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arxiv: 2605.22912 · v1 · pith:YF27O54Wnew · submitted 2026-05-21 · ✦ hep-th

Sharpening the Supersymmetric Axion Weak Gravity Conjecture

Muldrow Etheredge , Matthew Reece , Tom Rudelius , Christopher Tudball This is my paper

Pith reviewed 2026-05-25 05:46 UTC · model grok-4.3

classification ✦ hep-th
keywords axion weak gravity conjecturesupersymmetryinstantonsstring landscapeswampland conjecturesquantum gravity
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The pith

Supersymmetric instantons in four dimensions obey the sharpened bound fS over absolute n at most sqrt(7/2) over kappa four.

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

The paper verifies a sharpened form of the axion weak gravity conjecture across multiple string theory axion sectors. It confirms that the ratio of axion decay constant times instanton action over charge stays below a specific coefficient involving pi and spacetime dimension. Three separate methods are used to check examples from the landscape and support the proposed bound. For supersymmetric instantons in four dimensions the bound tightens further to one over kappa four times the square root of seven over two. This supplies concrete limits on axion parameters that follow from quantum gravity.

Core claim

The authors verify that axion instantons across string landscape sectors satisfy fS over absolute n at most pi over two kappa d times the square root of d minus one over d minus two. They further argue that supersymmetric instantons in four dimensions obey the stronger bound fS over absolute n at most one over kappa four times the square root of seven over two.

What carries the argument

The ratio fS over absolute n, where f is the axion decay constant, S the instanton action, and n the integer charge, bounded relative to the reduced Planck scale set by kappa d.

If this is right

  • The axion weak gravity conjecture holds with a definite numerical coefficient rather than an unspecified order-one factor.
  • Supersymmetric axion models receive stronger restrictions on allowed decay constants and instanton actions.
  • The bound depends explicitly on spacetime dimension and applies uniformly to checked sectors of the string landscape.
  • Instanton contributions to axion potentials must respect the tighter supersymmetric limit in four dimensions.

Where Pith is reading between the lines

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

  • The sharpened bound could further restrict viable parameter ranges in axion-driven inflation models.
  • Similar tightening might appear in other swampland conjectures when supersymmetry is imposed.
  • Systematic scans of additional string compactifications could test whether the stronger four-dimensional bound holds universally.

Load-bearing premise

The three complementary approaches identify all dominant instantons in the examined axion sectors without missing any lighter ones that would violate the bound.

What would settle it

An explicit supersymmetric four-dimensional string compactification in which the lightest instanton has fS over absolute n larger than sqrt(7/2) over kappa four.

read the original abstract

The Axion Weak Gravity Conjecture provides one of the most effective quantum gravity tools for constraining particle physics and cosmology, but it has long been thought of as a slightly fuzzy statement: given an axion with decay constant $f$ there should exist an instanton of charge $n$ and action $S$ with $fS/|n|$ at most an order-one number in Planck units. Recent work related to axion wormholes motivated a specific order-one coefficient, $\frac{fS}{|n|} \leq \frac{\pi}{2 \kappa_d} \sqrt{\frac{d-1}{d-2}}$. In this work, we verify this bound in various axion sectors across the string landscape using three complementary approaches. In the process, we derive even tighter bounds on instantons in such sectors. For example, we argue that supersymmetric instantons in 4d satisfy the stronger bound of $\frac{fS}{|n|}\leq \frac 1{\kappa_4}\sqrt{\frac{7}{2}}$.

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 claims that the Axion Weak Gravity Conjecture can be sharpened to the specific coefficient fS/|n| ≤ (π/(2 κ_d)) sqrt((d-1)/(d-2)), verifies this bound across various axion sectors in the string landscape via three complementary approaches, and argues that supersymmetric instantons in 4d obey the tighter inequality fS/|n| ≤ (1/κ_4) sqrt(7/2).

Significance. If the stronger bound and its verification hold, the result would supply a more precise quantum-gravity constraint on axion decay constants and instanton actions, with direct utility for model-building in particle physics and cosmology. The multi-method checks performed in concrete string examples constitute a concrete strength of the work.

major comments (2)
  1. [Abstract and the section describing the three complementary approaches] The central verification claim rests on the three complementary approaches correctly identifying all dominant (lightest) instantons without omission. The manuscript provides no general argument that these methods are exhaustive across all relevant 4d axion sectors or that post-hoc selection of examples was avoided; any missed lighter instanton would falsify the reported inequality. This is load-bearing for the claim that the bound is verified in the string landscape.
  2. [Section deriving the stronger supersymmetric bound] The derivation of the stronger 4d supersymmetric bound fS/|n| ≤ (1/κ_4) sqrt(7/2) is presented as an argument internal to the paper; however, the text does not clarify whether this follows from a parameter-free derivation or relies on assumptions about the instanton spectrum that are only checked in the selected examples.
minor comments (2)
  1. [Introduction] Notation for the Planck mass and the constant κ_4 should be defined explicitly on first use and kept uniform throughout.
  2. [Figures] Figure captions should state the precise string compactifications and axion sectors shown, rather than generic labels.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their positive evaluation of the significance of our results and for their detailed comments on the verification methods and the supersymmetric bound. We respond to each major comment below.

read point-by-point responses

  1. Referee: [Abstract and the section describing the three complementary approaches] The central verification claim rests on the three complementary approaches correctly identifying all dominant (lightest) instantons without omission. The manuscript provides no general argument that these methods are exhaustive across all relevant 4d axion sectors or that post-hoc selection of examples was avoided; any missed lighter instanton would falsify the reported inequality. This is load-bearing for the claim that the bound is verified in the string landscape.

    Authors: We agree that the manuscript does not contain a general theorem establishing that the three approaches are exhaustive in every conceivable 4d axion sector of the string landscape; such a result would require a complete classification of all compactifications, which lies beyond present capabilities. The three methods are instead applied as complementary tools to representative classes of axion sectors arising in explicit string constructions, with cross-consistency among the methods serving as an internal check that the lightest instantons have been identified. The examples were chosen for their direct relevance to the axion weak gravity conjecture rather than to fit the bound after the fact. We will add a clarifying paragraph in the relevant section that explicitly states the scope of the verification and notes this limitation. revision: partial

  2. Referee: [Section deriving the stronger supersymmetric bound] The derivation of the stronger 4d supersymmetric bound fS/|n| ≤ (1/κ_4) sqrt(7/2) is presented as an argument internal to the paper; however, the text does not clarify whether this follows from a parameter-free derivation or relies on assumptions about the instanton spectrum that are only checked in the selected examples.

    Authors: The stronger bound is obtained from the BPS saturation condition for supersymmetric instantons together with the general form of the superpotential in 4d N=1 supergravity; the derivation is therefore parameter-free and does not invoke any assumptions about the detailed instanton spectrum beyond the existence of supersymmetric solutions. The concrete string examples are used solely to verify that the general bound is realized and not to derive it. We will insert a short clarifying statement in the section to make this independence explicit. revision: partial

Circularity Check

0 steps flagged

No significant circularity; sharpened bound derived from independent string example checks

full rationale

The paper verifies the original Axion WGC bound (motivated by prior wormhole work) via three complementary approaches applied to explicit string landscape axion sectors, then derives a tighter supersymmetric bound in 4d as a byproduct. No load-bearing step reduces by construction to a self-defined quantity, fitted input renamed as prediction, or unverified self-citation chain; the verification relies on external string constructions rather than tautological redefinition of inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard assumptions of string theory compactifications and supersymmetry preservation; no new free parameters or invented entities are introduced in the abstract. The bound itself is taken from recent work and verified rather than derived from scratch.

axioms (2)
  • domain assumption String theory provides consistent UV completions of quantum gravity with axion sectors that can be explicitly constructed.
    Invoked when the authors state they verify the bound across the string landscape.
  • domain assumption The instantons identified in the constructions are the ones that control the Weak Gravity Conjecture bound.
    Implicit in the verification claim; if lighter instantons exist the bound could be violated.

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Reference graph

Works this paper leans on

100 extracted references · 93 canonical work pages · 46 internal anchors

  1. [1]

    The String Landscape, Black Holes and Gravity as the Weakest Force

    N. Arkani-Hamed, L. Motl, A. Nicolis and C. Vafa,The String landscape, black holes and gravity as the weakest force,JHEP0706(2007) 060, [hep-th/0601001]

    work page internal anchor Pith review Pith/arXiv arXiv 2007

  2. [2]

    A. R. Liddle, A. Mazumdar and F. E. Schunck,Assisted inflation,Phys. Rev.D58 (1998) 061301, [astro-ph/9804177]

    work page internal anchor Pith review Pith/arXiv arXiv 1998

  3. [3]

    N-flation

    S. Dimopoulos, S. Kachru, J. McGreevy and J. G. Wacker,N-flation,JCAP0808 (2008) 003, [hep-th/0507205]

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  4. [4]

    J. E. Kim, H. P. Nilles and M. Peloso,Completing natural inflation,JCAP01(2005) 005, [hep-ph/0409138]

    work page internal anchor Pith review Pith/arXiv arXiv 2005

  5. [5]

    On the Possibility of Large Axion Moduli Spaces

    T. Rudelius,On the Possibility of Large Axion Moduli Spaces,JCAP1504(2015) 049, [1409.5793]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  6. [6]

    Constraints on Axion Inflation from the Weak Gravity Conjecture

    T. Rudelius,Constraints on Axion Inflation from the Weak Gravity Conjecture, JCAP09(2015) 020, [1503.00795]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  7. [7]

    Transplanckian axions !?

    M. Montero, A. M. Uranga and I. Valenzuela,Transplanckian axions!?,JHEP08 (2015) 032, [1503.03886]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  8. [8]

    Fencing in the Swampland: Quantum Gravity Constraints on Large Field Inflation

    J. Brown, W. Cottrell, G. Shiu and P. Soler,Fencing in the Swampland: Quantum Gravity Constraints on Large Field Inflation,JHEP10(2015) 023, [1503.04783]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  9. [9]

    Weak Gravity Strongly Constrains Large-Field Axion Inflation

    B. Heidenreich, M. Reece and T. Rudelius,Weak Gravity Strongly Constrains Large-Field Axion Inflation,JHEP12(2015) 108, [1506.03447]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  10. [10]

    K. Choi, E. J. Chun, S. H. Im and K. S. Jeong,Diluting the inflationary axion fluctuation by a stronger QCD in the early Universe,Phys. Lett. B750(2015) 26–30, [1505.00306]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  11. [11]

    Axion Experiments to Algebraic Geometry: Testing Quantum Gravity via the Weak Gravity Conjecture

    B. Heidenreich, M. Reece and T. Rudelius,Axion Experiments to Algebraic Geometry: Testing Quantum Gravity via the Weak Gravity Conjecture,Int. J. Mod. Phys. D25(2016) 1643005, [1605.05311]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  12. [12]

    Heidenreich, M

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

    work page arXiv 2021

  13. [13]

    Reece, TASI Lectures: (No) Global Symmetries to Axion Physics , PoS TASI2022 (2024) 008, [2304.08512]

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

    work page arXiv 2024

  14. [14]

    Seo,Axion species scale and axion weak gravity conjecture-like bound,JHEP11 (2024) 082, [2407.16156]

    M.-S. Seo,Axion species scale and axion weak gravity conjecture-like bound,JHEP11 (2024) 082, [2407.16156]

    work page arXiv 2024

  15. [15]

    Euclidean wormholes, baby universes, and their impact on particle physics and cosmology

    A. Hebecker, T. Mikhail and P. Soler,Euclidean wormholes, baby universes, and their impact on particle physics and cosmology,Front. Astron. Space Sci.5(2018) 35, [1807.00824]. – 36 –

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  16. [16]

    Cicoli, V

    M. Cicoli, V. Guidetti, N. Righi and A. Westphal,Fuzzy Dark Matter candidates from string theory,JHEP05(2022) 107, [2110.02964]

    work page arXiv 2022

  17. [17]

    Sheridan, F

    E. Sheridan, F. Carta, N. Gendler, M. Jain, D. J. E. Marsh, L. McAllister et al., Fuzzy axions and associated relics,JHEP09(2025) 016, [2412.12012]

    work page arXiv 2025

  18. [18]

    M. Ibe, M. Yamazaki and T. T. Yanagida,Quintessence Axion Revisited in Light of Swampland Conjectures,Class. Quant. Grav.36(2019) 235020, [1811.04664]

    work page arXiv 2019

  19. [19]

    G. Shiu, F. Tonioni and H. V. Tran,Bounding axion dark energy,2604.09141

    work page internal anchor Pith review Pith/arXiv arXiv

  20. [20]

    Cosmological implications of ultra-light axion-like fields

    V. Poulin, T. L. Smith, D. Grin, T. Karwal and M. Kamionkowski,Cosmological implications of ultralight axionlike fields,Phys. Rev. D98(2018) 083525, [1806.10608]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  21. [21]

    Early Dark Energy Can Resolve The Hubble Tension

    V. Poulin, T. L. Smith, T. Karwal and M. Kamionkowski,Early Dark Energy Can Resolve The Hubble Tension,Phys. Rev. Lett.122(2019) 221301, [1811.04083]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  22. [22]

    Rudelius,Constraints on early dark energy from the axion weak gravity conjecture, JCAP01(2023) 014, [2203.05575]

    T. Rudelius,Constraints on early dark energy from the axion weak gravity conjecture, JCAP01(2023) 014, [2203.05575]

    work page arXiv 2023

  23. [23]

    Harlow, B

    D. Harlow, B. Heidenreich, M. Reece and T. Rudelius,Weak gravity conjecture,Rev. Mod. Phys.95(2023) 035003, [2201.08380]

    work page arXiv 2023

  24. [24]

    Rudelius,An Introduction to the Weak Gravity Conjecture,Contemp

    T. Rudelius,An Introduction to the Weak Gravity Conjecture,Contemp. Phys.1 (2024) 14, [2409.02161]

    work page arXiv 2024

  25. [25]

    The Swampland: Introduction and Review

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

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  26. [26]

    Positivity of the gravitational path integral implies the axionic weak gravity conjecture

    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

    work page internal anchor Pith review Pith/arXiv arXiv

  27. [27]

    Wormholes and the imaginary distance bound

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

    work page internal anchor Pith review Pith/arXiv arXiv

  28. [28]

    S. B. Giddings and A. Strominger,Axion Induced Topology Change in Quantum Gravity and String Theory,Nucl. Phys. B306(1988) 890–907

    1988

  29. [29]

    Stout,Instanton expansions and phase transitions,JHEP05(2022) 168, [2012.11605]

    J. Stout,Instanton expansions and phase transitions,JHEP05(2022) 168, [2012.11605]

    work page arXiv 2022

  30. [30]

    The Weak Gravity Conjecture and Scalar Fields

    E. Palti,The Weak Gravity Conjecture and Scalar Fields,JHEP08(2017) 034, [1705.04328]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  31. [31]

    S.-J. Lee, W. Lerche and T. Weigand,A Stringy Test of the Scalar Weak Gravity Conjecture,Nucl. Phys. B938(2019) 321–350, [1810.05169]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  32. [32]

    Gonzalo and L

    E. Gonzalo and L. E. Ib´ a˜ nez,A Strong Scalar Weak Gravity Conjecture and Some Implications,JHEP08(2019) 118, [1903.08878]. – 37 –

    work page arXiv 2019

  33. [33]

    Andriot, N

    D. Andriot, N. Cribiori and D. Erkinger,The web of swampland conjectures and the TCC bound,JHEP07(2020) 162, [2004.00030]

    work page arXiv 2020

  34. [34]

    Benakli, C

    K. Benakli, C. Branchina and G. Lafforgue-Marmet,Revisiting the scalar weak gravity conjecture,Eur. Phys. J. C80(2020) 742, [2004.12476]

    work page arXiv 2020

  35. [35]

    Calder´ on-Infante, A

    J. Calder´ on-Infante, A. M. Uranga and I. Valenzuela,The Convex Hull Swampland Distance Conjecture and Bounds on Non-geodesics,JHEP03(2021) 299, [2012.00034]

    work page arXiv 2021

  36. [36]

    Etheredge, B

    M. Etheredge, B. Heidenreich, S. Kaya, Y. Qiu and T. Rudelius,Sharpening the Distance Conjecture in diverse dimensions,JHEP12(2022) 114, [2206.04063]

    work page arXiv 2022

  37. [37]

    Etheredge, B

    M. Etheredge, B. Heidenreich, J. McNamara, T. Rudelius, I. Ruiz and I. Valenzuela, Running decompactification, sliding towers, and the distance conjecture,JHEP12 (2023) 182, [2306.16440]

    work page arXiv 2023

  38. [38]

    Castellano, I

    A. Castellano, I. Ruiz and I. Valenzuela,Stringy evidence for a universal pattern at infinite distance,JHEP06(2024) 037, [2311.01536]

    work page arXiv 2024

  39. [39]

    Castellano, I

    A. Castellano, I. Ruiz and I. Valenzuela,Universal Pattern in Quantum Gravity at Infinite Distance,Phys. Rev. Lett.132(2024) 181601, [2311.01501]

    work page arXiv 2024

  40. [40]

    Lanza, F

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

    work page arXiv 2021

  41. [41]

    Etheredge,Dense geodesics, tower alignment, and the Sharpened Distance Conjecture,JHEP01(2024) 122, [2308.01331]

    M. Etheredge,Dense geodesics, tower alignment, and the Sharpened Distance Conjecture,JHEP01(2024) 122, [2308.01331]

    work page arXiv 2024

  42. [42]

    Etheredge and B

    M. Etheredge and B. Heidenreich,Geodesic gradient flows in moduli space,JHEP03 (2025) 035, [2311.18693]

    work page arXiv 2025

  43. [43]

    Etheredge, B

    M. Etheredge, B. Heidenreich and T. Rudelius,A Distance Conjecture for branes, JHEP09(2025) 155, [2407.20316]

    work page arXiv 2025

  44. [44]

    Etheredge, B

    M. Etheredge, B. Heidenreich, T. Rudelius, I. Ruiz and I. Valenzuela,Taxonomy of infinite distance limits,JHEP03(2025) 213, [2405.20332]

    work page arXiv 2025

  45. [45]

    Etheredge,Taxonomy of branes in infinite distance limits,JHEP10(2025) 200, [2505.10615]

    M. Etheredge,Taxonomy of branes in infinite distance limits,JHEP10(2025) 200, [2505.10615]

    work page arXiv 2025

  46. [46]

    Naturalness and the Weak Gravity Conjecture

    C. Cheung and G. N. Remmen,Naturalness and the Weak Gravity Conjecture,Phys. Rev. Lett.113(2014) 051601, [1402.2287]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  47. [47]

    Heidenreich,Black Holes, Moduli, and Long-Range Forces,JHEP11(2020) 029, [2006.09378]

    B. Heidenreich,Black Holes, Moduli, and Long-Range Forces,JHEP11(2020) 029, [2006.09378]

    work page arXiv 2020

  48. [48]

    Heidenreich, M

    B. Heidenreich, M. Reece and T. Rudelius,Repulsive Forces and the Weak Gravity Conjecture,JHEP10(2019) 055, [1906.02206]

    work page arXiv 2019

  49. [49]

    Instantons and Wormholes In Minkowski and (A)dS Spaces

    M. Gutperle and W. Sabra,Instantons and wormholes in Minkowski and (A)dS – 38 – spaces,Nucl. Phys. B647(2002) 344–356, [hep-th/0206153]

    work page internal anchor Pith review Pith/arXiv arXiv 2002

  50. [50]

    Non-extremal D-instantons

    E. Bergshoeff, A. Collinucci, U. Gran, D. Roest and S. Vandoren,Non-extremal D-instantons,JHEP10(2004) 031, [hep-th/0406038]

    work page internal anchor Pith review Pith/arXiv arXiv 2004

  51. [51]

    Non-extremal instantons and wormholes in string theory

    E. Bergshoeff, A. Collinucci, U. Gran, D. Roest and S. Vandoren,Non-extremal instantons and wormholes in string theory,Fortsch. Phys.53(2005) 990–996, [hep-th/0412183]

    work page internal anchor Pith review Pith/arXiv arXiv 2005

  52. [52]

    Sharpening the Weak Gravity Conjecture with Dimensional Reduction

    B. Heidenreich, M. Reece and T. Rudelius,Sharpening the Weak Gravity Conjecture with Dimensional Reduction,JHEP02(2016) 140, [1509.06374]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  53. [53]

    Can Gravitational Instantons Really Constrain Axion Inflation?

    A. Hebecker, P. Mangat, S. Theisen and L. T. Witkowski,Can Gravitational Instantons Really Constrain Axion Inflation?,JHEP02(2017) 097, [1607.06814]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  54. [54]

    Marchesano and M

    F. Marchesano and M. Wiesner,Instantons and infinite distances,JHEP08(2019) 088, [1904.04848]

    work page arXiv 2019

  55. [55]

    T. W. Grimm and D. Van De Heisteeg,Infinite Distances and the Axion Weak Gravity Conjecture,JHEP03(2020) 020, [1905.00901]

    work page arXiv 2020

  56. [56]

    Hamada, E

    Y. Hamada, E. Kiritsis, F. Nitti and L. T. Witkowski,Axion RG flows and the holographic dynamics of instanton densities,J. Phys. A52(2019) 454003, [1905.03663]

    work page arXiv 2019

  57. [57]

    Hamada, E

    Y. Hamada, E. Kiritsis and F. Nitti,Holographic Theories at Finiteθ-Angle, CP-Violation, Glueball Spectra and Strong-Coupling Instabilities,Fortsch. Phys.69 (2021) 2000111, [2007.13535]

    work page arXiv 2021

  58. [58]

    R. F. Dashen,Some features of chiral symmetry breaking,Phys. Rev. D3(1971) 1879–1889

    1971

  59. [59]

    Witten,Large N Chiral Dynamics,Annals Phys.128(1980) 363

    E. Witten,Large N Chiral Dynamics,Annals Phys.128(1980) 363

    1980

  60. [60]

    Theta, Time Reversal, and Temperature

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

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  61. [61]

    Witten,Some Properties of O(32) Superstrings,Phys

    E. Witten,Some Properties of O(32) Superstrings,Phys. Lett. B149(1984) 351–356

    1984

  62. [62]

    Axions In String Theory

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

    work page internal anchor Pith review Pith/arXiv arXiv 2006

  63. [63]

    J. P. Conlon,The QCD axion and moduli stabilisation,JHEP05(2006) 078, [hep-th/0602233]

    work page internal anchor Pith review Pith/arXiv arXiv 2006

  64. [64]

    Reece,Extra-dimensional axion expectations,JHEP07(2025) 130, [2406.08543]

    M. Reece,Extra-dimensional axion expectations,JHEP07(2025) 130, [2406.08543]

    work page arXiv 2025

  65. [65]

    Axion Monodromy and the Weak Gravity Conjecture

    A. Hebecker, F. Rompineve and A. Westphal,Axion Monodromy and the Weak Gravity Conjecture,JHEP04(2016) 157, [1512.03768]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  66. [66]

    Lanza, F

    S. Lanza, F. Marchesano, L. Martucci and I. Valenzuela,The EFT stringy viewpoint – 39 – on large distances,JHEP09(2021) 197, [2104.05726]

    work page arXiv 2021

  67. [67]

    Grieco, I

    A. Grieco, I. Ruiz and I. Valenzuela,EFT strings and dualities in 4dN= 1, 2504.16984

    work page arXiv

  68. [68]

    T. W. Grimm and J. Louis,The Effective action of N = 1 Calabi-Yau orientifolds, Nucl. Phys. B699(2004) 387–426, [hep-th/0403067]

    work page internal anchor Pith review Pith/arXiv arXiv 2004

  69. [69]

    Axion bitowers in quantum gravity

    M. Etheredge, B. Heidenreich, M. Reece and T. Rudelius, “Axion bitowers in quantum gravity.”

  70. [70]

    T. W. Grimm and J. Louis,The Effective action of type IIA Calabi-Yau orientifolds, Nucl. Phys. B718(2005) 153–202, [hep-th/0412277]

    work page internal anchor Pith review Pith/arXiv arXiv 2005

  71. [71]

    Martucci, N

    L. Martucci, N. Risso, A. Valenti and L. Vecchi,Wormholes in the axiverse, and the species scale,JHEP07(2024) 240, [2404.14489]

    work page arXiv 2024

  72. [72]

    S.-J. Lee, W. Lerche and T. Weigand,Emergent strings from infinite distance limits, JHEP02(2022) 190, [1910.01135]

    work page arXiv 2022

  73. [73]

    van de Heisteeg, C

    D. van de Heisteeg, C. Vafa and M. Wiesner,Bounds on Species Scale and the Distance Conjecture,Fortsch. Phys.71(2023) 2300143, [2303.13580]

    work page arXiv 2023

  74. [74]

    van de Heisteeg, C

    D. van de Heisteeg, C. Vafa, M. Wiesner and D. H. Wu,Bounds on field range for slowly varying positive potentials,JHEP02(2024) 175, [2305.07701]

    work page arXiv 2024

  75. [75]

    van de Heisteeg, C

    D. van de Heisteeg, C. Vafa, M. Wiesner and D. H. Wu,Species scale in diverse dimensions,JHEP05(2024) 112, [2310.07213]

    work page arXiv 2024

  76. [76]

    Marchesano, L

    F. Marchesano, L. Melotti and L. Paoloni,On the moduli space curvature at infinity, JHEP02(2024) 103, [2311.07979]

    work page arXiv 2024

  77. [77]

    Reece, T

    M. Reece, T. Rudelius and C. Tudball,Co-scaling and alignment of electric and magnetic towers,JHEP09(2025) 146, [2505.22713]

    work page arXiv 2025

  78. [78]

    Etheredge, A

    M. Etheredge, A. Herraez, L. Melotti and D. Luest,Proving the integral scaling conjecture with brane taxonomy, 2026

    2026

  79. [79]

    On the Geometry of the String Landscape and the Swampland

    H. Ooguri and C. Vafa,On the Geometry of the String Landscape and the Swampland, Nucl. Phys. B766(2007) 21–33, [hep-th/0605264]

    work page internal anchor Pith review Pith/arXiv arXiv 2007

  80. [80]

    T. W. Grimm, E. Palti and I. Valenzuela,Infinite Distances in Field Space and Massless Towers of States,JHEP08(2018) 143, [1802.08264]

    work page arXiv 2018

Showing first 80 references.