categorical (rather than group-like) symmetries. It argues that these notions permit new classes of anomalies that impose constraints on QFT dynamics and provides a broad overview of recent applications and transformative examples drawn from the literature.

Significance. If the summaries of the cited constructions and anomaly derivations are faithful, the paper is a useful consolidation of an active research area. It collects results on defect-acting and categorical symmetries and their anomaly implications, which can help the community identify constraints on possible QFTs. The review format appropriately aggregates prior work rather than introducing new derivations.

minor comments (2)
  1. The abstract and introduction would benefit from one or two concrete, referenced examples of how a generalized symmetry produces a previously inaccessible anomaly constraint, to make the high-level claims more immediately accessible to readers outside the subfield.
  2. A short table or bullet list summarizing the main classes of generalized symmetries, the type of anomaly each generates, and key references would improve navigability of the broad-brush overview.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of the manuscript and for recommending acceptance. We appreciate the recognition that the review consolidates recent results on generalized symmetries and their anomaly implications in a useful way for the community.

Circularity Check

0 steps flagged

No significant circularity in this review white paper

full rationale

This Snowmass White Paper is a broad review summarizing existing literature on generalized symmetries (including those acting on defects and categorical symmetries) and their anomaly implications for QFT dynamics. It does not introduce new derivations, first-principles calculations, or predictions that could reduce to the paper's own inputs by construction. The central claims depend on the faithful representation of prior results from the cited literature, which constitutes standard review practice rather than internal circularity. No self-definitional steps, fitted inputs presented as predictions, or load-bearing self-citation chains are present in the paper's structure. Any author self-citations are incidental to the review format and do not form the load-bearing justification for new claims.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

This review rests on the standard framework of quantum field theory and the accuracy of the cited recent literature rather than introducing new fitted parameters or entities.

axioms (1)
  • standard math Standard axioms and consistency conditions of quantum field theory
    The discussion of symmetries and anomalies presupposes the usual QFT setup.

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discussion (0)

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Lean theorems connected to this paper

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    echoes

    ECHOES: this paper passage has the same mathematical shape or conceptual pattern as the Recognition theorem, but is not a direct formal dependency.

    Recent developments include symmetries that act on defects and other subsystems, and symmetries that are categorical rather than group-like. These generalized notions of symmetry allow for new kinds of anomalies that constrain dynamics.

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Forward citations

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Reference graph

Works this paper leans on

300 extracted references · 300 canonical work pages · cited by 20 Pith papers · 115 internal anchors

  1. [1]

    Invariant Variation Problems

    E. Noether, Invariant Variation Problems, Gott. Nachr. 1918 (1918) 235–257, [physics/0503066]

    work page internal anchor Pith review Pith/arXiv arXiv 1918

  2. [2]

    E. Noether's Discovery of the Deep Connection Between Symmetries and Conservation Laws

    N. Byers, E. Noether’s discovery of the deep connection between symmetries and conservation laws, in Symposium on the Heritage of Emmy Noether, 7, 1998. physics/9807044

    work page internal anchor Pith review Pith/arXiv arXiv 1998

  3. [3]

    L. D. Landau, On the theory of phase transitions, Zh. Eksp. Teor. Fiz.7 (1937) 19–32

    work page 1937

  4. [4]

    McGreevy, Generalized Symmetries in Condensed Matter, arXiv:2204.03045

    J. McGreevy, Generalized Symmetries in Condensed Matter, arXiv:2204.03045

    work page arXiv

  5. [5]

    Elitzur, Impossibility of Spontaneously Breaking Local Symmetries, Phys

    S. Elitzur, Impossibility of Spontaneously Breaking Local Symmetries, Phys. Rev. D 12 (1975) 3978–3982

    work page 1975

  6. [6]

    S. L. Adler, Axial vector vertex in spinor electrodynamics, Phys. Rev. 177 (1969) 2426–2438

    work page 1969

  7. [7]

    J. S. Bell and R. Jackiw, A PCAC puzzle: π0→ γγ in the σ model, Nuovo Cim. A 60 (1969) 47–61

    work page 1969

  8. [8]

    Y . Choi, H. T. Lam, and S.-H. Shao,Non-invertible Global Symmetries in the Standard Model, arXiv:2205.05086

    work page arXiv

  9. [9]

    C ´ordova and K

    C. C ´ordova and K. Ohmori, Non-Invertible Chiral Symmetry and Exponential Hierarchies, arXiv:2205.06243

    work page arXiv

  10. [10]

    ’t Hooft, How Instantons Solve the U(1) Problem, Phys

    G. ’t Hooft, How Instantons Solve the U(1) Problem, Phys. Rept. 142 (1986) 357–387

    work page 1986

  11. [11]

    Coleman, Aspects of Symmetry: Selected Erice Lectures

    S. Coleman, Aspects of Symmetry: Selected Erice Lectures. Cambridge University Press, Cambridge, U.K., 1985

    work page 1985

  12. [12]

    ’t Hooft, Naturalness, chiral symmetry, and spontaneous chiral symmetry breaking, NATO Sci

    G. ’t Hooft, Naturalness, chiral symmetry, and spontaneous chiral symmetry breaking, NATO Sci. Ser. B 59 (1980) 135–157

    work page 1980

  13. [13]

    Harlow, B

    D. Harlow, B. Heidenreich, M. Reece, and T. Rudelius, The Weak Gravity Conjecture: A Review, arXiv:2201.08380

    work page arXiv

  14. [14]

    A. B. Zamolodchikov and A. B. Zamolodchikov, Factorized s Matrices in Two-Dimensions as the Exact Solutions of Certain Relativistic Quantum Field Models, Annals Phys. 120 (1979) 253–291

    work page 1979

  15. [15]

    S. R. Coleman and J. Mandula, All Possible Symmetries of the S Matrix, Phys. Rev. 159 (1967) 1251–1256. 10

    work page 1967

  16. [16]

    Constraining conformal field theories with a higher spin symmetry

    J. Maldacena and A. Zhiboedov, Constraining Conformal Field Theories with A Higher Spin Symmetry, J. Phys. A 46 (2013) 214011, [arXiv:1112.1016]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  17. [17]

    R. Haag, J. T. Lopuszanski, and M. Sohnius, All Possible Generators of Supersymmetries of the s Matrix, Nucl. Phys. B 88 (1975) 257

    work page 1975

  18. [18]

    Nahm, Supersymmetries and their Representations, Nucl

    W. Nahm, Supersymmetries and their Representations, Nucl. Phys. B 135 (1978) 149

    work page 1978

  19. [19]

    P. C. Argyres, J. J. Heckman, K. Intriligator, and M. Martone, Snowmass White Paper on SCFTs, arXiv:2202.07683

    work page arXiv

  20. [20]

    Poland and D

    D. Poland and D. Simmons-Duffin, Snowmass White Paper: The Numerical Conformal Bootstrap, in 2022 Snowmass Summer Study, 3, 2022. arXiv:2203.08117

    work page arXiv 2022

  21. [21]

    Generalized Global Symmetries

    D. Gaiotto, A. Kapustin, N. Seiberg, and B. Willett, Generalized Global Symmetries, JHEP 02 (2015) 172, [arXiv:1412.5148]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  22. [22]

    Symmetries in quantum field theory and quantum gravity

    D. Harlow and H. Ooguri, Symmetries in quantum field theory and quantum gravity, Commun. Math. Phys. 383 (2021), no. 3 1669–1804, [arXiv:1810.05338]

    work page internal anchor Pith review Pith/arXiv arXiv 2021

  23. [23]

    T. T. Dumitrescu and N. Seiberg, Supercurrents and Brane Currents in Diverse Dimensions, JHEP 07 (2011) 095, [arXiv:1106.0031]

    work page arXiv 2011

  24. [24]

    Coupling a QFT to a TQFT and Duality

    A. Kapustin and N. Seiberg, Coupling a QFT to a TQFT and Duality, JHEP 04 (2014) 001, [arXiv:1401.0740]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  25. [25]

    Notes on generalized global symmetries in QFT

    E. Sharpe, Notes on generalized global symmetries in QFT, Fortsch. Phys. 63 (2015) 659–682, [arXiv:1508.04770]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  26. [26]

    Theta, Time Reversal, and Temperature

    D. Gaiotto, A. Kapustin, Z. Komargodski, and N. Seiberg, Theta, Time Reversal, and Temperature, JHEP 05 (2017) 091, [arXiv:1703.00501]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  27. [27]

    D. M. Hofman and N. Iqbal, Generalized global symmetries and holography, SciPost Phys. 4 (2018), no. 1 005, [arXiv:1707.08577]

    work page arXiv 2018

  28. [28]

    P.-S. Hsin, H. T. Lam, and N. Seiberg, Comments on One-Form Global Symmetries and Their Gauging in 3d and 4d, SciPost Phys. 6 (2019), no. 3 039, [arXiv:1812.04716]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  29. [29]

    Hsin and S.-H

    P.-S. Hsin and S.-H. Shao, Lorentz Symmetry Fractionalization and Dualities in (2+1)d, SciPost Phys. 8 (2020) 018, [arXiv:1909.07383]

    work page arXiv 2020

  30. [30]

    D. R. Morrison, S. Schafer-Nameki, and B. Willett, Higher-Form Symmetries in 5d, JHEP 09 (2020) 024, [arXiv:2005.12296]

    work page arXiv 2020

  31. [31]

    Del Zotto, I

    M. Del Zotto, I. n. Garc ´ıa Etxebarria, and S. S. Hosseini, Higher form symmetries of Argyres-Douglas theories, JHEP 10 (2020) 056, [arXiv:2007.15603]

    work page arXiv 2020

  32. [32]

    Gukov, P.-S

    S. Gukov, P.-S. Hsin, and D. Pei, Generalized global symmetries of T [M] theories. Part I, JHEP 04 (2021) 232, [arXiv:2010.15890]

    work page arXiv 2021

  33. [33]

    A. M. Polyakov, Quark Confinement and Topology of Gauge Groups, Nucl. Phys. B 120 (1977) 429–458. 11

    work page 1977

  34. [34]

    Affleck, J

    I. Affleck, J. A. Harvey, and E. Witten, Instantons and (Super)Symmetry Breaking in (2+1)-Dimensions, Nucl. Phys. B 206 (1982) 413–439

    work page 1982

  35. [35]

    New Look at QED$_4$: the Photon as a Goldstone Boson and the Topological Interpretation of Electric Charge

    A. Kovner and B. Rosenstein, New look at QED in four-dimensions: The Photon as a Goldstone boson and the topological interpretation of electric charge, Phys. Rev. D 49 (1994) 5571–5581, [hep-th/9210154]

    work page internal anchor Pith review Pith/arXiv arXiv 1994

  36. [36]

    D. M. Hofman and N. Iqbal, Goldstone modes and photonization for higher form symmetries, SciPost Phys. 6 (2019), no. 1 006, [arXiv:1802.09512]

    work page arXiv 2019

  37. [37]

    Higher-form symmetries and spontaneous symmetry breaking

    E. Lake, Higher-form symmetries and spontaneous symmetry breaking, arXiv:1802.07747

    work page internal anchor Pith review Pith/arXiv arXiv

  38. [38]

    A. M. Polyakov, Thermal Properties of Gauge Fields and Quark Liberation, Phys. Lett. B 72 (1978) 477–480

    work page 1978

  39. [39]

    Bhardwaj and Y

    L. Bhardwaj and Y . Tachikawa,On finite symmetries and their gauging in two dimensions, JHEP 03 (2018) 189, [arXiv:1704.02330]

    work page arXiv 2018

  40. [40]

    Tachikawa,On gauging finite subgroups, SciPost Phys

    Y . Tachikawa,On gauging finite subgroups, SciPost Phys. 8 (2020), no. 1 015, [arXiv:1712.09542]

    work page arXiv 2020

  41. [41]

    Roumpedakis, S

    K. Roumpedakis, S. Seifnashri, and S.-H. Shao, Higher Gauging and Non-invertible Condensation Defects, arXiv:2204.02407

    work page arXiv

  42. [42]

    Braided fusion categories, gravitational anomalies, and the mathematical framework for topological orders in any dimensions

    L. Kong and X.-G. Wen, Braided fusion categories, gravitational anomalies, and the mathematical framework for topological orders in any dimensions, arXiv:1405.5858

    work page internal anchor Pith review Pith/arXiv arXiv

  43. [43]

    D. V . Else and C. Nayak,Cheshire charge in (3+1)-dimensional topological phases, Phys. Rev. B 96 (2017), no. 4 045136, [arXiv:1702.02148]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  44. [44]

    Gaiotto and T

    D. Gaiotto and T. Johnson-Freyd, Condensations in higher categories, arXiv:1905.09566

    work page arXiv 1905

  45. [45]

    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. 2 (2020), no. 4 043086, [arXiv:2005.14178]

    work page arXiv 2020

  46. [46]

    Johnson-Freyd, (3+1)D topological orders with only a Z2-charged particle, arXiv:2011.11165

    T. Johnson-Freyd, (3+1)D topological orders with only a Z2-charged particle, arXiv:2011.11165

    work page arXiv 2011

  47. [47]

    Y . Choi, C. C´ordova, P.-S. Hsin, H. T. Lam, and S.-H. Shao,Non-invertible Condensation, Duality, and Triality Defects in 3+1 Dimensions, arXiv:2204.09025

    work page arXiv

  48. [48]

    J. C. Baez and A. D. Lauda, Higher-dimensional algebra v: 2-groups, Version 3 (2004) 423–491

    work page 2004

  49. [49]

    Higher Gauge Theory: 2-Connections on 2-Bundles

    J. Baez and U. Schreiber, Higher gauge theory: 2-connections on 2-bundles, hep-th/0412325

    work page internal anchor Pith review Pith/arXiv arXiv

  50. [50]

    Connections on non-abelian Gerbes and their Holonomy

    U. Schreiber and K. Waldorf, Connections on non-Abelian Gerbes and their Holonomy, Theory Appl. Categ. 28 (2013) 476–540, [arXiv:0808.1923]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  51. [51]

    Topological Field Theory on a Lattice, Discrete Theta-Angles and Confinement

    A. Kapustin and R. Thorngren, Topological Field Theory on a Lattice, Discrete Theta-Angles and Confinement, Adv. Theor. Math. Phys.18 (2014), no. 5 1233–1247, [arXiv:1308.2926]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  52. [52]

    Higher symmetry and gapped phases of gauge theories

    A. Kapustin and R. Thorngren, Higher symmetry and gapped phases of gauge theories, arXiv:1309.4721. 12

    work page internal anchor Pith review Pith/arXiv arXiv

  53. [53]

    Topological Quantum Field Theory, Nonlocal Operators, and Gapped Phases of Gauge Theories

    S. Gukov and A. Kapustin, Topological Quantum Field Theory, Nonlocal Operators, and Gapped Phases of Gauge Theories, arXiv:1307.4793

    work page internal anchor Pith review Pith/arXiv arXiv

  54. [54]

    Higher SPT's and a generalization of anomaly in-flow

    R. Thorngren and C. von Keyserlingk, Higher SPT’s and a generalization of anomaly in-flow, arXiv:1511.02929

    work page internal anchor Pith review Pith/arXiv arXiv

  55. [55]

    Gaiotto and T

    D. Gaiotto and T. Johnson-Freyd, Symmetry Protected Topological phases and Generalized Cohomology, JHEP 05 (2019) 007, [arXiv:1712.07950]

    work page arXiv 2019

  56. [56]

    State sum constructions of spin-TFTs and string net constructions of fermionic phases of matter

    L. Bhardwaj, D. Gaiotto, and A. Kapustin, State sum constructions of spin-TFTs and string net constructions of fermionic phases of matter, JHEP 04 (2017) 096, [arXiv:1605.01640]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  57. [57]

    From gauge to higher gauge models of topological phases

    C. Delcamp and A. Tiwari, From gauge to higher gauge models of topological phases, JHEP 10 (2018) 049, [arXiv:1802.10104]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  58. [58]

    Exploring 2-Group Global Symmetries

    C. C ´ordova, T. T. Dumitrescu, and K. Intriligator,Exploring 2-Group Global Symmetries, JHEP 02 (2019) 184, [arXiv:1802.04790]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  59. [59]

    On 2-Group Global Symmetries and Their Anomalies

    F. Benini, C. C ´ordova, and P.-S. Hsin,On 2-Group Global Symmetries and their Anomalies, JHEP 03 (2019) 118, [arXiv:1803.09336]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  60. [60]

    Tanizaki and M

    Y . Tanizaki and M. ¨Unsal, Modified instanton sum in QCD and higher-groups, JHEP 03 (2020) 123, [arXiv:1912.01033]

    work page arXiv 2020

  61. [61]

    I. Bah, F. Bonetti, and R. Minasian, Discrete and higher-form symmetries in SCFTs from wrapped M5-branes, JHEP 03 (2021) 196, [arXiv:2007.15003]

    work page arXiv 2021

  62. [62]

    Bhardwaj and S

    L. Bhardwaj and S. Sch ¨afer-Nameki, Higher-form symmetries of 6d and 5d theories, JHEP 02 (2021) 159, [arXiv:2008.09600]

    work page arXiv 2021

  63. [63]

    Hsin and H

    P.-S. Hsin and H. T. Lam, Discrete theta angles, symmetries and anomalies, SciPost Phys. 10 (2021), no. 2 032, [arXiv:2007.05915]

    work page arXiv 2021

  64. [64]

    C ´ordova, T

    C. C ´ordova, T. T. Dumitrescu, and K. Intriligator,2-Group Global Symmetries and Anomalies in Six-Dimensional Quantum Field Theories, JHEP 04 (2021) 252, [arXiv:2009.00138]

    work page arXiv 2021

  65. [65]

    Del Zotto and K

    M. Del Zotto and K. Ohmori, 2-Group Symmetries of 6D Little String Theories and T-Duality, Annales Henri Poincare 22 (2021), no. 7 2451–2474, [arXiv:2009.03489]

    work page arXiv 2021

  66. [66]

    Iqbal and N

    N. Iqbal and N. Poovuttikul, 2-group global symmetries, hydrodynamics and holography, arXiv:2010.00320

    work page arXiv 2010

  67. [67]

    Hidaka, M

    Y . Hidaka, M. Nitta, and R. Yokokura,Global 3-group symmetry and ’t Hooft anomalies in axion electrodynamics, JHEP 01 (2021) 173, [arXiv:2009.14368]

    work page arXiv 2021

  68. [68]

    T. D. Brennan and C. C ´ordova, Axions, higher-groups, and emergent symmetry, JHEP 02 (2022) 145, [arXiv:2011.09600]

    work page arXiv 2022

  69. [69]

    Y . Lee, K. Ohmori, and Y . Tachikawa,Matching higher symmetries across Intriligator-Seiberg duality, JHEP 10 (2021) 114, [arXiv:2108.05369]

    work page arXiv 2021

  70. [70]

    Apruzzi, L

    F. Apruzzi, L. Bhardwaj, J. Oh, and S. Schafer-Nameki, The Global Form of Flavor Symmetries and 2-Group Symmetries in 5d SCFTs, arXiv:2105.08724. 13

    work page arXiv

  71. [71]

    Apruzzi, F

    F. Apruzzi, F. Bonetti, I. n. G. Etxebarria, S. S. Hosseini, and S. Schafer-Nameki, Symmetry TFTs from String Theory, arXiv:2112.02092

    work page arXiv

  72. [72]

    Bhardwaj, 2-Group Symmetries in Class S, arXiv:2107.06816

    L. Bhardwaj, 2-Group Symmetries in Class S, arXiv:2107.06816

    work page arXiv

  73. [73]

    Apruzzi, L

    F. Apruzzi, L. Bhardwaj, D. S. W. Gould, and S. Schafer-Nameki, 2-Group Symmetries and their Classification in 6d, arXiv:2110.14647

    work page arXiv

  74. [74]

    P.-S. Hsin, W. Ji, and C.-M. Jian, Exotic Invertible Phases with Higher-Group Symmetries, arXiv:2105.09454

    work page arXiv

  75. [75]

    Del Zotto, I

    M. Del Zotto, I. n. G. Etxebarria, and S. Schafer-Nameki, 2-Group Symmetries and M-Theory, arXiv:2203.10097

    work page arXiv

  76. [76]

    Cveti ˇc, J

    M. Cveti ˇc, J. J. Heckman, M. H¨ubner, and E. Torres, 0-Form, 1-Form and 2-Group Symmetries via Cutting and Gluing of Orbifolds, arXiv:2203.10102

    work page arXiv

  77. [77]

    Sharpe, An introduction to decomposition, arXiv:2204.09117

    E. Sharpe, An introduction to decomposition, arXiv:2204.09117

    work page arXiv

  78. [78]

    Pantev, D

    T. Pantev, D. Robbins, E. Sharpe, and T. Vandermeulen, Orbifolds by 2-groups and decomposition, arXiv:2204.13708

    work page arXiv

  79. [79]

    Del Zotto, J

    M. Del Zotto, J. J. Heckman, S. N. Meynet, R. Moscrop, and H. Y . Zhang,Higher Symmetries of 5d Orbifold SCFTs, arXiv:2201.08372

    work page arXiv

  80. [80]

    Del Zotto and I

    M. Del Zotto and I. n. G. Etxebarria, Global Structures from the Infrared, arXiv:2204.06495

    work page arXiv

Showing first 80 references.