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arxiv: 2606.26004 · v1 · pith:4R5CPOFRnew · submitted 2026-06-24 · ✦ hep-th

Non-invertible symmetries in the axiverse, and the imaginary wormholes

Daniele Licciardello , Luca Martucci This is my paper

Pith reviewed 2026-06-25 19:35 UTC · model grok-4.3

classification ✦ hep-th
keywords axiversenon-invertible symmetrieswormholesaxion shift symmetriesBPS instantonssuperpotentialN=1 modelseffective field theory
0
0 comments X

The pith

Wormholes and the Imaginary Distance Bound break non-invertible axion shift symmetries, forcing towers of BPS EFT instantons to generate infinitely many superpotential terms in N=1 axiverses.

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

The paper examines the symmetry structure of four-dimensional axiverse effective field theories with multiple axions coupled to abelian gauge sectors and their N=1 extensions. It identifies invertible and non-invertible generalized symmetries along with their breaking mechanisms and resulting energy scale hierarchies. The central focus is the quantum-gravitational breaking of non-invertible axion shift symmetries, which follows from the existence of wormholes together with the Imaginary Distance Bound. In N=1 axiverses this breaking implies that towers of BPS EFT instantons play a distinguished role and produce infinitely many superpotential terms.

Core claim

In N=1 axiverse models, the existence of wormholes and the recently proposed Imaginary Distance Bound predict the quantum-gravitational breaking of non-invertible axion shift symmetries; as a direct consequence, towers of BPS EFT instantons play a distinguished role and generate infinitely many superpotential terms.

What carries the argument

Wormholes together with the Imaginary Distance Bound, which enforce the breaking of non-invertible axion shift symmetries and thereby select towers of BPS EFT instantons as the source of infinitely many superpotential terms.

If this is right

  • Hierarchies of energy scales emerge from the distinct breaking mechanisms of invertible and non-invertible symmetries.
  • Towers of BPS EFT instantons become the dominant contributors to the superpotential in N=1 axiverses.
  • Non-invertible axion shift symmetries are broken at quantum-gravitational scales rather than at lower EFT scales.
  • The effective theory must incorporate infinitely many instanton-generated terms to remain consistent with the symmetry-breaking pattern.

Where Pith is reading between the lines

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

  • The same wormhole-based logic could restrict the allowed axion potentials arising from string compactifications that realize N=1 axiverses.
  • Similar breaking arguments may apply to non-supersymmetric axiverse models if the Imaginary Distance Bound can be extended beyond N=1.
  • The requirement of infinite superpotential terms offers a possible consistency condition that could be checked in concrete string-theory realizations of multiple axions.
  • The distinction between invertible and non-invertible symmetries may influence the pattern of axion masses and couplings observable in cosmology.

Load-bearing premise

The existence of wormholes combined with the Imaginary Distance Bound is sufficient to guarantee the quantum-gravitational breaking of non-invertible axion shift symmetries.

What would settle it

An explicit N=1 axiverse construction in which wormholes are present yet the superpotential remains finite with only finitely many terms generated by BPS instantons.

Figures

Figures reproduced from arXiv: 2606.26004 by Daniele Licciardello, Luca Martucci.

Figure 1
Figure 1. Figure 1: Saxionic cone and dual saxionic cone of the [PITH_FULL_IMAGE:figures/full_fig_p011_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The violet and orange bullets represent the set [PITH_FULL_IMAGE:figures/full_fig_p022_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: The bullets represent the set C EFT I of EFT instanton charges of the P 1 ,→ X → P 2 F-theory model, with twist parameter p = 2, discussed in Section 2.3. The black-encircled bullets represent the subset CWH of wormhole charges. Cf. also [PITH_FULL_IMAGE:figures/full_fig_p035_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Profiles of ρ+ and ρ˜+ for k = 4. In each plot, the left branch corresponds to the lower half-wormhole and the right branch to the higher half-wormhole.. to the N = 1 supergravity action (see e.g. [126]), where gi¯ı and Ri¯ıjȷ¯ denote the metric and curvature on the moduli space, in chiral coordinates. This conclusion is compatible with the interpretation of the wormhole as encoding coarse-grained informat… view at source ↗
Figure 6
Figure 6. Figure 6: Profiles of ρ+ and ρ˜+ for k = 3(1 + ε), with ε = 10−4 . In each plot, the left branch corresponds to the lower half-wormhole and the right branch to the higher half-wormhole. The above observations imply that ρ˜+ and ρ−, and hence χ˜ iα˙ + and χ iα − give the most relevant contribution at long distances. Quantitatively, this can be implemented in the bilocal effective theory by integrating out the fermion… view at source ↗
read the original abstract

We study the symmetry structure of four-dimensional axiverse effective field theories with multiple axions coupled to abelian gauge sectors, including their extensions to broad classes of N=1 models. We identify the invertible and non-invertible generalized symmetries, and discuss the associated symmetry-breaking mechanisms together with the resulting hierarchies of energy scales. In particular, we discuss the quantum-gravitational breaking of non-invertible axion shift symmetries predicted by the existence of wormholes and by the corresponding recently proposed Imaginary Distance Bound. In N=1 axiverses, these wormhole-based arguments imply that towers of BPS EFT instantons play a distinguished role and generate infinitely many superpotential terms.

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

2 major / 2 minor

Summary. The manuscript studies the structure of invertible and non-invertible generalized symmetries in four-dimensional axiverse EFTs with multiple axions coupled to abelian gauge sectors, including extensions to broad classes of N=1 models. It examines associated symmetry-breaking mechanisms and resulting energy-scale hierarchies, with particular focus on the quantum-gravitational breaking of non-invertible axion shift symmetries induced by wormholes together with the recently proposed Imaginary Distance Bound; the central claim is that this implies towers of BPS EFT instantons play a distinguished role and generate infinitely many superpotential terms in N=1 axiverses.

Significance. If the application of the Imaginary Distance Bound to non-invertible symmetries is rigorously justified and the resulting hierarchies are derived without circularity, the work would provide a concrete link between gravitational instanton effects and the structure of superpotentials in supersymmetric axiverse models, offering falsifiable constraints on the landscape of string-derived axion potentials.

major comments (2)
  1. [Abstract, §1] Abstract and §1: The central implication that wormholes plus the Imaginary Distance Bound predict quantum-gravitational breaking of non-invertible axion shift symmetries (leading to infinitely many superpotential terms) is load-bearing, yet the bound is introduced only as 'recently proposed'; the manuscript must explicitly demonstrate that the bound applies directly to the non-invertible case and produces the stated hierarchies without unstated auxiliary assumptions or external inputs.
  2. [§3] §3 (or equivalent section deriving the N=1 implications): The claim that towers of BPS EFT instantons generate infinitely many superpotential terms follows from the wormhole argument only if the non-invertible symmetry breaking is shown to be parametrically stronger than other effects; the manuscript should provide a concrete comparison of the instanton action scales versus the Imaginary Distance Bound cutoff to establish this dominance.
minor comments (2)
  1. [§2] Notation for generalized symmetries (e.g., the distinction between invertible and non-invertible axion shifts) should be introduced with explicit group or category definitions in the first section where they appear, rather than relying on prior literature.
  2. [Figures] Figure captions (if present) describing energy-scale hierarchies should include explicit numerical estimates or parametric expressions for the scales involved.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and the recommendation for major revision. The two major comments identify areas where the manuscript can be strengthened by making the application of the Imaginary Distance Bound more explicit and by adding scale comparisons. We address each point below and will revise accordingly.

read point-by-point responses

  1. Referee: [Abstract, §1] Abstract and §1: The central implication that wormholes plus the Imaginary Distance Bound predict quantum-gravitational breaking of non-invertible axion shift symmetries (leading to infinitely many superpotential terms) is load-bearing, yet the bound is introduced only as 'recently proposed'; the manuscript must explicitly demonstrate that the bound applies directly to the non-invertible case and produces the stated hierarchies without unstated auxiliary assumptions or external inputs.

    Authors: We agree that the manuscript introduces the bound as recently proposed and does not contain a self-contained derivation of its direct applicability to the non-invertible symmetries. In the revised version we will add a short subsection (or expanded paragraph) in §1 that derives the applicability from the bound's original formulation in terms of field-space distance, showing that it constrains the non-invertible axion shift symmetries identified in our EFT without additional assumptions beyond those already stated for the wormhole contributions. The resulting hierarchies will be stated explicitly from this derivation. revision: yes

  2. Referee: [§3] §3 (or equivalent section deriving the N=1 implications): The claim that towers of BPS EFT instantons generate infinitely many superpotential terms follows from the wormhole argument only if the non-invertible symmetry breaking is shown to be parametrically stronger than other effects; the manuscript should provide a concrete comparison of the instanton action scales versus the Imaginary Distance Bound cutoff to establish this dominance.

    Authors: We agree that a concrete parametric comparison is required to establish dominance. In the revised §3 we will insert an explicit comparison of the BPS instanton actions (scaling as 2π n / g² for the tower index n) against the exponential suppression set by the Imaginary Distance Bound cutoff. This will demonstrate that the wormhole-induced breaking is parametrically stronger than other potential effects for the range of axiverse parameters considered, thereby justifying the conclusion that the infinite tower generates the superpotential terms. revision: yes

Circularity Check

1 steps flagged

Central claim reduces to application of recently proposed Imaginary Distance Bound

specific steps
  1. self citation load bearing [Abstract]
    "we discuss the quantum-gravitational breaking of non-invertible axion shift symmetries predicted by the existence of wormholes and by the corresponding recently proposed Imaginary Distance Bound. In N=1 axiverses, these wormhole-based arguments imply that towers of BPS EFT instantons play a distinguished role and generate infinitely many superpotential terms."

    The prediction of symmetry breaking (and the consequent infinite superpotential terms) is stated to follow from wormholes together with the Imaginary Distance Bound. Because the bound is introduced only as 'recently proposed' without derivation or external verification inside this manuscript, the central implication reduces to acceptance of that prior input rather than an independent derivation from the paper's own equations or data.

full rationale

The paper's key implication—that wormholes plus the Imaginary Distance Bound force quantum-gravitational breaking of non-invertible axion shift symmetries, which in turn implies towers of BPS EFT instantons generate infinitely many superpotential terms—rests on the bound as an external input. The abstract explicitly presents the bound as 'recently proposed' rather than deriving it, and no independent derivation or external benchmark is supplied in the provided text. This matches self-citation load-bearing (pattern 3) when the cited source overlaps with the authors. The remainder of the symmetry classification appears self-contained, but the load-bearing prediction step is not.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Central claims rest on domain assumptions about wormholes and the Imaginary Distance Bound; no free parameters or new entities are explicitly introduced in the abstract.

axioms (2)
  • domain assumption Existence of wormholes in quantum gravity that break non-invertible axion shift symmetries
    Invoked to predict symmetry breaking and energy scale hierarchies
  • domain assumption Validity of the Imaginary Distance Bound for axion symmetries
    Used as the basis for quantum-gravitational breaking arguments

pith-pipeline@v0.9.1-grok · 5637 in / 1358 out tokens · 36329 ms · 2026-06-25T19:35:38.463377+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

132 extracted references · 1 canonical work pages

  1. [1]

    R. D. Peccei and H. R. Quinn,CP Conservation in the Presence of Instantons,Phys. Rev. Lett.38(1977) 1440

    1977

  2. [2]

    Weinberg,A New Light Boson?,Phys

    S. Weinberg,A New Light Boson?,Phys. Rev. Lett.40(1978) 223

    1978

  3. [3]

    Wilczek,Problem of StrongPandTInvariance in the Presence of Instantons,Phys

    F. Wilczek,Problem of StrongPandTInvariance in the Presence of Instantons,Phys. Rev. Lett.40(1978) 279

    1978

  4. [4]

    W. Hu, R. Barkana and A. Gruzinov,Cold and fuzzy dark matter,Phys. Rev. Lett.85 (2000) 1158 [astro-ph/0003365]

    Pith/arXiv arXiv 2000

  5. [5]

    J. A. Frieman, C. T. Hill, A. Stebbins and I. Waga,Cosmology with ultralight pseudo Nambu-Goldstone bosons,Phys. Rev. Lett.75(1995) 2077 [astro-ph/9505060]

    Pith/arXiv arXiv 1995

  6. [6]

    Svrcek and E

    P. Svrcek and E. Witten,Axions In String Theory,JHEP06(2006) 051 [hep-th/0605206]

    Pith/arXiv arXiv 2006

  7. [7]

    Arvanitaki, S

    A. Arvanitaki, S. Dimopoulos, S. Dubovsky, N. Kaloper and J. March-Russell,String Axiverse,Phys. Rev. D81(2010) 123530 [0905.4720]

    Pith/arXiv arXiv 2010

  8. [8]

    McAllister and F

    L. McAllister and F. Quevedo,Moduli Stabilization in String Theory,2310.20559

    arXiv

  9. [9]

    C. W. Misner and J. A. Wheeler,Classical physics as geometry: Gravitation, electromagnetism, unquantized charge, and mass as properties of curved empty space, Annals Phys.2(1957) 525

    1957

  10. [10]

    S. W. Hawking,The Unpredictability of Quantum Gravity,Commun. Math. Phys.87 (1982) 395

    1982

  11. [11]

    Banks and N

    T. Banks and N. Seiberg,Symmetries and Strings in Field Theory and Gravity,Phys. Rev.D83(2011) 084019 [1011.5120]

    Pith/arXiv arXiv 2011

  12. [12]

    Harlow and H

    D. Harlow and H. Ooguri,Symmetries in quantum field theory and quantum gravity, Commun. Math. Phys.383(2021) 1669 [1810.05338]

    Pith/arXiv arXiv 2021

  13. [13]

    Harlow, B

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

    arXiv

  14. [14]

    Reece,TASI Lectures: (No) Global Symmetries to Axion Physics,PoST ASI2022 (2024) 008 [2304.08512]

    M. Reece,TASI Lectures: (No) Global Symmetries to Axion Physics,PoST ASI2022 (2024) 008 [2304.08512]

    arXiv 2024

  15. [15]

    Vafa,The String landscape and the swampland,hep-th/0509212

    C. Vafa,The String landscape and the swampland,hep-th/0509212

    Pith/arXiv arXiv

  16. [16]

    Ooguri and C

    H. Ooguri and C. Vafa,On the geometry of the string landscape and the swampland, Nucl.Phys.B766(2007) 21 [hep-th/0605264]

    Pith/arXiv arXiv 2007

  17. [17]

    T. D. Brennan, F. Carta and C. Vafa,The String Landscape, the Swampland, and the Missing Corner,PoST ASI2017(2017) 015 [1711.00864]

    Pith/arXiv arXiv 2017

  18. [18]

    Palti,The Swampland: Introduction and Review,Fortsch

    E. Palti,The Swampland: Introduction and Review,Fortsch. Phys.67(2019) 1900037 [1903.06239]. 55

    Pith/arXiv arXiv 2019

  19. [19]

    van Beest, J

    M. van Beest, J. Calder´ on-Infante, D. Mirfendereski and I. Valenzuela,Lectures on the Swampland Program in String Compactifications,2102.01111

    arXiv

  20. [20]

    Gra˜ na and A

    M. Gra˜ na and A. Herr´ aez,The Swampland Conjectures: A Bridge from Quantum Gravity to Particle Physics,Universe7(2021) 273 [2107.00087]

    arXiv 2021

  21. [21]

    N. B. Agmon, A. Bedroya, M. J. Kang and C. Vafa,Lectures on the string landscape and the Swampland,2212.06187

    arXiv

  22. [22]

    Van Riet and G

    T. Van Riet and G. Zoccarato,Beginners lectures on flux compactifications and related Swampland topics,Phys. Rept.1049(2024) 1 [2305.01722]

    arXiv 2024

  23. [23]

    Gaiotto, A

    D. Gaiotto, A. Kapustin, N. Seiberg and B. Willett,Generalized Global Symmetries, JHEP02(2015) 172 [1412.5148]

    Pith/arXiv arXiv 2015

  24. [24]

    Cordova, T

    C. Cordova, T. T. Dumitrescu, K. Intriligator and S.-H. Shao,Snowmass White Paper: Generalized Symmetries in Quantum Field Theory and Beyond, inSnowmass 2021, 5, 2022,2205.09545

    Pith/arXiv arXiv 2021

  25. [25]

    McGreevy,Generalized Symmetries in Condensed Matter,Ann

    J. McGreevy,Generalized Symmetries in Condensed Matter,Ann. Rev. Condensed Matter Phys.14(2023) 57 [2204.03045]

    arXiv 2023

  26. [26]

    D. S. Freed,Introduction to topological symmetry in QFT.,Proc. Symp. Pure Math.107 (2024) 93 [2212.00195]

    arXiv 2024

  27. [27]

    P. R. S. Gomes,An introduction to higher-form symmetries,SciPost Phys. Lect. Notes74 (2023) 1 [2303.01817]

    arXiv 2023

  28. [28]

    Schafer-Nameki,ICTP lectures on (non-)invertible generalized symmetries,Phys

    S. Schafer-Nameki,ICTP lectures on (non-)invertible generalized symmetries,Phys. Rept. 1063(2024) 1 [2305.18296]

    Pith/arXiv arXiv 2024

  29. [29]

    T. D. Brennan and S. Hong,Introduction to Generalized Global Symmetries in QFT and Particle Physics,2306.00912

    arXiv

  30. [30]

    Bhardwaj, L

    L. Bhardwaj, L. E. Bottini, L. Fraser-Taliente, L. Gladden, D. S. W. Gould, A. Platschorre et al.,Lectures on generalized symmetries,Phys. Rept.1051(2024) 1 [2307.07547]

    Pith/arXiv arXiv 2024

  31. [31]

    Shao,What’s Done Cannot Be Undone: TASI Lectures on Non-Invertible Symmetries,2308.00747

    S.-H. Shao,What’s Done Cannot Be Undone: TASI Lectures on Non-Invertible Symmetries,2308.00747

    Pith/arXiv arXiv

  32. [32]

    Luo, Q.-R

    R. Luo, Q.-R. Wang and Y.-N. Wang,Lecture notes on generalized symmetries and applications,Phys. Rept.1065(2024) 1 [2307.09215]

    arXiv 2024

  33. [33]

    Carqueville, M

    N. Carqueville, M. Del Zotto and I. Runkel,Topological defects, 11, 2023,2311.02449, DOI

    arXiv 2023

  34. [34]

    Costa et al.,Simons Lectures on Categorical Symmetries, 11, 2024,2411.09082

    D. Costa et al.,Simons Lectures on Categorical Symmetries, 11, 2024,2411.09082

    arXiv 2024

  35. [35]

    Rudelius and S.-H

    T. Rudelius and S.-H. Shao,Topological Operators and Completeness of Spectrum in Discrete Gauge Theories,JHEP12(2020) 172 [2006.10052]. 56

    arXiv 2020

  36. [36]

    Heidenreich, J

    B. Heidenreich, J. McNamara, M. Montero, M. Reece, T. Rudelius and I. Valenzuela, Non-invertible global symmetries and completeness of the spectrum,JHEP09(2021) 203 [2104.07036]

    arXiv 2021

  37. [37]

    McNamara,Gravitational Solitons and Completeness,2108.02228

    J. McNamara,Gravitational Solitons and Completeness,2108.02228

    arXiv

  38. [38]

    Cordova, K

    C. Cordova, K. Ohmori and T. Rudelius,Generalized symmetry breaking scales and weak gravity conjectures,JHEP11(2022) 154 [2202.05866]

    arXiv 2022

  39. [39]

    J. J. Heckman, J. McNamara, M. Montero, A. Sharon, C. Vafa and I. Valenzuela,Fate of stringy noninvertible symmetries,Phys. Rev. D110(2024) 106001 [2402.00118]

    arXiv 2024

  40. [40]

    Rudelius,A symmetry-centric perspective on the geometry of the string landscape and the swampland,Int

    T. Rudelius,A symmetry-centric perspective on the geometry of the string landscape and the swampland,Int. J. Mod. Phys. D33(2024) 2441003 [2405.12980]

    arXiv 2024

  41. [41]

    Basile, B

    I. Basile, B. Knorr, A. Platania and M. Schiffer,Asymptotic safety, quantum gravity, and the swampland: a conceptual assessment,2502.12290

    arXiv

  42. [42]

    Gagliano,Quantifying non-invertible chiral symmetry breaking,2508.09254

    F. Gagliano,Quantifying non-invertible chiral symmetry breaking,2508.09254

    arXiv

  43. [43]

    Apruzzi and L

    F. Apruzzi and L. Martucci,Gaillard-Zumino non-invertible symmetries,2510.18997

    arXiv

  44. [44]

    Cordova and K

    C. Cordova and K. Ohmori,Noninvertible Chiral Symmetry and Exponential Hierarchies, Phys. Rev. X13(2023) 011034 [2205.06243]

    arXiv 2023

  45. [45]

    Y. Choi, H. T. Lam and S.-H. Shao,Non-invertible Gauss law and axions,JHEP09 (2023) 067 [2212.04499]

    arXiv 2023

  46. [46]

    Di Ubaldo, L

    G. Di Ubaldo, L. V. Iliesiu, H. W. Lin and C. Yan,Positivity of the gravitational path integral implies the axionic weak gravity conjecture,2605.05305

    Pith/arXiv arXiv

  47. [47]

    Maldacena, A

    J. Maldacena, A. Maloney and B. McPeak,Wormholes and the imaginary distance bound, 2605.05336

    Pith/arXiv arXiv

  48. [48]

    Y. Choi, H. T. Lam and S.-H. Shao,Noninvertible Global Symmetries in the Standard Model,Phys. Rev. Lett.129(2022) 161601 [2205.05086]

    arXiv 2022

  49. [49]

    Yokokura,Non-invertible symmetries in axion electrodynamics,2212.05001

    R. Yokokura,Non-invertible symmetries in axion electrodynamics,2212.05001

    arXiv

  50. [50]

    S. Hong, H. Kim, S. M. Lee and D. Seo,Multi-instantons, multi-axions, and non-invertible symmetries in 4d QFT,JHEP03(2026) 204 [2510.18404]

    arXiv 2026

  51. [51]

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

    arXiv 2022

  52. [52]

    Sehayek and N

    D. Sehayek and N. Craig,Generalized symmetries and emergence in axion effective field theories,2604.11877

    Pith/arXiv arXiv

  53. [53]

    S. B. Giddings and A. Strominger,Axion Induced Topology Change in Quantum Gravity and String Theory,Nucl. Phys. B306(1988) 890

    1988

  54. [54]

    Arkani-Hamed, J

    N. Arkani-Hamed, J. Orgera and J. Polchinski,Euclidean wormholes in string theory, JHEP12(2007) 018 [0705.2768]. 57

    Pith/arXiv arXiv 2007

  55. [55]

    Lanza, F

    S. Lanza, F. Marchesano, L. Martucci and I. Valenzuela,Swampland Conjectures for Strings and Membranes,JHEP02(2021) 006 [2006.15154]

    arXiv 2021

  56. [56]

    Lanza, F

    S. Lanza, F. Marchesano, L. Martucci and I. Valenzuela,The EFT stringy viewpoint on large distances,JHEP09(2021) 197 [2104.05726]

    arXiv 2021

  57. [57]

    Lanza, F

    S. Lanza, F. Marchesano, L. Martucci and I. Valenzuela,Large Field Distances from EFT strings, in21st Hellenic School and Workshops on Elementary Particle Physics and Gravity, 5, 2022,2205.04532

    arXiv 2022

  58. [58]

    Martucci, N

    L. Martucci, N. Risso, A. Valenti and L. Vecchi,Wormholes in the axiverse, and the species scale,2404.14489

    arXiv

  59. [59]

    G. W. Gibbons and S. W. Hawking,Action Integrals and Partition Functions in Quantum Gravity,Phys. Rev. D15(1977) 2752

    1977

  60. [60]

    Witten,Duality and Axion Wormholes,2601.01587

    E. Witten,Duality and Axion Wormholes,2601.01587

    arXiv

  61. [61]

    Martucci, N

    L. Martucci, N. Risso and T. Weigand,Quantum Gravity Bounds on N=1 Effective Theories in Four Dimensions,2210.10797

    arXiv

  62. [62]

    Lanza, F

    S. Lanza, F. Marchesano, L. Martucci and D. Sorokin,How many fluxes fit in an EFT?, JHEP10(2019) 110 [1907.11256]

    arXiv 2019

  63. [63]

    Donnelly, B

    W. Donnelly, B. Michel and A. Wall,Electromagnetic Duality and Entanglement Anomalies,Phys. Rev. D96(2017) 045008 [1611.05920]

    Pith/arXiv arXiv 2017

  64. [64]

    Kaufmann, J

    L. Kaufmann, J. Monnee, T. Weigand and M. Wiesner,Quantum obstructions for N = 1 infinite distance limits – Part I:g s obstructions,2603.12315

    Pith/arXiv arXiv

  65. [65]

    Kaufmann, J

    L. Kaufmann, J. Monnee, T. Weigand and M. Wiesner,Quantum obstructions for N = 1 infinite distance limits – Part II: K¨ ahler obstructions,2603.13470

    arXiv

  66. [66]

    Del Zotto, M

    M. Del Zotto, M. Dell’Acqua and E. Riedel G˚ arding,The Higher Structure of Symmetries of Axion-Maxwell Theory,2411.09685

    arXiv

  67. [67]

    Hidaka, M

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

    2020

  68. [68]

    Hidaka, M

    Y. Hidaka, M. Nitta and R. Yokokura,Global 3-group symmetry and ’t Hooft anomalies in axion electrodynamics,JHEP01(2021) 173 [2009.14368]

    arXiv 2021

  69. [69]

    Hidaka, M

    Y. Hidaka, M. Nitta and R. Yokokura,Global 4-group symmetry and ’t Hooft anomalies in topological axion electrodynamics,PTEP2022(2022) 04A109 [2108.12564]

    arXiv 2022

  70. [70]

    M. K. Gaillard and B. Zumino,Duality Rotations for Interacting Fields,Nucl.Phys.B193 (1981) 221

    1981

  71. [71]

    C. G. Callan, Jr. and J. A. Harvey,Anomalies and Fermion Zero Modes on Strings and Domain Walls,Nucl. Phys. B250(1985) 427

    1985

  72. [72]

    S. G. Naculich,Axionic Strings: Covariant Anomalies and Bosonization of Chiral Zero Modes,Nucl. Phys. B296(1988) 837. 58

    1988

  73. [73]

    Fukuda and K

    H. Fukuda and K. Yonekura,Witten effect, anomaly inflow, and charge teleportation, JHEP01(2021) 119 [2010.02221]

    arXiv 2021

  74. [74]

    J. Fan, K. Fraser, M. Reece and J. Stout,Axion Mass from Magnetic Monopole Loops, Phys. Rev. Lett.127(2021) 131602 [2105.09950]

    arXiv 2021

  75. [75]

    Heidenreich, M

    B. Heidenreich, M. Reece and T. Rudelius,The Weak Gravity Conjecture and axion strings,JHEP11(2021) 004 [2108.11383]

    arXiv 2021

  76. [76]

    Witten,Dyons of Charge e theta/2 pi,Phys

    E. Witten,Dyons of Charge e theta/2 pi,Phys. Lett. B86(1979) 283

    1979

  77. [77]

    C´ ordova, D

    C. C´ ordova, D. S. Freed, H. T. Lam and N. Seiberg,Anomalies in the Space of Coupling Constants and Their Dynamical Applications I,SciPost Phys.8(2020) 001 [ 1905.09315]

    arXiv 2020

  78. [78]

    C´ ordova, D

    C. C´ ordova, D. S. Freed, H. T. Lam and N. Seiberg,Anomalies in the Space of Coupling Constants and Their Dynamical Applications II,SciPost Phys.8(2020) 002 [ 1905.13361]

    arXiv 2020

  79. [79]

    Jackiw,Charge and Mass Spectrum of Quantum Solitons,Conf

    R. Jackiw,Charge and Mass Spectrum of Quantum Solitons,Conf. Proc. C750926 (1975) 377

    1975

  80. [80]

    Gaiotto, A

    D. Gaiotto, A. Kapustin, Z. Komargodski and N. Seiberg,Theta, Time Reversal, and Temperature,JHEP05(2017) 091 [1703.00501]

    Pith/arXiv arXiv 2017

Showing first 80 references.