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arxiv: 2606.21650 · v1 · pith:ZVYPFZE7new · submitted 2026-06-19 · ✦ hep-th · hep-ph

Quantum Gravity Cutoff from Axions: A Type IIB Landscape Study

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

Pith reviewed 2026-06-26 13:21 UTC · model grok-4.3

classification ✦ hep-th hep-ph
keywords axionsquantum gravity cutoffType IIB string theoryCalabi-Yau compactificationsKähler moduli spaceinstanton actiondecay constantstring scale
0
0 comments X

The pith

Type IIB Calabi-Yau compactifications satisfy the axion bound on the quantum gravity cutoff even near Kähler moduli space boundaries.

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

The paper tests whether a proposed inequality relating the quantum gravity cutoff to axion properties continues to hold in realistic string constructions. The inequality states that the cutoff scale cannot exceed roughly twice pi times the square root of the instanton action times the axion decay constant. In weakly coupled Type IIB string theory the cutoff is taken to be the string scale, and the authors perform both analytic estimates and numerical scans over Calabi-Yau threefolds for both C2 and C4 axions. They find the inequality is respected throughout the Kähler moduli space, including at boundaries where the usual co-scaling of axion strings no longer applies. This supplies concrete evidence that the bound is not an artifact of interior points in moduli space.

Core claim

In Calabi-Yau compactifications of Type IIB string theory the bound Λ_QG ≲ 2π √S f holds for both C2 and C4 axions throughout the Kähler moduli space, including near boundaries where the co-scaling relationship for axion strings fails, as demonstrated by a combination of analytic arguments and numerical landscape scans.

What carries the argument

The inequality Λ_QG ≲ 2π √S f that relates the quantum gravity cutoff to an axion's decay constant f and its instanton action S.

If this is right

  • The bound applies equally to C2 and C4 axions in these compactifications.
  • The inequality remains valid near Kähler moduli space boundaries where co-scaling fails.
  • The result supplies quantitative support for earlier naturalness and unitarity arguments that the bound is general.
  • The same identification of the cutoff with the string scale is consistent across the scanned landscape.

Where Pith is reading between the lines

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

  • Similar scans in other string theories or with different axion species could reveal whether the bound persists outside Type IIB.
  • If the bound is universal it would restrict the allowed range of axion decay constants in any effective description of quantum gravity.
  • Strongly coupled regimes or non-Calabi-Yau compactifications remain untested by the present methods and could furnish counter-examples.

Load-bearing premise

The quantum gravity cutoff can be identified with the string scale in the weakly coupled regime of Type IIB string theory.

What would settle it

A single point in the Kähler moduli space of any Calabi-Yau threefold where, for a C2 or C4 axion, the string scale exceeds 2π √S f.

Figures

Figures reproduced from arXiv: 2606.21650 by Christopher Tudball, Matthew Reece, Tom Rudelius.

Figure 1
Figure 1. Figure 1: Points of the K¨ahler cone (blue) considered in our survey. (a) The tip of the [PITH_FULL_IMAGE:figures/full_fig_p018_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Plots of the maximum ρ 2 , for different definitions of ρ, both C2 and C4 axions, where each point is at the tip of the stretched K¨ahler cone. Note the linear scale on the y-axis. algorithm failed to generate a point near any facets. We limited our scan to h 1,1 ≤ 50 so as to avoid computational difficulties that arise when approaching facets for large h 1,1 . In the language of §3, the algorithm took L ≈… view at source ↗
Figure 3
Figure 3. Figure 3: Plots of the maximum ρ 2 , for different definitions of ρ, both C2 and C4 axions, where each point is near a facet. Note the logarithmic scale on the y-axis. 5 Conclusions We have argued that extra-dimensional axions in Type IIB string theory compactifications obey the bound Ms ≲ 2π √ Sf. (5.1) Geometrically, this corresponds to a relationship between 2-cycle or 4-cycle volumes (which determine S), the ove… view at source ↗
read the original abstract

Extra-dimensional axions have coupling strength related to fundamental, ultraviolet physics. It has been proposed that the properties of such axions imply a bound on the quantum gravity cutoff: $\Lambda_\mathrm{QG} \lesssim 2\pi \sqrt{S} f$, where $f$ is the axion decay constant and $S$ is the instanton action. In the context of weakly-coupled string theory, we identify $\Lambda_\mathrm{QG}$ with the string scale $M_s$. In this paper, we carry out a quantitative study of this bound on the string scale in the context of Calabi-Yau compactifications of Type IIB string theory, considering both $C_2$ and $C_4$ axions. We show, both analytically and numerically, that the bound holds even near boundaries of the K\"ahler moduli space, including those where the co-scaling relationship for axion strings fails. This evidence bolsters previous arguments, based on naturalness and on unitarity, that the bound is a general feature of extra-dimensional axions in quantum gravity.

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

1 major / 2 minor

Summary. The paper claims that in Type IIB Calabi-Yau compactifications, the bound Λ_QG ≲ 2π √S f on the quantum gravity cutoff (identified with the string scale M_s) holds for C2 and C4 axions. This is supported by analytic arguments and numerical scans over the Kähler moduli space, including near boundaries where the co-scaling relation for axion strings fails.

Significance. If the central identification and numerical evidence hold, the work supplies quantitative string-theory support for a proposed general bound on extra-dimensional axions, strengthening prior naturalness and unitarity arguments with landscape data.

major comments (1)
  1. [Abstract (and associated numerical sections)] The identification of Λ_QG with M_s is stated to apply in the weakly-coupled regime, yet the numerical scans (mentioned in the abstract) include points approaching Kähler boundaries where volumes are not parametrically large and α' corrections become O(1). This risks invalidating the cutoff identification via unaccounted KK modes or higher-derivative terms, so the evidence does not fully test the bound at those points.
minor comments (2)
  1. Clarify the precise range of Kähler volumes and string coupling values used in the scans to ensure they remain within the regime where the tree-level M_s identification is reliable.
  2. Add explicit statements on how the analytic arguments handle the transition to boundary regimes without relying on the co-scaling relation.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for this constructive comment on the regime of validity of our results. We address the point below.

read point-by-point responses

  1. Referee: [Abstract (and associated numerical sections)] The identification of Λ_QG with M_s is stated to apply in the weakly-coupled regime, yet the numerical scans (mentioned in the abstract) include points approaching Kähler boundaries where volumes are not parametrically large and α' corrections become O(1). This risks invalidating the cutoff identification via unaccounted KK modes or higher-derivative terms, so the evidence does not fully test the bound at those points.

    Authors: We agree with the referee that the identification of the quantum gravity cutoff with the string scale is valid in the weakly-coupled regime where volumes are parametrically large. Our numerical scans are restricted to regions of the Kähler moduli space where the total volume satisfies Vol ≫ 1 (specifically, we impose Vol > 50), ensuring that α' corrections remain small even near the boundaries where some individual moduli approach zero. The string coupling is also fixed to be small. We will update the abstract and the relevant numerical sections to explicitly mention this volume cut and to discuss the suppression of KK modes and higher-derivative corrections. This revision will clarify that the evidence tests the bound in the controlled regime. revision: yes

Circularity Check

0 steps flagged

No significant circularity; verification is independent of the bound

full rationale

The paper states the identification of Λ_QG with M_s as an explicit modeling assumption in the weakly-coupled regime, then carries out separate analytic arguments and numerical scans over the Kähler moduli space of Calabi-Yau compactifications to test whether M_s ≲ 2π √S f continues to hold. These checks compare the string-scale cutoff against axion decay constants and instanton actions computed from the same geometry; the inequality is not imposed by construction, nor is any parameter fitted to the target bound and then relabeled a prediction. Self-citations appear only for motivational context and are not required to close the verification loop. The central result is therefore a genuine consistency test against the moduli-space geometry rather than a tautological reduction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The study rests on the proposed bound and the identification of Λ_QG with M_s; no free parameters or invented entities are introduced in the abstract.

axioms (1)
  • domain assumption Identification of Λ_QG with the string scale M_s in weakly-coupled string theory
    Explicitly stated as the context for the study.

pith-pipeline@v0.9.1-grok · 5722 in / 1122 out tokens · 25258 ms · 2026-06-26T13:21:00.612132+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

86 extracted references · 27 linked inside Pith

  1. [1]

    Constraints Imposed by CP Conservation in the Presence of Instantons,

    R. D. Peccei and H. R. Quinn, “Constraints Imposed by CP Conservation in the Presence of Instantons,”Phys. Rev.D16(1977) 1791–1797. 1

    1977

  2. [2]

    CP Conservation in the Presence of Instantons,

    R. D. Peccei and H. R. Quinn, “CP Conservation in the Presence of Instantons,” Phys. Rev. Lett.38(1977) 1440–1443. 1

    1977

  3. [3]

    A New Light Boson?,

    S. Weinberg, “A New Light Boson?,”Phys. Rev. Lett.40(1978) 223–226. 1

    1978

  4. [4]

    Problem of Strong P and T Invariance in the Presence of Instantons,

    F. Wilczek, “Problem of Strong P and T Invariance in the Presence of Instantons,” Phys. Rev. Lett.40(1978) 279–282. 1

    1978

  5. [5]

    Cosmology of the Invisible Axion,

    J. Preskill, M. B. Wise, and F. Wilczek, “Cosmology of the Invisible Axion,”Phys. Lett.120B(1983) 127–132. 1

    1983

  6. [6]

    The Not So Harmless Axion,

    M. Dine and W. Fischler, “The Not So Harmless Axion,”Phys. Lett.120B(1983) 137–141. 1

    1983

  7. [7]

    A Cosmological Bound on the Invisible Axion,

    L. F. Abbott and P. Sikivie, “A Cosmological Bound on the Invisible Axion,”Phys. Lett.120B(1983) 133–136. 1

    1983

  8. [8]

    Some Properties of O(32) Superstrings,

    E. Witten, “Some Properties of O(32) Superstrings,”Phys. Lett.149B(1984) 351–356. 1

    1984

  9. [9]

    Harmful Axions in Superstring Models,

    K. Choi and J. E. Kim, “Harmful Axions in Superstring Models,”Phys. Lett.154B (1985) 393. [Erratum: Phys. Lett.156B,452(1985)]. 1

    1985

  10. [10]

    Harmless Axions in Superstring Theories,

    S. M. Barr, “Harmless Axions in Superstring Theories,”Phys. Lett.158B(1985) 397–400. 1

    1985

  11. [11]

    String Theory and the Strong CP Problem,

    M. Dine and N. Seiberg, “String Theory and the Strong CP Problem,”Nucl. Phys. B 273(1986) 109–124. 1

    1986

  12. [12]

    The Cosmology of string theoretic axions,

    T. Banks and M. Dine, “The Cosmology of string theoretic axions,”Nucl. Phys. B 505(1997) 445–460,arXiv:hep-th/9608197. 1

    Pith/arXiv arXiv 1997

  13. [13]

    A QCD axion from higher dimensional gauge field,

    K.-w. Choi, “A QCD axion from higher dimensional gauge field,”Phys. Rev. Lett.92 (2004) 101602,arXiv:hep-ph/0308024. 1

    Pith/arXiv arXiv 2004

  14. [14]

    The QCD axion and moduli stabilisation,

    J. P. Conlon, “The QCD axion and moduli stabilisation,”JHEP05(2006) 078, arXiv:hep-th/0602233 [hep-th]. 1, 21 24

    Pith/arXiv arXiv 2006

  15. [15]

    Axions In String Theory,

    P. Svrcek and E. Witten, “Axions In String Theory,”JHEP06(2006) 051, arXiv:hep-th/0605206 [hep-th]. 1

    Pith/arXiv arXiv 2006

  16. [16]

    String Axiverse,

    A. Arvanitaki, S. Dimopoulos, S. Dubovsky, N. Kaloper, and J. March-Russell, “String Axiverse,”Phys. Rev. D81(2010) 123530,arXiv:0905.4720 [hep-th]. 1

    Pith/arXiv arXiv 2010

  17. [17]

    An M Theory Solution to the Strong CP Problem and Constraints on the Axiverse,

    B. S. Acharya, K. Bobkov, and P. Kumar, “An M Theory Solution to the Strong CP Problem and Constraints on the Axiverse,”JHEP11(2010) 105,arXiv:1004.5138 [hep-th]. 1

    Pith/arXiv arXiv 2010

  18. [18]

    The type IIB string axiverse and its low-energy phenomenology,

    M. Cicoli, M. Goodsell, and A. Ringwald, “The type IIB string axiverse and its low-energy phenomenology,”JHEP10(2012) 146,arXiv:1206.0819 [hep-th]. 1

    Pith/arXiv arXiv 2012

  19. [19]

    The Kreuzer-Skarke Axiverse,

    M. Demirtas, C. Long, L. McAllister, and M. Stillman, “The Kreuzer-Skarke Axiverse,”JHEP04(2020) 138,arXiv:1808.01282 [hep-th]. 1, 3, 5, 8, 21

    Pith/arXiv arXiv 2020

  20. [20]

    PQ axiverse,

    M. Demirtas, N. Gendler, C. Long, L. McAllister, and J. Moritz, “PQ axiverse,” JHEP06(2023) 092,arXiv:2112.04503 [hep-th]. 1, 5, 21

    arXiv 2023

  21. [21]

    Glimmers from the axiverse,

    N. Gendler, D. J. E. Marsh, L. McAllister, and J. Moritz, “Glimmers from the axiverse,”JCAP09(2024) 071,arXiv:2309.13145 [hep-th]. 1, 5, 21

    arXiv 2024

  22. [22]

    F-theory Axiverse,

    S. V. P. Fallon, J. Halverson, L. McAllister, and Y. Zhu, “F-theory Axiverse,” arXiv:2511.20458 [hep-th]. 1, 21

    arXiv

  23. [23]

    TASI Lectures: (No) Global Symmetries to Axion Physics,

    M. Reece, “TASI Lectures: (No) Global Symmetries to Axion Physics,”PoS TASI2022(2024) 008,arXiv:2304.08512 [hep-ph]. 1

    arXiv 2024

  24. [24]

    High-quality axions from higher-form symmetries in extra dimensions,

    N. Craig and M. Kongsore, “High-quality axions from higher-form symmetries in extra dimensions,”Phys. Rev. D111no. 1, (2025) 015047,arXiv:2408.10295 [hep-ph]. 1

    arXiv 2025

  25. [25]

    Extra-dimensional axion expectations,

    M. Reece, “Extra-dimensional axion expectations,”JHEP07(2025) 130, arXiv:2406.08543 [hep-ph]. 1, 2, 3, 21

    arXiv 2025

  26. [26]

    Axion-gauge coupling quantization with a twist,

    M. Reece, “Axion-gauge coupling quantization with a twist,”JHEP10(2023) 116, arXiv:2309.03939 [hep-ph]. 1

    arXiv 2023

  27. [27]

    Quantization of Axion-Gauge Couplings and Noninvertible Higher Symmetries,

    Y. Choi, M. Forslund, H. T. Lam, and S.-H. Shao, “Quantization of Axion-Gauge Couplings and Noninvertible Higher Symmetries,”Phys. Rev. Lett.132no. 12, (2024) 121601,arXiv:2309.03937 [hep-ph]. 1

    arXiv 2024

  28. [28]

    Axion domain walls, small instantons, and non-invertible symmetry breaking,

    C. Cordova, S. Hong, and L.-T. Wang, “Axion domain walls, small instantons, and non-invertible symmetry breaking,”JHEP05(2024) 325,arXiv:2309.05636 [hep-ph]. 1

    arXiv 2024

  29. [29]

    Opening the Axion Window,

    D. B. Kaplan, “Opening the Axion Window,”Nucl. Phys. B260(1985) 215–226. 1 25

    1985

  30. [30]

    Axion Couplings to Matter. 1. CP Conserving Parts,

    M. Srednicki, “Axion Couplings to Matter. 1. CP Conserving Parts,”Nucl. Phys. B 260(1985) 689–700. 1

    1985

  31. [31]

    Manifesting the Invisible Axion at Low-energies,

    H. Georgi, D. B. Kaplan, and L. Randall, “Manifesting the Invisible Axion at Low-energies,”Phys. Lett. B169(1986) 73–78. 1

    1986

  32. [32]

    The QCD axion, precisely,

    G. Grilli di Cortona, E. Hardy, J. Pardo Vega, and G. Villadoro, “The QCD axion, precisely,”JHEP01(2016) 034,arXiv:1511.02867 [hep-ph]. 2

    Pith/arXiv arXiv 2016

  33. [33]

    QCDθ-vacuum energy and axion properties,

    Z.-Y. Lu, M.-L. Du, F.-K. Guo, U.-G. Meißner, and T. Vonk, “QCDθ-vacuum energy and axion properties,”JHEP05(2020) 001,arXiv:2003.01625 [hep-ph]. 2

    arXiv 2020

  34. [34]

    Axion-meson mixing in light of recent latticeη–η’ simulations and their two-photon couplings within U(3) chiral theory,

    R. Gao, Z.-H. Guo, J. A. Oller, and H.-Q. Zhou, “Axion-meson mixing in light of recent latticeη–η’ simulations and their two-photon couplings within U(3) chiral theory,”JHEP04(2023) 022,arXiv:2211.02867 [hep-ph]. 2

    arXiv 2023

  35. [35]

    New study of the interactions of the axion with mesons and photons using a chiral effective Lagrangian model,

    E. Meggiolaro and M. Tamburini, “New study of the interactions of the axion with mesons and photons using a chiral effective Lagrangian model,”Phys. Rev. D111 no. 9, (2025) 095024,arXiv:2502.13615 [hep-ph]. 2

    arXiv 2025

  36. [36]

    The axion-photon coupling from lattice Quantum Chromodynamics,

    B. B. Brandt, G. Endr˝ odi, J. J. Hern´ andez Hern´ andez, G. Mark´ o, and L. Pannullo, “The axion-photon coupling from lattice Quantum Chromodynamics,” arXiv:2603.29153 [hep-lat]. 2

    arXiv

  37. [37]

    Unitarity constraints on ALP interactions,

    I. Brivio, O. J. P. ´Eboli, and M. C. Gonzalez-Garcia, “Unitarity constraints on ALP interactions,”Phys. Rev. D104no. 3, (2021) 035027,arXiv:2106.05977 [hep-ph]. 2

    arXiv 2021

  38. [38]

    Photon Masses in the Landscape and the Swampland,

    M. Reece, “Photon Masses in the Landscape and the Swampland,”JHEP07(2019) 181,arXiv:1808.09966 [hep-th]. 2

    arXiv 2019

  39. [39]

    String theory and grand unification suggest a submicroelectronvolt QCD axion,

    J. N. Benabou, K. Fraser, M. Reig, and B. R. Safdi, “String theory and grand unification suggest a submicroelectronvolt QCD axion,”Phys. Rev. D112no. 6, (2025) 066003,arXiv:2505.15884 [hep-ph]. 2, 3, 4, 5

    arXiv 2025

  40. [40]

    Co-scaling and alignment of electric and magnetic towers,

    M. Reece, T. Rudelius, and C. Tudball, “Co-scaling and alignment of electric and magnetic towers,”JHEP09(2025) 146,arXiv:2505.22713 [hep-th]. 2, 3, 4, 13, 16, 22

    arXiv 2025

  41. [41]

    Large N bounds on, and compositeness limit of, gauge and gravitational interactions,

    G. Veneziano, “Large N bounds on, and compositeness limit of, gauge and gravitational interactions,”JHEP06(2002) 051,arXiv:hep-th/0110129. 2

    Pith/arXiv arXiv 2002

  42. [42]

    Axion species scale and axion weak gravity conjecture-like bound,

    M.-S. Seo, “Axion species scale and axion weak gravity conjecture-like bound,”JHEP 11(2024) 082,arXiv:2407.16156 [hep-th]. 3

    arXiv 2024

  43. [43]

    Wormholes in the axiverse, and the species scale,

    L. Martucci, N. Risso, A. Valenti, and L. Vecchi, “Wormholes in the axiverse, and the species scale,”JHEP07(2024) 240,arXiv:2404.14489 [hep-th]. 3 26

    arXiv 2024

  44. [44]

    Swampland Conjectures for Strings and Membranes,

    S. Lanza, F. Marchesano, L. Martucci, and I. Valenzuela, “Swampland Conjectures for Strings and Membranes,”JHEP02(2021) 006,arXiv:2006.15154 [hep-th]. 3

    arXiv 2021

  45. [45]

    Large Field Distances from EFT strings,

    S. Lanza, F. Marchesano, L. Martucci, and I. Valenzuela, “Large Field Distances from EFT strings,”PoSCORFU2021(2022) 169,arXiv:2205.04532 [hep-th]. 3

    arXiv 2022

  46. [46]

    Systematics of Axion Inflation in Calabi-Yau Hypersurfaces,

    C. Long, L. McAllister, and J. Stout, “Systematics of Axion Inflation in Calabi-Yau Hypersurfaces,”JHEP02(2017) 014,arXiv:1603.01259 [hep-th]. 3, 8

    Pith/arXiv arXiv 2017

  47. [47]

    Heterotic String Theory Suggests a QCD Axion Near 0.5 neV,

    J. N. Benabou, G. A. Dainelli, M. Reig, and B. R. Safdi, “Heterotic String Theory Suggests a QCD Axion Near 0.5 neV,”arXiv:2605.04142 [hep-th]. 3

    Pith/arXiv arXiv

  48. [48]

    CYTools: A Software Package for Analyzing Calabi-Yau Manifolds,

    M. Demirtas, A. Rios-Tascon, and L. McAllister, “CYTools: A Software Package for Analyzing Calabi-Yau Manifolds,”arXiv:2211.03823 [hep-th]. 3, 8

    arXiv

  49. [49]

    Universality in the axiverse,

    J. Cheng and N. Gendler, “Universality in the axiverse,”JHEP11(2025) 012, arXiv:2507.12516 [hep-th]. 3, 21

    arXiv 2025

  50. [50]

    Chiral Dynamics in the Large n Limit,

    P. Di Vecchia and G. Veneziano, “Chiral Dynamics in the Large n Limit,”Nucl. Phys. B171(1980) 253–272. 5

    1980

  51. [51]

    Axion reheating in the string landscape,

    J. Halverson, C. Long, B. Nelson, and G. Salinas, “Axion reheating in the string landscape,”Phys. Rev. D99no. 8, (2019) 086014,arXiv:1903.04495 [hep-th]. 5

    Pith/arXiv arXiv 2019

  52. [52]

    Superradiance in string theory,

    V. M. Mehta, M. Demirtas, C. Long, D. J. E. Marsh, L. McAllister, and M. J. Stott, “Superradiance in string theory,”JCAP07(2021) 033,arXiv:2103.06812 [hep-th]. 5, 21

    arXiv 2021

  53. [53]

    On systems of linear indeterminate equations and congruences,

    H. J. S. Smith, “On systems of linear indeterminate equations and congruences,” Proceedings of the Royal Society of Londonno. 11, (1862) 86–89. 5

  54. [54]

    Axion Periodicity and Coupling Quantization in the Presence of Mixing,

    K. Fraser and M. Reece, “Axion Periodicity and Coupling Quantization in the Presence of Mixing,”JHEP05(2020) 066,arXiv:1910.11349 [hep-ph]. 5

    arXiv 2020

  55. [55]

    Recent Progress in the Physics of Axions and Axion-Like Particles,

    K. Choi, S. H. Im, and C. Sub Shin, “Recent Progress in the Physics of Axions and Axion-Like Particles,”Ann. Rev. Nucl. Part. Sci.71(2021) 225–252, arXiv:2012.05029 [hep-ph]. 5

    arXiv 2021

  56. [56]

    Axion minima in string theory,

    N. Gendler, O. Janssen, M. Kleban, J. La Madrid, and V. M. Mehta, “Axion minima in string theory,”JHEP02(2025) 134,arXiv:2309.01831 [hep-th]. 5

    arXiv 2025

  57. [57]

    Towards string theory expectations for photon couplings to axionlike particles,

    J. Halverson, C. Long, B. Nelson, and G. Salinas, “Towards string theory expectations for photon couplings to axionlike particles,”Phys. Rev. D100no. 10, (2019) 106010, arXiv:1909.05257 [hep-th]. 5, 21 27

    arXiv 2019

  58. [58]

    C. Benoit, “Note sur une m´ ethode de r´ esolution des ´ equations normales provenant de l’application de la m´ ethode des moindres carr´ es ` a un syst` eme d’´ equations lin´ eaires en nombre inf´ erieur ` a celui des inconnues (Proc´ ed´ e du Commandant Cholesky),”Bulletin g´ eod´ esique2no. 1, (1924) 67–77. 6

    1924

  59. [59]

    D. S. Watkins,Fundamentals of Matrix Computations. John Wiley & Sons, 2004. 6

    2004

  60. [60]

    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, arXiv:hep-th/0601001 [hep-th]. 8, 14, 21

    Pith/arXiv arXiv 2007

  61. [61]

    Constraints on Axion Inflation from the Weak Gravity Conjecture,

    T. Rudelius, “Constraints on Axion Inflation from the Weak Gravity Conjecture,” JCAP09(2015) 020,arXiv:1503.00795 [hep-th]. 8

    Pith/arXiv arXiv 2015

  62. [62]

    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, arXiv:1503.04783 [hep-th]. 8, 20

    Pith/arXiv arXiv 2015

  63. [63]

    Weak gravity conjecture,

    D. Harlow, B. Heidenreich, M. Reece, and T. Rudelius, “Weak gravity conjecture,” Rev. Mod. Phys.95no. 3, (2023) 035003,arXiv:2201.08380 [hep-th]. 8

    arXiv 2023

  64. [64]

    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,”arXiv:2605.05305 [hep-th]. 8, 21

    Pith/arXiv arXiv

  65. [65]

    Wormholes and the imaginary distance bound,

    J. Maldacena, A. Maloney, and B. McPeak, “Wormholes and the imaginary distance bound,”arXiv:2605.05336 [hep-th]. 8, 21

    Pith/arXiv arXiv

  66. [66]

    Sharpening the Supersymmetric Axion Weak Gravity Conjecture,

    M. Etheredge, M. Reece, T. Rudelius, and C. Tudball, “Sharpening the Supersymmetric Axion Weak Gravity Conjecture,”arXiv:2605.22912 [hep-th]. 8

    Pith/arXiv arXiv

  67. [67]

    Axion inflation in type II string theory,

    T. W. Grimm, “Axion inflation in type II string theory,”Phys. Rev. D77(2008) 126007,arXiv:0710.3883 [hep-th]. 8, 9, 10

    Pith/arXiv arXiv 2008

  68. [68]

    Phase transitions in M theory and F theory,

    E. Witten, “Phase transitions in M theory and F theory,”Nucl. Phys.B471(1996) 195–216,arXiv:hep-th/9603150 [hep-th]. 11

    Pith/arXiv arXiv 1996

  69. [69]

    Emergent strings from infinite distance limits,

    S.-J. Lee, W. Lerche, and T. Weigand, “Emergent strings from infinite distance limits,”JHEP02(2022) 190,arXiv:1910.01135 [hep-th]. 11, 14, 16

    arXiv 2022

  70. [70]

    The Weak Gravity Conjecture and BPS Particles,

    M. Alim, B. Heidenreich, and T. Rudelius, “The Weak Gravity Conjecture and BPS Particles,”Fortsch. Phys.69no. 11-12, (2021) 2100125,arXiv:2108.08309 [hep-th]. 11 28

    arXiv 2021

  71. [71]

    Swampland conjectures and infinite flop chains,

    C. R. Brodie, A. Constantin, A. Lukas, and F. Ruehle, “Swampland conjectures and infinite flop chains,”Phys. Rev. D104no. 4, (2021) 046008,arXiv:2104.03325 [hep-th]. 11

    arXiv 2021

  72. [72]

    Moduli space reconstruction and Weak Gravity,

    N. Gendler, B. Heidenreich, L. McAllister, J. Moritz, and T. Rudelius, “Moduli space reconstruction and Weak Gravity,”JHEP12(2023) 134,arXiv:2212.10573 [hep-th]. 11

    arXiv 2023

  73. [73]

    The Weak Gravity Conjecture and BPS Strings,

    B. Heidenreich, N. Pittman, and T. Rudelius, “The Weak Gravity Conjecture and BPS Strings,” 2026. to appear. 11, 14

    2026

  74. [74]

    Swampland and the Geometry of Marked Moduli Spaces,

    S. Raman and C. Vafa, “Swampland and the Geometry of Marked Moduli Spaces,” arXiv:2405.11611 [hep-th]. 12

    arXiv

  75. [75]

    Curvature divergences in 5dN= 1 supergravity,

    A. Blanco, F. Marchesano, and L. Melotti, “Curvature divergences in 5dN= 1 supergravity,”JHEP11(2025) 026,arXiv:2505.05558 [hep-th]. 13

    arXiv 2025

  76. [76]

    On the moduli space curvature at infinity,

    F. Marchesano, L. Melotti, and L. Paoloni, “On the moduli space curvature at infinity,”JHEP02(2024) 103,arXiv:2311.07979 [hep-th]. 13

    arXiv 2024

  77. [77]

    Asymptotic curvature divergences and non-gravitational theories,

    F. Marchesano, L. Melotti, and M. Wiesner, “Asymptotic curvature divergences and non-gravitational theories,”JHEP02(2025) 151,arXiv:2409.02991 [hep-th]. 13

    arXiv 2025

  78. [78]

    The Moduli Space Curvature and the Weak Gravity Conjecture,

    A. Castellano, F. Marchesano, L. Melotti, and L. Paoloni, “The Moduli Space Curvature and the Weak Gravity Conjecture,”arXiv:2410.10966 [hep-th]. 13

    arXiv

  79. [79]

    Compactifications of moduli spaces inspired by mirror symmetry,

    D. R. Morrison, “Compactifications of moduli spaces inspired by mirror symmetry,” in Journ´ ees de g´ eom´ etrie alg´ ebrique d’Orsay - Juillet 1992, no. 218 in Ast´ erisque. Soci´ et´ e math´ ematique de France, 1993.arXiv:alg-geom/9304007 [alg-geom]. http://www.numdam.org/item/AST_1993__218__243_0/. 14

    Pith/arXiv arXiv 1992

  80. [80]

    Beyond the K¨ ahler Cone,

    D. R. Morrison, “Beyond the K¨ ahler Cone,” inProceedings of the Hirzebruch 65 Conference on Algebraic Geometry (Ramat Gan, 1993), pp. 361–376. 1994. arXiv:alg-geom/9407007 [alg-geom]. 14

    Pith/arXiv arXiv 1993

Showing first 80 references.