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REVIEW 3 major objections 4 minor 2 cited by

Approximate Symmetries and Gravity

T0 review · 3 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read The paper asserts the Swampland Symmetry Conjecture: in the presence of gravity, every approximate global symmetry must be violated by local EFT processes at least as fast as thermal black holes violate it, with explicit lower bounds on…

desk verdict Makes the 'gravity kills global symmetries' intuition into a concrete, checkable conjecture with careful thermal black-hole rate calculations; the main caveat is that the quantitative floor is calibrated by an unproven assumption about the black-hole population. read the letter →

arxiv 1909.02002 v2 pith:CZMGF5MV submitted 2019-09-04 hep-th

Sylvain Fichet , Prashant Saraswat This is my paper · ORCID
classification hep-th PACS 04.60.-m04.70.-s11.30.-j11.15.-q
keywords approximateglobalsymmetriesswamplandblackholeseffectivefieldtheoryweakgravityconjecturechargeviolationthermalbathemergent
topics Quantum Gravity
open problems Quantum Gravity
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

Global symmetries are useful approximate notions in particle physics, but quantum gravity is thought to forbid them from being exact. This paper asks how inexact they must be, and answers with a quantitative conjecture: at any sub-Planckian temperature, local effective-field-theory processes that break a global symmetry must destroy global charge at least as fast as a thermal population of microscopic black holes does. The black-hole rate is computed from particle capture by the smallest semiclassical black holes, giving a universal, Boltzmann-suppressed floor. The resulting Swampland Symmetry Conjecture translates into explicit lower bounds on symmetry-violating operator coefficients, upper bounds on operator dimensions, and upper bounds on the masses of fields involved (Eqs. 8.3–8.5). If correct, it turns the old qualitative prohibition of global symmetries in gravity into a quantitative constraint on model building.

What carries the argument

The load-bearing mechanism is the thermal population of minimal black holes of radius $R_*\approx \Lambda^{-1}$ in a static universe at temperature $T<\Lambda/8\pi$, whose capture of charged particles, using the Unruh absorption cross-section, sets the irreducible rate $\Gamma_{\rm BH}$. The local rate bound compares this rate with the thermal rate $\Gamma_{\rm EFT}$ from a local operator of dimension $d_{\not G}$, and the comparison is carried out logarithmically because both rates are dominated by Boltzmann factors. The inequality $\Gamma_{\rm BH}\lesssim (\Delta G)^2\Gamma_{\rm EFT}$ is the machinery that converts gravitational reasoning into constraints on operator coefficients, operator dimensions, and field masses.

What would settle it

Take a specific UV-complete quantum-gravity construction with an approximate global symmetry, compute the thermal rate of global-charge decay at T = Lambda/8 pi from the EFT operators, and compare with the black-hole capture rate; finding the EFT rate smaller than the black-hole rate would refute the local rate bound, as would showing that black-hole nucleation near the critical radius outruns the formation of the minimal black-hole population.

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Extended reading notes

Core claim

The central discovery is a proposed quantitative version of the quantum-gravity prohibition on global symmetries: the local rate bound $\Gamma_{\rm BH}\lesssim \Gamma_{\rm EFT}$ for global-charge violation. The authors compute $\Gamma_{\rm BH}$ for a hot static universe containing a Boltzmann-suppressed density of the smallest black holes, of radius $R_*\sim \Lambda^{-1}$, using particle capture as the dominant charge-destroying process. They then conjecture—the Swampland Symmetry Conjecture—that any effective field theory with an exact or approximate global symmetry is UV-completed, at a cutoff $\Lambda\lesssim M_{\rm Pl}$, into an EFT with no exact global symmetry and with all approximate symmetries satisfying the local rate bound for $T<\Lambda/8\pi$. The paper derives sufficient bounds on a single symmetry-violating operator: $\log c_{\not G}\gtrsim -4\pi/(G_N\Lambda^2)$, $d_{\not G}\log d_{\not G}\lesssim 4\pi/(G_N\Lambda^2)$, and $\sum_i m_i\lesssim 1/(G_N\Lambda)$. It also shows that gauging the symmetry and applying the Weak Gravity Conjecture enforces these bounds in models of accidental symmetry, and that Froggatt–Nielsen, clockwork, and extra-dimensional localization mechanisms either satisfy the bound or are completed by new physics below the scale the bound predicts.

Load-bearing premise

The central assumption is that microscopic black holes of radius roughly the EFT cutoff form in a hot bath and stay the fastest gravity-induced way to destroy global charge, before larger black holes nucleate and engulf the space.

Editorial extensions

If this is right

  • If the SSC holds, the most complete sub-Planckian EFT of any quantum-gravity theory must violate every approximate global symmetry at a rate at least as large as the black-hole capture rate, with the explicit bounds of Eqs. (8.3)–(8.5).
  • Gauge symmetries cannot hide global symmetries: in models where high-dimensional gauge-charge assignments make a global symmetry accidental, the Lattice or Tower Weak Gravity Conjecture supplies enough charged states to break the symmetry at the required level, so the SSC follows from the WGC.
  • In Froggatt–Nielsen, clockwork, and extra-dimensional localization models, exponentially exact symmetries are either consistent with the bound at low energy or predict a cutoff $\Lambda_{\rm SSC}$ below the Planck scale, giving a concrete target for new physics; the exception found is the case of an exponentially large discrete symmetry.
  • The bounds depend only on the black-hole capture rate and extend to higher-dimensional theories with the appropriate higher-dimensional Planck scale, as used for the extra-dimensional models in the paper.
  • A low-energy observer measuring a very small symmetry-violating coefficient $c$ can compute $\Lambda_{\rm SSC}=M_{\rm Pl}\sqrt{-32\pi^2/\log c}$; if this lies below $M_{\rm Pl}$, the observer predicts new degrees of freedom below that scale.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The paper's logic gives a quantitative handle on the axion-quality problem: for a Peccei-Quinn-like shift symmetry broken only by a small coefficient, Eq. (8.3) fixes the maximum cutoff at which the symmetry can be as exact as observed, so either symmetry-breaking physics appears below that scale or the symmetry cannot be that exact.
  • The rate bound could be tested in holographic or other controlled UV completions by computing the thermal decay rate of a global U(1) charge at $T<\Lambda/8\pi$ and comparing with the black-hole capture rate; a controlled example with $\Gamma_{\rm EFT}<\Gamma_{\rm BH}$ would require modifying the SSC.
  • If the conjecture is true, exact global symmetries cannot be recovered even as limits: any limit that makes a symmetry exact—infinite localization, infinite discrete charge, or zero gauge coupling—is obstructed at a scale set by the black-hole floor, in the same way the Weak Gravity Conjecture obstructs $g\to 0$.
  • The discrete-symmetry case is the least settled: the paper leaves open a swampland constraint on $\mathbb{Z}_N$ size, and adding the assumption that discrete symmetries are always gauged and bounded would likely remove the clockwork large-discrete-symmetry exception.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper addresses the question of how exact an approximate global symmetry can be in an effective field theory coupled to gravity. It sets up a finite-temperature thought experiment in which a thermal population of small semiclassical black holes produces an irreducible rate Γ^G_BH for the destruction of global charge, primarily through capture. The paper then conjectures a “local rate bound” (Eq. 8.1) and elevates it to a Swampland Symmetry Conjecture (SSC): in any quantum-gravity-consistent EFT, local symmetry-violating processes should be at least as fast as the black-hole processes for T < Λ/8π. Combining this conjecture with explicit EFT operator rates yields quantitative bounds on operator coefficients, operator dimensions, and particle masses (Eqs. 8.3–8.5). The remainder of the paper checks the consistency of this proposal with the Weak Gravity Conjecture and with QFT models of emergent symmetries (Froggatt–Nielsen, clockwork, and extra-dimensional localization), finding that existing swampland constraints often enforce the bound.

Significance. If the local rate bound is valid, the paper establishes a novel quantitative swampland constraint on approximate global symmetries, with concrete bounds on operator coefficients, dimensions, and masses. The paper’s main strengths are its careful analytic treatment of the thermal black-hole population and capture rates (Sec. 5), the non-relativistic n-body rate calculation (App. A), and the Boltzmann equations for charge decay (Sec. 7.1). The consistency checks with the WGC and the species bound are also valuable and give nontrivial support to the proposal. However, the central statement is explicitly a conjecture, and two technical issues—the calibration of the black-hole floor and a factor-of-two error in the operator rate formula—need attention before the quantitative bounds can be taken at face value.

major comments (3)
  1. [Secs. 5.3, 5.5, and Eq. (7.12)] The calibration of Γ^G_BH as an irreducible floor depends on the claim that a thermal population of minimal black holes (radius R_* = Λ^{-1}) builds up before the nucleation of unstable large black holes. At the maximal temperature T_* = Λ/(8π), the rates have the same exponential suppression: M_*/T_* = 1/(16πG_N T_*^2) = 4π/(G_NΛ^2). The separation therefore rests on the subleading entropy factor e^{4πG_N M_*^2} in the capture rate and on the unproven assumption that semiclassical gravity is valid down to R_* = Λ^{-1}; the paper explicitly argues only at the level of logarithms in Sec. 5.3. If Λ is close to M_Pl, or if quantum-gravity effects set in at distances larger than Λ^{-1}, the computed Γ^G_BH is not an irreducible floor and the bounds (Eqs. 8.3–8.5) shift by exponentially large factors. I ask the authors to provide a quantitative control of the timescale separation, including prefactors, or to state this limitation as a clearly quantified condition on the validity of the SSC.
  2. [Sec. 6 and Eq. (8.3)] The operator O_G has Lagrangian coefficient c_G in Eq. (6.2), so a process with one insertion has amplitude proportional to c_G and rate proportional to c_G^2. The displayed rate formulas (6.4) and (6.5), however, use log c_G as if the rate were linear in c_G; App. A even omits c_G entirely from |M|^2. Consequently the logarithms in Eqs. (6.8)–(6.9) and the log-coefficient bound (8.3) miss a factor of 2. With the standard normalization of the Lagrangian coefficient, the bound should be log c_G ≳ -2π/(G_NΛ^2) (up to O(1) corrections), not -4π/(G_NΛ^2). This factor is numerically significant because the right-hand side is large. Please clarify the convention for c_G and propagate the factor through Eqs. (7.15), (7.16), and (8.3).
  3. [Sec. 8, SSC statement] As stated, the SSC does not directly constrain any EFT defined below M_Pl: one can always postulate a completion just below the Planck scale that satisfies the local rate bound, a point the authors themselves acknowledge in Sec. 8. In its present form the conjecture is therefore difficult to falsify with sub-Planckian data, and the examples in Secs. 9 and 10, while consistent with the SSC, do not test it against low-energy EFTs that would violate it. I recommend making the conjecture more predictive, for example by requiring the completion scale to be bounded in terms of the symmetry-violating parameters of the original EFT, or by sharply specifying a class of EFTs for which the local rate bound itself is conjectured to hold.
minor comments (4)
  1. [Sec. 10.1 and table of contents] The name is spelled “Frogatt-Nielsen” in the section heading and in the text; it should be “Froggatt–Nielsen.”
  2. [Eq. (6.5)] There is an unbalanced parenthesis in the denominator: “Γ(3n_G/4 − 3/2))” contains an extra closing parenthesis.
  3. [Sec. 5.3, discussion after Eq. (5.12)] The sentence “the formation rate of these black holes, ∝ exp(−1/(4πG_NT^2), is always less than the thermalization time Eq. (5.12) for black holes much smaller than Mc” compares a rate with a time and is dimensionally confusing; please rephrase to state explicitly which rate is being compared with which time.
  4. [Eq. (10.9)] The symbol “&” is used in Eq. (10.9) as a comparison; it should be “≳” (or the text should define the notation) to avoid confusion.

Circularity Check

0 steps flagged · score 2.0 of 10

No circular derivation: the central local rate bound is explicitly conjectural, and the supporting checks use independent swampland principles rather than the bound itself.

full rationale

The derivation chain is not circular. The black-hole rate Γ_BH is computed from standard semiclassical black-hole thermodynamics and Unruh's absorption cross-section (Sec. 5), while the EFT rate Γ_EFT is computed from operator power counting (Sec. 6); neither side is fitted to the other. The central inequality Γ_BH ≲ Γ_EFT is not claimed to be derived: Sec. 3 states, 'This bound is well motivated, but is not proven either. In the following we will take it as a conjecture,' and Sec. 8 formalizes it as the Swampland Symmetry Conjecture. The bounds in Eqs. (8.3)-(8.5) are conditional consequences of that conjecture, not fitted parameters renamed as predictions. The model checks in Secs. 9-10 import independent external ingredients: the Weak Gravity Conjecture [2,21-24], the species bound [45,52-54], and holographic no-global-symmetry results [3,4], none of which is equivalent to the SSC. The only self-citations ([43] for the gauge-clockwork example, [55] and [57] for technical points in extra-dimensional localization) are illustrative or side remarks and carry none of the argument's weight. The paper also explicitly invites counterexamples in the Conclusions, reinforcing that the SSC is a falsifiable conjecture rather than a conclusion built into its inputs. Accordingly, no step reduces by construction to its input; the residual score reflects only the presence of minor non-load-bearing self-citations.

Assumptions & free parameters 1 free parameters · 6 assumptions · 0 invented entities

The paper introduces a conjecture (SSC) and a local rate bound, not new physical entities. The main scale, Λ, is a free input controlling the strength of the bounds. Most inputs are established semiclassical results or conjectures from the swampland literature (WGC, species bound); these are listed as domain assumptions since the paper relies on them without proof.

free parameters (1)
  • Universal cutoff Λ (with Λ_grav = Λ)
    The strength of all bounds and the minimal black hole mass M* = 1/(2 G_N Λ) depend on this scale. The paper notes that taking a single universal cutoff is 'not fully mandatory' (Sec. 7.2) but uses it throughout, e.g., Eq. (7.13).
assumptions (6)
  • ad hoc to paper Local rate bound: Γ⁄G_BH ≲ Γ⁄G_EFT for T < Λ/8π (Eq. 8.1)
    Core unproven conjecture introduced in Sec. 3 ('we will take it as a conjecture') and used to define the SSC.
  • domain assumption Semiclassical black hole formation cross-section γ2(s) ≈ (π/4) G_N^2 s^2 for s > M*^2 (Eq. 5.2)
    Standard semiclassical estimate from Banks-Fischler, Giddings-Thomas, Dimopoulos-Landsberg, assumed without derivation.
  • domain assumption Small black holes reach thermal equilibrium before large black holes nucleate and destabilize hot flat space (Sec. 5.3)
    Justifies considering only M ≪ Mc; depends on rate estimates and the finite static-universe construction.
  • domain assumption Weak Gravity Conjecture (Lattice/Tower forms) holds for gauge theories coupled to gravity (Sec. 9.1)
    Unproven background conjecture used to show the SSC is satisfied in models with accidental global symmetries from gauged U(1)s.
  • domain assumption Species bound Λ ≲ M_Pl/√N (Eq. 10.8)
    Unproven conjecture from Dvali et al. used in the clockwork-model consistency check (Sec. 10.2).
  • domain assumption Black hole entropy S = A/(4 G_N) is finite and counts all microstates, so exact continuous global symmetries are inconsistent (Sec. 1)
    Standard quantum-gravity lore used to motivate the search for a quantitative bound.

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Pith. "Pith review of Approximate Symmetries and Gravity." pith.science (2026). https://pith.science/paper/CZMGF5MV

@misc{pith2026190902002,
  author       = {Pith},
  title        = {Pith review of: Approximate Symmetries and Gravity},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/CZMGF5MV}},
  note         = {Machine review of arXiv:1909.02002}
}
read the original abstract

There are strong reasons to believe that global symmetries of quantum theories cannot be exact in the presence of gravity. While this has been argued at the qualitative level, establishing a quantitative statement is more challenging. In this work we take new steps towards quantifying symmetry violation in EFTs with gravity. First, we evaluate global charge violation by microscopic black holes present in a thermal system, which represents an irreducible, universal effect at finite temperature. Second, based on general QFT considerations, we propose that local symmetry-violating processes should be faster than black hole-induced processes at any sub-Planckian temperature. Such a proposal can be seen as part of the "swampland" program to constrain EFTs emerging from quantum gravity. Considering an EFT perspective, we formulate a conjecture which requires the existence of operators violating global symmetry and places quantitative bounds on them. We study the interplay of our conjecture with emergent symmetries in QFT. In models where gauged U(1)'s enforce accidental symmetries, we find that constraints from the Weak Gravity Conjecture can ensure that our conjecture is satisfied. We also study the consistency of the conjecture with QFT models of emergent symmetries such as extradimensional localization, the Froggatt-Nielsen mechanism, and the clockwork mechanism.

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Works this paper leans on

58 extracted references · 18 canonical work pages · cited by 2 Pith papers

  1. [1]

    Banks and N

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

    arXiv 2011

  2. [2]

    Arkani-Hamed, L

    N. Arkani-Hamed, L. Motl, A. Nicolis, and C. Vafa, The String landscape, black holes and gravity as the weakest force , JHEP 06 (2007) 060, [ hep-th/0601001]

    arXiv 2007

  3. [3]

    Harlow and H

    D. Harlow and H. Ooguri, Symmetries in quantum field theory and quantum gravity , arXiv:1810.05338

    arXiv

  4. [4]

    Harlow and H

    D. Harlow and H. Ooguri, Constraints on Symmetries from Holography , Phys. Rev. Lett. 122 (2019), no. 19 191601, [ arXiv:1810.05337]

    arXiv 2019

  5. [5]

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

    work page 1988

  6. [6]

    Rey, The Axion Dynamics in Wormhole Background , Phys

    S.-J. Rey, The Axion Dynamics in Wormhole Background , Phys. Rev. D39 (1989) 3185

    work page 1989

  7. [7]

    Kallosh, A

    R. Kallosh, A. D. Linde, D. A. Linde, and L. Susskind, Gravity and global symmetries , Phys. Rev. D52 (1995) 912–935, [ hep-th/9502069]

    arXiv 1995

  8. [8]

    Alonso and A

    R. Alonso and A. Urbano, Wormholes and masses for Goldstone bosons , JHEP 02 (2019) 136, [arXiv:1706.07415]

    arXiv 2019

Show all 58 references
  1. [9]

    S. R. Coleman, Black Holes as Red Herrings: Topological Fluctuations and the Loss of Quantum Coherence, Nucl. Phys. B307 (1988) 867–882

    1988

  2. [10]

    S. B. Giddings and A. Strominger, Loss of Incoherence and Determination of Coupling Constants in Quantum Gravity , Nucl. Phys. B307 (1988) 854–866

    1988

  3. [11]

    L. F. Abbott and M. B. Wise, Wormholes and Global Symmetries , Nucl. Phys. B325 (1989) 687–704

    1989

  4. [12]

    S. R. Coleman, Why There Is Nothing Rather Than Something: A Theory of the Cosmological Constant, Nucl. Phys. B310 (1988) 643–668

    1988

  5. [13]

    Hebecker, T

    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, [arXiv:1807.00824]

    2018 arXiv

  6. [14]

    Rudelius, Constraints on Axion Inflation from the Weak Gravity Conjecture , JCAP 1509 (2015), no

    T. Rudelius, Constraints on Axion Inflation from the Weak Gravity Conjecture , JCAP 1509 (2015), no. 09 020, [ arXiv:1503.00795]. 42

    2015 arXiv

  7. [15]

    Brown, W

    J. Brown, W. Cottrell, G. Shiu, and P. Soler, Fencing in the Swampland: Quantum Gravity Constraints on Large Field Inflation , JHEP 10 (2015) 023, [ arXiv:1503.04783]

    2015 arXiv

  8. [16]

    Heidenreich, M

    B. Heidenreich, M. Reece, and T. Rudelius, Weak Gravity Strongly Constrains Large-Field Axion Inflation, JHEP 12 (2015) 108, [ arXiv:1506.03447]

    2015 arXiv

  9. [17]

    Hebecker and P

    A. Hebecker and P. Henkenjohann, Gauge and gravitational instantons: From 3-forms and fermions to Weak Gravity and flat axion potentials , JHEP 09 (2019) 038, [arXiv:1906.07728]

    2019 arXiv

  10. [18]

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

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

    arXiv

  11. [19]

    Ooguri and C

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

    2007 arXiv

  12. [20]

    Palti, The Swampland: Introduction and Review , Fortsch

    E. Palti, The Swampland: Introduction and Review , Fortsch. Phys. 67 (2019), no. 6 1900037, [arXiv:1903.06239]

    2019 arXiv

  13. [21]

    Cheung and G

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

    2014 arXiv

  14. [22]

    Heidenreich, M

    B. Heidenreich, M. Reece, and T. Rudelius, Sharpening the Weak Gravity Conjecture with Dimensional Reduction, JHEP 02 (2016) 140, [ arXiv:1509.06374]

    2016 arXiv

  15. [23]

    Heidenreich, M

    B. Heidenreich, M. Reece, and T. Rudelius, Evidence for a sublattice weak gravity conjecture , JHEP 08 (2017) 025, [ arXiv:1606.08437]

    2017 arXiv

  16. [24]

    Andriolo, D

    S. Andriolo, D. Junghans, T. Noumi, and G. Shiu, A Tower Weak Gravity Conjecture from Infrared Consistency, Fortsch. Phys. 66 (2018), no. 5 1800020, [ arXiv:1802.04287]

    2018 arXiv

  17. [25]

    Grossman and M

    Y. Grossman and M. Neubert, Neutrino masses and mixings in nonfactorizable geometry , Phys. Lett. B474 (2000) 361–371, [ hep-ph/9912408]

    2000 arXiv

  18. [26]

    C. D. Froggatt and H. B. Nielsen, Hierarchy of Quark Masses, Cabibbo Angles and CP Violation, Nucl. Phys. B147 (1979) 277–298

    1979

  19. [27]

    Dvali, C

    G. Dvali, C. Gomez, R. S. Isermann, D. L¨ ust, and S. Stieberger, Black hole formation and classicalization in ultra-Planckian 2→N scattering, Nucl. Phys. B893 (2015) 187–235, [arXiv:1409.7405]

    2015 arXiv

  20. [28]

    Dvali, Strong Coupling and Classicalization , Subnucl

    G. Dvali, Strong Coupling and Classicalization , Subnucl. Ser. 53 (2017) 189–200, [arXiv:1607.07422]

    2017 arXiv

  21. [29]

    D. J. Gross, M. J. Perry, and L. G. Yaffe, Instability of Flat Space at Finite Temperature , Phys. Rev. D25 (1982) 330–355

    1982

  22. [30]

    E. R. Harrison, Normal Modes of Vibrations of the Universe , Rev. Mod. Phys. 39 (1967) 862–882

    1967

  23. [31]

    J. D. Barrow, G. F. R. Ellis, R. Maartens, and C. G. Tsagas, On the stability of the Einstein static universe, Class. Quant. Grav. 20 (2003) L155–L164, [ gr-qc/0302094]

    2003 arXiv

  24. [32]

    J. W. York, Jr., Black hole thermodynamics and the Euclidean Einstein action , Phys. Rev. D33 (1986) 2092–2099

    1986

  25. [33]

    Banks and W

    T. Banks and W. Fischler, A Model for high-energy scattering in quantum gravity , hep-th/9906038

    arXiv

  26. [34]

    S. B. Giddings and S. D. Thomas, High-energy colliders as black hole factories: The End of short distance physics , Phys. Rev. D65 (2002) 056010, [ hep-ph/0106219]. 43

    2002 arXiv

  27. [35]

    Dimopoulos and G

    S. Dimopoulos and G. L. Landsberg, Black holes at the LHC , Phys. Rev. Lett. 87 (2001) 161602, [hep-ph/0106295]

    2001 arXiv

  28. [36]

    J. A. Conley and T. Wizansky, Microscopic Primordial Black Holes and Extra Dimensions , Phys. Rev. D75 (2007) 044006, [ hep-ph/0611091]

    2007 arXiv

  29. [37]

    Borunda and M

    M. Borunda and M. Masip, Black hole gas in the early universe , JCAP 1001 (2010) 027, [arXiv:0910.4532]

    2010 arXiv

  30. [38]

    Nakama and J

    T. Nakama and J. Yokoyama, Micro black holes formed in the early Universe and their cosmological implications, Phys. Rev. D99 (2019), no. 6 061303, [ arXiv:1811.05049]

    2019 arXiv

  31. [39]

    Piran and R

    T. Piran and R. M. Wald, Rate of Black Hole Formation in a Thermal Box , Phys. Lett. 90A (1982) 20–22

    1982

  32. [40]

    H. W. Braden, B. F. Whiting, and J. W. York, Jr., Density of States for the Gravitational Field in Black Hole Topologies , Phys. Rev. D36 (1987) 3614

    1987

  33. [41]

    W. G. Unruh, Absorption Cross-Section of Small Black Holes , Phys. Rev. D14 (1976) 3251–3259

    1976

  34. [42]

    S.-J. Lee, W. Lerche, and T. Weigand, Modular Fluxes, Elliptic Genera, and Weak Gravity Conjectures in Four Dimensions , arXiv:1901.08065

    1901 arXiv

  35. [43]

    Saraswat, Weak gravity conjecture and effective field theory , Phys

    P. Saraswat, Weak gravity conjecture and effective field theory , Phys. Rev. D95 (2017), no. 2 025013, [arXiv:1608.06951]

    2017 arXiv

  36. [44]

    Dvali, M

    G. Dvali, M. Redi, S. Sibiryakov, and A. Vainshtein, Gravity Cutoff in Theories with Large Discrete Symmetries, Phys. Rev. Lett. 101 (2008) 151603, [ arXiv:0804.0769]

    2008 arXiv

  37. [45]

    Dvali, Black Holes and Large N Species Solution to the Hierarchy Problem , Fortsch

    G. Dvali, Black Holes and Large N Species Solution to the Hierarchy Problem , Fortsch. Phys. 58 (2010) 528–536, [ arXiv:0706.2050]

    2010 arXiv

  38. [46]

    Craig, I

    N. Craig, I. Garcia Garcia, and S. Koren, Discrete Gauge Symmetries and the Weak Gravity Conjecture, JHEP 05 (2019) 140, [ arXiv:1812.08181]

    2019 arXiv

  39. [47]

    K. Choi, H. Kim, and S. Yun, Natural inflation with multiple sub-Planckian axions , Phys. Rev. D90 (2014) 023545, [ arXiv:1404.6209]

    2014 arXiv

  40. [48]

    Higaki and F

    T. Higaki and F. Takahashi, Natural and Multi-Natural Inflation in Axion Landscape , JHEP 07 (2014) 074, [ arXiv:1404.6923]

    2014 arXiv

  41. [49]

    Choi and S

    K. Choi and S. H. Im, Realizing the relaxion from multiple axions and its UV completion with high scale supersymmetry , JHEP 01 (2016) 149, [ arXiv:1511.00132]

    2016 arXiv

  42. [50]

    D. E. Kaplan and R. Rattazzi, Large field excursions and approximate discrete symmetries from a clockwork axion , Phys. Rev. D93 (2016), no. 8 085007, [ arXiv:1511.01827]

    2016 arXiv

  43. [51]

    P. W. Graham, D. E. Kaplan, and S. Rajendran, Cosmological Relaxation of the Electroweak Scale, Phys. Rev. Lett. 115 (2015), no. 22 221801, [ arXiv:1504.07551]

    2015 arXiv

  44. [52]

    G. R. Dvali, G. Gabadadze, M. Kolanovic, and F. Nitti, Scales of gravity, Phys. Rev. D65 (2002) 024031, [ hep-th/0106058]

    2002 arXiv

  45. [53]

    Veneziano, Large N bounds on, and compositeness limit of, gauge and gravitational interactions, JHEP 06 (2002) 051, [ hep-th/0110129]

    G. Veneziano, Large N bounds on, and compositeness limit of, gauge and gravitational interactions, JHEP 06 (2002) 051, [ hep-th/0110129]

    2002 arXiv

  46. [54]

    Dvali and M

    G. Dvali and M. Redi, Black Hole Bound on the Number of Species and Quantum Gravity at LHC, Phys. Rev. D77 (2008) 045027, [ arXiv:0710.4344]. 44

    2008 arXiv

  47. [55]

    Fichet and G

    S. Fichet and G. von Gersdorff, Anomalous gauge couplings from composite Higgs and warped extra dimensions, JHEP 03 (2014) 102, [ arXiv:1311.6815]

    2014 arXiv

  48. [56]

    W. D. Goldberger and I. Z. Rothstein, High-energy field theory in truncated AdS backgrounds, Phys. Rev. Lett. 89 (2002) 131601, [ hep-th/0204160]

    2002 arXiv

  49. [57]

    Fichet, Opacity and effective field theory in antide Sitter backgrounds , Phys

    S. Fichet, Opacity and effective field theory in antide Sitter backgrounds , Phys. Rev. D100 (2019), no. 9 095002, [ arXiv:1905.05779]

    2019 arXiv

  50. [58]

    Creminelli, A

    P. Creminelli, A. Nicolis, and R. Rattazzi, Holography and the electroweak phase transition , JHEP 03 (2002) 051, [ hep-th/0107141]. 45

    2002 arXiv

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Reviewed August 14, 2026 · model on record in the stance chip above.