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arxiv: 2604.11877 · v1 · submitted 2026-04-13 · ✦ hep-th

Generalized symmetries and emergence in axion effective field theories

Dan Sehayek , Nathaniel Craig This is my paper

Pith reviewed 2026-05-10 15:30 UTC · model grok-4.3

classification ✦ hep-th
keywords axion effective field theoryhigher-group symmetriesnon-invertible symmetriesanomaly inflowtopological defectsemergence constraintsultraviolet completiongauge bosons
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0 comments X

The pith

In axion effective field theories, higher-group and non-invertible symmetries impose parametric constraints on infrared emergence scales that are saturated by anomaly inflow onto topological defects.

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

The paper analyzes how higher symmetries constrain the energy scales at which different symmetries can appear in the infrared limit of axion models coupled to gauge bosons. It shows that these constraints are always met through anomaly inflow from topological defects, regardless of the specific ultraviolet details. In contrast, when the ultraviolet completion is perturbative, the constraints become unnecessary because the relevant scales are parametrically separated. This distinction offers a general way to connect infrared axion phenomenology to possible ultraviolet physics.

Core claim

Higher-group and non-invertible symmetries in axion effective field theories coupled to abelian and non-abelian gauge bosons, with or without charged matter, impose parametric constraints on the scales of infrared symmetry emergence; these constraints are universally saturated by anomaly inflow onto topological defects, while in perturbative ultraviolet completions they are supererogatory owing to the parametric separation of scales.

What carries the argument

Anomaly inflow onto topological defects, which saturates the emergence constraints from higher-group and non-invertible symmetries.

If this is right

  • The constraints provide a model-independent guide to which ultraviolet completions are compatible with a given infrared axion effective field theory.
  • Non-perturbative effects must be included to saturate emergence constraints in non-perturbative ultraviolet scenarios.
  • Perturbative ultraviolet completions automatically evade the constraints due to scale separation between the axion and gauge sectors.
  • The analysis applies equally to abelian and non-abelian gauge groups and to theories with or without charged matter fields.

Where Pith is reading between the lines

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

  • Axion models intended for dark matter or inflation may need to incorporate non-perturbative ultraviolet sectors if they exhibit specific infrared symmetry emergence patterns.
  • The universal saturation by defects suggests that lattice or string-theoretic embeddings of axions could be tested by checking whether their symmetry scales match the predicted bounds.
  • Scale separation in perturbative cases might relax constraints on low-energy axion couplings without requiring additional symmetry protection mechanisms.

Load-bearing premise

That higher-group and non-invertible symmetries are realized in the axion effective field theories in the assumed manner, so that infrared emergence can be parametrically constrained independently of specific ultraviolet dynamics.

What would settle it

A concrete perturbative ultraviolet completion of an axion effective field theory in which an infrared symmetry emerges at a scale that violates the predicted parametric bound while no topological defects are present to provide anomaly inflow.

read the original abstract

We study the phenomenological consequences of higher symmetry structures in axion effective field theories. Higher-group and non-invertible symmetries impose parametric constraints on the energy scales at which different symmetries can emerge in the infrared, providing a guide to the ultraviolet physics. We clarify and analyze these emergence constraints in axion EFTs coupled to abelian and non-abelian gauge bosons, with and without charged matter. We show that emergence constraints are universally saturated by anomaly inflow onto topological defects, while in perturbative UV completions they are supererogatory owing to the parametric separation of scales.

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 paper examines higher-group and non-invertible symmetries in axion effective field theories coupled to abelian or non-abelian gauge fields, with or without charged matter. It argues that these symmetries impose parametric constraints on the infrared emergence scales of different symmetries, which are universally saturated by anomaly inflow onto topological defects; in perturbative UV completions the constraints are automatically satisfied due to parametric scale separation.

Significance. If the central claims hold, the work supplies a symmetry-based organizing principle for axion EFTs that links IR generalized symmetries to UV completion scales without requiring explicit model building. This could guide model-building in axion phenomenology and string-inspired scenarios by clarifying when emergence constraints are automatically satisfied versus when they must be imposed by hand.

minor comments (2)
  1. [Abstract] The abstract states that emergence constraints are 'universally saturated' by anomaly inflow, but the manuscript should include an explicit statement of the class of axion EFTs for which this saturation is proven (e.g., whether it requires the absence of certain higher-form currents or specific anomaly coefficients).
  2. [Introduction] Notation for the higher-group structure constants and the non-invertible symmetry defects should be introduced with a short table or diagram in the introductory section to aid readers unfamiliar with the generalized-symmetry literature.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of our manuscript on generalized symmetries and emergence in axion EFTs, including the recommendation for minor revision. No specific major comments were raised in the report, so we have no individual points to address point-by-point. We will incorporate any minor editorial suggestions in the revised version.

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained in symmetry structure

full rationale

The paper derives emergence constraints on axion EFTs from the structure of higher-group and non-invertible symmetries, showing they are saturated by anomaly inflow onto topological defects and supererogatory in perturbative UV completions due to scale separation. This follows directly from the assumed realization of the symmetries in abelian/non-abelian cases with/without matter, without any parameter fitting, self-definition of scales in terms of themselves, or load-bearing self-citations that reduce the central claim to unverified inputs. The analysis is presented as a universal consequence of the symmetry and anomaly framework rather than a renaming or ansatz imported circularly, rendering the derivation self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The analysis rests on the existence and consistency of higher-group and non-invertible symmetries in the EFT, standard anomaly inflow mechanisms, and the validity of the effective field theory description below certain scales. No explicit free parameters or invented entities are stated in the abstract.

axioms (2)
  • domain assumption Higher-group and non-invertible symmetries are well-defined and impose parametric constraints on symmetry emergence in the infrared.
    Invoked as the starting point for analyzing phenomenological consequences in axion EFTs.
  • domain assumption Anomaly inflow onto topological defects saturates the emergence constraints.
    Used to establish the universal saturation result.

pith-pipeline@v0.9.0 · 5377 in / 1290 out tokens · 34956 ms · 2026-05-10T15:30:33.168996+00:00 · methodology

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Reference graph

Works this paper leans on

137 extracted references · 137 canonical work pages

  1. [1]

    Baez and U

    J. Baez and U. Schreiber,Higher gauge theory: 2-connections on 2-bundles, 2004

    work page 2004

  2. [2]

    Baez and J

    J.C. Baez and J. Huerta,An invitation to higher gauge theory,General Relativity and Gravitation43(2011) 2335

    work page 2011

  3. [3]

    Gukov and A

    S. Gukov and A. Kapustin,Topological quantum field theory, nonlocal operators, and gapped phases of gauge theories, 2013

    work page 2013

  4. [4]

    Gaiotto, A

    D. Gaiotto, A. Kapustin, N. Seiberg and B. Willett,Generalized global symmetries,Journal of High Energy Physics2015(2015) 172

    work page 2015

  5. [5]

    Kapustin and R

    A. Kapustin and R. Thorngren,Higher symmetry and gapped phases of gauge theories, in Algebra, Geometry, and Physics in the 21st Century: Kontsevich Festschrift, D. Auroux, L. Katzarkov, T. Pantev, Y. Soibelman and Y. Tschinkel, eds., (Cham), pp. 177–202, Springer International Publishing (2017), DOI

    work page 2017

  6. [6]

    C´ ordova, T.T

    C. C´ ordova, T.T. Dumitrescu and K. Intriligator,Exploring 2-group global symmetries, Journal of High Energy Physics2019(2019) 184

    work page 2019

  7. [7]

    Tachikawa,On gauging finite subgroups,SciPost Phys.8(2020) 015

    Y. Tachikawa,On gauging finite subgroups,SciPost Phys.8(2020) 015

    work page 2020

  8. [8]

    C´ ordova, T.T

    C. C´ ordova, T.T. Dumitrescu and K. Intriligator,2-group global symmetries and anomalies in six-dimensional quantum field theories,Journal of High Energy Physics2021(2021) 252

    work page 2021

  9. [9]

    Brennan and C

    T.D. Brennan and C. C´ ordova,Axions, higher-groups, and emergent symmetry,Journal of High Energy Physics2022(2022) 145

    work page 2022

  10. [10]

    Universal non-invertible sym- metries,

    L. Bhardwaj, S. Sch¨ afer-Nameki and J. Wu,Universal non-invertible symmetries, Fortschritte der Physik70(2022) 2200143 [https://onlinelibrary.wiley.com/doi/pdf/10.1002/prop.202200143]

    work page doi:10.1002/prop.202200143 2022

  11. [11]

    Choi, H.T

    Y. Choi, H.T. Lam and S.-H. Shao,Noninvertible global symmetries in the standard model, Phys. Rev. Lett.129(2022) 161601

    work page 2022

  12. [12]

    Bhardwaj, L.E

    L. Bhardwaj, L.E. Bottini, S. Sch¨ afer-Nameki and A. Tiwari,Non-invertible higher-categorical symmetries,SciPost Phys.14(2023) 007

    work page 2023

  13. [13]

    C´ ordova and K

    C. C´ ordova and K. Ohmori,Noninvertible chiral symmetry and exponential hierarchies, Phys. Rev. X13(2023) 011034

    work page 2023

  14. [14]

    Bartsch, M

    T. Bartsch, M. Bullimore and A. Grigoletto,Higher representations for extended operators, 2023

    work page 2023

  15. [15]

    Bartsch, M

    T. Bartsch, M. Bullimore and A. Grigoletto,Representation theory for categorical symmetries, 2023

    work page 2023

  16. [16]

    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,Communications in Mathematical Physics 402(2023) 489

    work page 2023

  17. [17]

    Choi, H.T

    Y. Choi, H.T. Lam and S.-H. Shao,Non-invertible gauss law and axions,Journal of High Energy Physics2023(2023) 67

    work page 2023

  18. [18]

    Bhardwaj, S

    L. Bhardwaj, S. Sch¨ afer-Nameki and A. Tiwari,Unifying constructions of non-invertible symmetries,SciPost Phys.15(2023) 122

    work page 2023

  19. [19]

    Bhardwaj, L.E

    L. Bhardwaj, L.E. Bottini, S. Sch¨ afer-Nameki and A. Tiwari,Non-invertible symmetry webs,SciPost Phys.15(2023) 160. – 34 –

    work page 2023

  20. [20]

    Bhardwaj and S

    L. Bhardwaj and S. Sch¨ afer-Nameki,Generalized charges, part I: Invertible symmetries and higher representations,SciPost Phys.16(2024) 093

    work page 2024

  21. [21]

    Bartsch, M

    T. Bartsch, M. Bullimore, A.E.V. Ferrari and J. Pearson,Non-invertible symmetries and higher representation theory I,SciPost Phys.17(2024) 015

    work page 2024

  22. [22]

    Bartsch, M

    T. Bartsch, M. Bullimore, A.E.V. Ferrari and J. Pearson,Non-invertible symmetries and higher representation theory II,SciPost Phys.17(2024) 067

    work page 2024

  23. [23]

    Bhardwaj and S

    L. Bhardwaj and S. Sch¨ afer-Nameki,Generalized charges, part II: Non-invertible symmetries and the symmetry TFT,SciPost Phys.19(2025) 098

    work page 2025

  24. [24]

    Cordova, T.T

    C. Cordova, T.T. Dumitrescu, K. Intriligator and S.-H. Shao,Snowmass white paper: Generalized symmetries in quantum field theory and beyond, 2022

    work page 2022

  25. [25]

    Brennan and S

    T.D. Brennan and S. Hong,Introduction to generalized global symmetries in qft and particle physics, 2023

    work page 2023

  26. [26]

    Bhardwaj, L.E

    L. Bhardwaj, L.E. Bottini, L. Fraser-Taliente, L. Gladden, D.S.W. Gould, A. Platschorre et al.,Lectures on generalized symmetries, 2023

    work page 2023

  27. [27]

    McGreevy,Generalized symmetries in condensed matter,Annual Review of Condensed Matter Physics14(2023) 57

    J. McGreevy,Generalized symmetries in condensed matter,Annual Review of Condensed Matter Physics14(2023) 57

    work page 2023

  28. [28]

    Luo, Q.-R

    R. Luo, Q.-R. Wang and Y.-N. Wang,Lecture notes on generalized symmetries and applications,Physics Reports1065(2024) 1

    work page 2024

  29. [29]

    Schafer-Nameki,Ictp lectures on (non-)invertible generalized symmetries, 2023

    S. Schafer-Nameki,Ictp lectures on (non-)invertible generalized symmetries, 2023

    work page 2023

  30. [30]

    ’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. B59(1980) 135

    work page 1980

  31. [31]

    Tong,Line operators in the standard model,Journal of High Energy Physics2017 (2017) 104

    D. Tong,Line operators in the standard model,Journal of High Energy Physics2017 (2017) 104

    work page 2017

  32. [32]

    Gaiotto, Z

    D. Gaiotto, Z. Komargodski and N. Seiberg,Time-reversal breaking in qcd4, walls, and dualities in 2 + 1 dimensions,Journal of High Energy Physics2018(2018) 110

    work page 2018

  33. [33]

    Hidaka, M

    Y. Hidaka, M. Nitta and R. Yokokura,Higher-form symmetries and 3-group in axion electrodynamics,Physics Letters B808(2020) 135672

    work page 2020

  34. [34]

    Tanizaki and M

    Y. Tanizaki and M. ¨Unsal,Modified instanton sum in qcd and higher-groups,Journal of High Energy Physics2020(2020) 123

    work page 2020

  35. [35]

    Hidaka, M

    Y. Hidaka, M. Nitta and R. Yokokura,Global 3-group symmetry and ’t hooft anomalies in axion electrodynamics,Journal of High Energy Physics2021(2021) 173

    work page 2021

  36. [36]

    Yokokura,Non-invertible symmetries in axion electrodynamics, 2022

    R. Yokokura,Non-invertible symmetries in axion electrodynamics, 2022

    work page 2022

  37. [37]

    Cordova and S

    C. Cordova and S. Koren,Higher flavor symmetries in the standard model, 2022

    work page 2022

  38. [38]

    Reece,Axion-gauge coupling quantization with a twist,Journal of High Energy Physics 2023(2023) 116

    M. Reece,Axion-gauge coupling quantization with a twist,Journal of High Energy Physics 2023(2023) 116

    work page 2023

  39. [39]

    Y. Choi, M. Forslund, H.T. Lam and S.-H. Shao,Quantization of axion-gauge couplings and noninvertible higher symmetries,Physical Review Letters132(2024) 121601 [2309.03937]

    work page arXiv 2024

  40. [40]

    C´ ordova, S

    C. C´ ordova, S. Hong and L.-T. Wang,Axion domain walls, small instantons, and non-invertible symmetry breaking,Journal of High Energy Physics2024(2024) 325. – 35 –

    work page 2024

  41. [41]

    Cheung, M

    C. Cheung, M. Derda, J.-H. Kim, V. Nevoa, I. Rothstein and N. Shah,Generalized symmetry in dynamical gravity, 2024

    work page 2024

  42. [42]

    Cordova, S

    C. C´ ordova, S. Hong, S. Koren and K. Ohmori,Neutrino masses from generalized symmetry breaking,Physical Review X14(2024) 031033 [2211.07639]

    work page arXiv 2024

  43. [43]

    Craig and M

    N. Craig and M. Kongsore,High-quality axions from higher-form symmetries in extra dimensions, 2024

    work page 2024

  44. [44]

    Putrov and J

    P. Putrov and J. Wang,Categorical symmetry of the standard model from gravitational anomaly,Physical Review D110(2024) 125028 [2302.14862]

    work page arXiv 2024

  45. [45]

    Koren and A

    S. Koren and A. Martin,Fractionally charged particles at the energy frontier: The SM gauge group and one-form global symmetry,SciPost Phys.18(2025) 004 [2406.17850]

    work page arXiv 2025

  46. [46]

    Noninvertible Peccei-Quinn Symmetry and the Massless Quark Solution to the Strong CP Problem,

    C. C´ ordova, S. Hong and S. Koren,Noninvertible peccei-quinn symmetry and the massless quark solution to the strong cp problem,Physical Review X15(2025) 031011 [2402.12453]

    work page arXiv 2025

  47. [47]

    Generalised Symmetries in Particle Physics,

    J. Davighi,Generalized symmetries in particle physics,PoSDISCRETE2024(2025) 076 [2504.05960]

    work page arXiv 2025

  48. [48]

    Aharony, N

    O. Aharony, N. Seiberg and Y. Tachikawa,Reading between the lines of four-dimensional gauge theories,Journal of High Energy Physics2013(2013) 115

    work page 2013

  49. [49]

    Damia, R

    J.A. Damia, R. Argurio and E. Garcia-Valdecasas,Non-invertible defects in 5d, boundaries and holography,SciPost Phys.14(2023) 067

    work page 2023

  50. [50]

    Damia, R

    J.A. Damia, R. Argurio and L. Tizzano,Continuous generalized symmetries in three dimensions,Journal of High Energy Physics2023(2023) 164

    work page 2023

  51. [51]

    Verlinde,Fusion rules and modular transformations in 2d conformal field theory,Nuclear Physics B300(1988) 360

    E. Verlinde,Fusion rules and modular transformations in 2d conformal field theory,Nuclear Physics B300(1988) 360

    work page 1988

  52. [52]

    Petkova and J.-B

    V. Petkova and J.-B. Zuber,Generalised twisted partition functions,Physics Letters B504 (2001) 157

    work page 2001

  53. [53]

    Fuchs, I

    J. Fuchs, I. Runkel and C. Schweigert,Tft construction of rcft correlators i: partition functions,Nuclear Physics B646(2002) 353

    work page 2002

  54. [54]

    Fr¨ ohlich, J

    J. Fr¨ ohlich, J. Fuchs, I. Runkel and C. Schweigert,Kramers-wannier duality from conformal defects,Phys. Rev. Lett.93(2004) 070601

    work page 2004

  55. [55]

    Fr¨ ohlich, J

    J. Fr¨ ohlich, J. Fuchs, I. Runkel and C. Schweigert,Duality and defects in rational conformal field theory,Nuclear Physics B763(2007) 354

    work page 2007

  56. [56]

    Aasen, R.S.K

    D. Aasen, R.S.K. Mong and P. Fendley,Topological defects on the lattice: I. the ising model, Journal of Physics A: Mathematical and Theoretical49(2016) 354001

    work page 2016

  57. [57]

    Bhardwaj and Y

    L. Bhardwaj and Y. Tachikawa,On finite symmetries and their gauging in two dimensions, Journal of High Energy Physics2018(2018) 189

    work page 2018

  58. [58]

    Chang, Y.-H

    C.-M. Chang, Y.-H. Lin, S.-H. Shao, Y. Wang and X. Yin,Topological defect lines and renormalization group flows in two dimensions,Journal of High Energy Physics2019 (2019) 26

    work page 2019

  59. [59]

    Lin and S.-H

    Y.-H. Lin and S.-H. Shao,Duality defect of the monster cft,Journal of Physics A: Mathematical and Theoretical54(2021) 065201

    work page 2021

  60. [60]

    Thorngren and Y

    R. Thorngren and Y. Wang,Fusion category symmetry. part i. anomaly in-flow and gapped phases,Journal of High Energy Physics2024(2024) 132. – 36 –

    work page 2024

  61. [61]

    Aasen, P

    D. Aasen, P. Fendley and R.S.K. Mong,Topological defects on the lattice: Dualities and degeneracies, 2020

    work page 2020

  62. [62]

    Sharpe,Topological operators, noninvertible symmetries and decomposition,Advances in Theoretical and Mathematical Physics27(2023) 2319–2407

    E. Sharpe,Topological operators, noninvertible symmetries and decomposition,Advances in Theoretical and Mathematical Physics27(2023) 2319–2407

    work page 2023

  63. [63]

    Huang, Y.-H

    T.-C. Huang, Y.-H. Lin and S. Seifnashri,Construction of two-dimensional topological field theories with non-invertible symmetries,Journal of High Energy Physics2021(2021) 28

    work page 2021

  64. [64]

    Chang, J

    C.-M. Chang, J. Chen and F. Xu,Topological defect lines in two dimensional fermionic CFTs,SciPost Phys.15(2023) 216

    work page 2023

  65. [65]

    Y.-H. Lin, M. Okada, S. Seifnashri and Y. Tachikawa,Asymptotic density of states in 2d cfts with non-invertible symmetries,Journal of High Energy Physics2023(2023) 94

    work page 2023

  66. [66]

    Seifnashri and S.-H

    S. Seifnashri and S.-H. Shao,Cluster state as a non-invertible symmetry protected topological phase, 2024

    work page 2024

  67. [67]

    Kramers and G.H

    H.A. Kramers and G.H. Wannier,Statistics of the two-dimensional ferromagnet. part i, Phys. Rev.60(1941) 252

    work page 1941

  68. [68]

    Shankar,Quantum Field Theory and Condensed Matter: An Introduction, Cambridge University Press (2017)

    R. Shankar,Quantum Field Theory and Condensed Matter: An Introduction, Cambridge University Press (2017)

    work page 2017

  69. [69]

    Shao,What’s done cannot be undone: Tasi lectures on non-invertible symmetries, 2024

    S.-H. Shao,What’s done cannot be undone: Tasi lectures on non-invertible symmetries, 2024

    work page 2024

  70. [70]

    Roumpedakis, S

    K. Roumpedakis, S. Seifnashri and S.-H. Shao,Higher gauging and non-invertible condensation defects,Communications in Mathematical Physics401(2023) 3043

    work page 2023

  71. [71]

    Cordova, D.B

    C. Cordova, D.B. Costa and P.-S. Hsin,Non-invertible symmetries in finite group gauge theory, 2024

    work page 2024

  72. [72]

    Y. Choi, Y. Sanghavi, S.-H. Shao and Y. Zheng,Non-invertible and higher-form symmetries in 2+1d lattice gauge theories, 2024

    work page 2024

  73. [73]

    Argurio and R

    R. Argurio and R. Vandepopeliere,WhenZ 2 one-form symmetry leads to non-invertible axial symmetries,Journal of High Energy Physics2023(2023) 205

    work page 2023

  74. [74]

    Koide, Y

    M. Koide, Y. Nagoya and S. Yamaguchi,Non-invertible topological defects in 4-dimensional Z2 pure lattice gauge theory, 2021

    work page 2021

  75. [76]

    Kaidi, K

    J. Kaidi, K. Ohmori and Y. Zheng,Kramers-wannier-like duality defects in(3 + 1)dgauge theories,Phys. Rev. Lett.128(2022) 111601

    work page 2022

  76. [77]

    C´ ordova, K

    C. C´ ordova, K. Ohmori and T. Rudelius,Generalized symmetry breaking scales and weak gravity conjectures,Journal of High Energy Physics2022(2022) 154

    work page 2022

  77. [78]

    Arias-Tamargo and D

    G. Arias-Tamargo and D. Rodr´ ıguez-G´ omez,Non-invertible symmetries from discrete gauging and completeness of the spectrum,Journal of High Energy Physics2023(2023) 93

    work page 2023

  78. [79]

    Kaidi, G

    J. Kaidi, G. Zafrir and Y. Zheng,Non-invertible symmetries ofN= 4sym and twisted compactification,Journal of High Energy Physics2022(2022) 53

    work page 2022

  79. [80]

    Bashmakov, M.D

    V. Bashmakov, M.D. Zotto and A. Hasan,On the 6d origin of non-invertible symmetries in 4d, 2022. – 37 –

    work page 2022

  80. [81]

    Choi, H.T

    Y. Choi, H.T. Lam and S.-H. Shao,Noninvertible time-reversal symmetry,Phys. Rev. Lett. 130(2023) 131602

    work page 2023

Showing first 80 references.