pith. machine review for the scientific record. sign in

arxiv: 2605.11068 · v1 · submitted 2026-05-11 · ✦ hep-th

Recognition: 2 theorem links

· Lean Theorem

Towards the Realization of the Dark Dimension Scenario in Hov{r}ava-Witten Theory

Ralph Blumenhagen , Antonia Paraskevopoulou
Authors on Pith no claims yet

Pith reviewed 2026-05-13 00:50 UTC · model grok-4.3

classification ✦ hep-th
keywords ava-wittendarkdimensionrealizationcouplingsgaugeincludinglimit
0
0 comments X

The pith

Hořava-Witten theory offers a potential string embedding of the dark dimension by localizing the Standard Model on the 11th interval, with symmetric tadpole cancellation and an infinite-distance limit helping derive the scalar potential and couplings from Schwinger integrals.

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

String theory often needs extra dimensions to work, but most must be tiny. The dark dimension idea proposes one extra dimension is large, around a micron, to explain dark energy. This paper looks at a version of string theory called Hořava-Witten theory, where the extra dimension is an interval between two walls. The Standard Model particles live on one wall or in the bulk of this interval. The authors note that requiring certain cancellations on the walls can reduce unwanted effects like fast proton decay. They argue that matching both the tiny dark energy and the observed strength of particle forces pushes the setup into a special limit where many quantities might be calculated simply by summing effects from many heavy particles.

Core claim

By taking not only the hierarchically small value of the dark energy but also the size of the Standard Model gauge couplings into account, one is driven to a special infinite distance limit, which is the Hořava-Witten analogue of a limit recently at the focus of the M-theoretic Emergence Proposal. Extrapolating results obtained for BPS-saturated amplitudes, we speculate about the possibility of obtaining the moduli dependence of the scalar potential, the gauge couplings and the Planck scale by simple one-loop Schwinger integrals over towers of states.

Load-bearing premise

That symmetric tadpole cancellation on the E8 walls works for generic Calabi-Yau manifolds with abelian factors and that extrapolating BPS-saturated amplitudes to the full moduli dependence of the potential and couplings is valid without additional corrections.

Figures

Figures reproduced from arXiv: 2605.11068 by Antonia Paraskevopoulou, Ralph Blumenhagen.

Figure 1
Figure 1. Figure 1: Moduli space of 4D N = 1 heterotic E8 × E8 compactifications on an isotropic Calabi-Yau described by the canonically normalized scalars corresponding to the universal saxion ˆs and the (single) K¨ahler modulus ˆτ . The arrows indicate the heterotic emergent string limit (in red) and the 5D M-theory limit (in black). The point in moduli space corresponding to the HW realization of the Dark Dimension Scenari… view at source ↗
read the original abstract

It has been suggested that Ho\v{r}ava-Witten theory could provide a concrete realization of the Dark Dimension Scenario. In this context, the observable Standard Model sector is naturally localized in the micron-sized large dimension, which is the interval in the eleventh direction. Considering Calabi-Yau manifolds supporting generic vector bundles including also abelian factors, we point out that symmetric tadpole cancellation on the $E_8$ walls has the potential to ameliorate some of the issues of such a realization, including too fast proton decay. By taking not only the hierarchically small value of the dark energy but also the size of the Standard Model gauge couplings into account, one is driven to a special infinite distance limit, which is the Ho\v{r}ava-Witten analogue of a limit recently at the focus of the M-theoretic Emergence Proposal. Extrapolating results obtained for BPS-saturated amplitudes, we speculate about the possibility of obtaining the moduli dependence of the scalar potential, the gauge couplings and the Planck scale by simple one-loop Schwinger integrals over towers of states.

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 / 1 minor

Summary. The manuscript suggests that Hořava-Witten theory can realize the Dark Dimension Scenario, with the Standard Model localized in the large eleventh dimension. It points out that symmetric tadpole cancellation on the E8 walls may ameliorate issues such as rapid proton decay for generic Calabi-Yau threefolds supporting vector bundles with abelian factors. Incorporating both the small dark energy scale and Standard Model gauge couplings drives the setup to a special infinite-distance limit analogous to those in the M-theoretic Emergence Proposal. The authors speculate that the moduli dependence of the scalar potential, gauge couplings, and Planck scale can be obtained from one-loop Schwinger integrals over towers of states by extrapolating BPS-saturated amplitude results.

Significance. If the key extrapolation from BPS amplitudes were justified and the tadpole cancellation mechanism were shown to work for generic bundles, the paper would provide a concrete string embedding of the dark dimension idea that links small dark energy, gauge couplings, and the Planck scale through an infinite-distance limit. The identification of this limit and the suggestion of a Schwinger-integral approach are potentially useful organizing ideas, but the absence of any derivation or check means the significance remains prospective rather than demonstrated.

major comments (2)
  1. [Abstract and the discussion of the infinite-distance limit] The central speculation that one-loop Schwinger integrals over towers of states yield the moduli dependence of the scalar potential, gauge couplings, and Planck scale (as stated in the abstract) rests on extrapolating results obtained only for BPS-saturated amplitudes. No argument is supplied showing why this dependence survives the inclusion of non-BPS states or higher-order corrections; this assumption is load-bearing for the proposed realization.
  2. [Abstract] The claim that symmetric tadpole cancellation on the E8 walls 'has the potential to ameliorate' issues including too-fast proton decay (abstract) is presented without an explicit check or derivation for generic Calabi-Yau threefolds with abelian factors in the bundles. This assumption underpins the phenomenological viability of the setup.
minor comments (1)
  1. The distinction between established results from prior BPS calculations and the new speculations could be made sharper to help readers assess the strength of the proposal.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments on our manuscript. We address the major comments point by point below. Revisions have been made to clarify the speculative and conjectural nature of the proposals while preserving the core ideas.

read point-by-point responses

  1. Referee: [Abstract and the discussion of the infinite-distance limit] The central speculation that one-loop Schwinger integrals over towers of states yield the moduli dependence of the scalar potential, gauge couplings, and Planck scale (as stated in the abstract) rests on extrapolating results obtained only for BPS-saturated amplitudes. No argument is supplied showing why this dependence survives the inclusion of non-BPS states or higher-order corrections; this assumption is load-bearing for the proposed realization.

    Authors: We agree that the proposal relies on an extrapolation from known BPS-saturated amplitude results, and that a full justification for the persistence of the leading moduli dependence in the presence of non-BPS states and higher-order corrections is not provided. The manuscript already presents this explicitly as a speculation ('we speculate about the possibility'), motivated by the analogy to the M-theoretic Emergence Proposal where BPS states are expected to dominate the leading behavior in the infinite-distance limit. A complete derivation would require detailed non-BPS computations that lie beyond the scope of the present work. We have revised the abstract and the relevant discussion sections to more prominently emphasize the conjectural character of the extrapolation and to note the assumption that BPS contributions control the leading moduli dependence. revision: partial

  2. Referee: [Abstract] The claim that symmetric tadpole cancellation on the E8 walls 'has the potential to ameliorate' issues including too-fast proton decay (abstract) is presented without an explicit check or derivation for generic Calabi-Yau threefolds with abelian factors in the bundles. This assumption underpins the phenomenological viability of the setup.

    Authors: The abstract employs the phrasing 'has the potential to ameliorate' precisely to signal that this is an observation with suggestive implications rather than a fully derived result. Symmetric tadpole cancellation is a standard feature of Hořava-Witten compactifications on the E8 walls, and for vector bundles containing abelian factors it can lead to cancellations among certain higher-dimensional operators that might otherwise mediate rapid proton decay. We acknowledge, however, that an explicit check or derivation for arbitrary Calabi-Yau threefolds is not carried out in the manuscript; such a check would require a systematic analysis of the matter spectrum and operator coefficients for generic bundles. We have updated the abstract and the corresponding discussion to underscore that this remains a promising direction for future model-building rather than a completed demonstration. revision: partial

Circularity Check

1 steps flagged

Moduli dependence of potential and couplings obtained by extrapolating BPS amplitudes fitted to dark energy and gauge coupling scales

specific steps
  1. fitted input called prediction [Abstract]
    "By taking not only the hierarchically small value of the dark energy but also the size of the Standard Model gauge couplings into account, one is driven to a special infinite distance limit... Extrapolating results obtained for BPS-saturated amplitudes, we speculate about the possibility of obtaining the moduli dependence of the scalar potential, the gauge couplings and the Planck scale by simple one-loop Schwinger integrals over towers of states."

    The infinite-distance limit is chosen to reproduce the input values of dark energy and gauge couplings; the subsequent claim that Schwinger integrals over towers give the moduli dependence is an extrapolation of BPS results rather than a derivation, so the functional form is forced by the same data used to select the limit.

full rationale

The paper selects a special infinite-distance limit by requiring the observed dark energy scale and SM gauge couplings to match, then extrapolates prior BPS-saturated amplitude results to claim that one-loop Schwinger integrals yield the full moduli dependence of the scalar potential, gauge couplings, and Planck scale. This reduces the claimed 'prediction' to a functional form already constrained by the input scales and the BPS results being extrapolated, with no independent derivation shown for non-BPS states or generic Calabi-Yau cases. The central claim therefore contains a fitted-input-called-prediction step rather than a first-principles derivation.

Axiom & Free-Parameter Ledger

2 free parameters · 3 axioms · 0 invented entities

The proposal rests on standard string-theory compactification assumptions plus the dark-dimension ansatz; no new entities are introduced, but several parameters are implicitly fitted to observed scales.

free parameters (2)
  • size of the large 11th dimension
    Chosen to match the observed dark energy scale and micron-scale gravity tests.
  • moduli values in the infinite-distance limit
    Determined by requiring both dark energy and Standard Model gauge coupling strengths.
axioms (3)
  • domain assumption Hořava-Witten theory provides a consistent M-theory compactification on an interval with E8 walls
    Invoked throughout as the underlying framework.
  • domain assumption Calabi-Yau manifolds admit generic vector bundles including abelian factors with symmetric tadpole cancellation
    Stated as the setting that ameliorates proton decay.
  • ad hoc to paper BPS-saturated amplitudes can be extrapolated to give the full moduli dependence of the scalar potential and couplings
    Central to the speculation about one-loop Schwinger integrals.

pith-pipeline@v0.9.0 · 5485 in / 1736 out tokens · 40757 ms · 2026-05-13T00:50:15.889904+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

71 extracted references · 71 canonical work pages · 4 internal anchors

  1. [1]

    The Swampland: Introduction and Review

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

    work page Pith review arXiv 2019

  2. [2]

    van Beest, J

    M. van Beest, J. Calder´ on-Infante, D. Mirfendereski, and I. Valenzuela, “Lectures on the Swampland Program in String Compactifications,”Phys. Rept.989(2022) 1–50, 2102.01111

    work page arXiv 2022

  3. [3]

    Gra˜ na and A

    M. Gra˜ na and A. Herr´ aez, “The Swampland Conjectures: A Bridge from Quantum Gravity to Particle Physics,”Universe7(2021), no. 8, 273,2107.00087

    work page arXiv 2021

  4. [4]

    Lectures on the string landscape and the Swampland,

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

    work page arXiv

  5. [5]

    The Dark Dimension and the Swampland,

    M. Montero, C. Vafa, and I. Valenzuela, “The dark dimension and the Swampland,” JHEP02(2023) 022,2205.12293

    work page arXiv 2023

  6. [6]

    Swamplandish Unification of the Dark Sector,

    C. Vafa, “Swamplandish Unification of the Dark Sector,”2402.00981

    work page arXiv

  7. [7]

    Landscape, Swampland, and Extra Dimensions,

    L. A. Anchordoqui, I. Antoniadis, and D. L¨ ust, “Landscape, Swampland, and Extra Dimensions,”PoSCORFU2023(2024) 215,2405.04427

    work page arXiv 2024

  8. [8]

    L¨ ust, E

    D. L¨ ust, E. Palti, and C. Vafa, “AdS and the Swampland,”Phys. Lett. B797(2019) 134867,1906.05225

    work page arXiv 2019

  9. [9]

    Emergent strings from infinite distance limits,

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

    work page arXiv 2022

  10. [10]

    Arkani-Hamed, S

    N. Arkani-Hamed, S. Dimopoulos, and G. R. Dvali, “Phenomenology, astrophysics and cosmology of theories with submillimeter dimensions and TeV scale quantum gravity,” Phys. Rev. D59(1999) 086004,hep-ph/9807344

    work page arXiv 1999

  11. [11]

    The Dark Dimension, the Swampland, and the Dark Matter Fraction Composed of Primordial Black Holes,

    L. A. Anchordoqui, I. Antoniadis, and D. L¨ ust, “Two Micron-Size Dark Dimensions,” Fortsch. Phys.73(2025), no. 8, e70015,2501.11690

    work page arXiv 2025

  12. [12]

    Stellar cooling limits on KK gravitons and dark dimensions,

    E. Hardy, A. Sokolov, and H. Stubbs, “Stellar cooling limits on KK gravitons and dark dimensions,”2510.18975

    work page arXiv

  13. [13]

    Dark dimension gravitons as dark matter,

    E. Gonzalo, M. Montero, G. Obied, and C. Vafa, “Dark dimension gravitons as dark matter,”JHEP11(2023) 109,2209.09249

    work page arXiv 2023

  14. [14]

    Dark dimension, the swampland, and the dark matter fraction composed of primordial black holes,

    L. A. Anchordoqui, I. Antoniadis, and D. L¨ ust, “Dark dimension, the swampland, and the dark matter fraction composed of primordial black holes,”Phys. Rev. D106 (2022), no. 8, 086001,2206.07071. 24 [15]DESICollaboration, M. Abdul Karimet al., “DESI DR2 results. II. Measurements of baryon acoustic oscillations and cosmological constraints,”Phys. Rev. D112...

    work page arXiv 2022

  15. [15]

    Evolving Dark Sector and the Dark Dimension Scenario,

    A. Bedroya, G. Obied, C. Vafa, and D. H. Wu, “Evolving Dark Sector and the Dark Dimension Scenario,”2507.03090

    work page arXiv

  16. [16]

    The dark dimension in a warped throat,

    R. Blumenhagen, M. Brinkmann, and A. Makridou, “The dark dimension in a warped throat,”Phys. Lett. B838(2023) 137699,2208.01057

    work page arXiv 2023

  17. [17]

    Comments concerning a hypothetical mesoscopic dark dimension,

    J. H. Schwarz, “Comments concerning a hypothetical mesoscopic dark dimension,”Int. J. Mod. Phys. A39(2024), no. 36, 2447010,2403.12899

    work page arXiv 2024

  18. [18]

    Dudas, S

    E. Dudas, S. Parameswaran, and M. Serra, “The Cosmological Constant and Dark Dimensions from Non-Supersymmetric Strings,”2512.20570

    work page arXiv

  19. [19]

    Heterotic and Type I String Dynamics from Eleven Dimensions

    P. Horava and E. Witten, “Heterotic and Type I string dynamics from eleven dimensions,”Nucl. Phys. B460(1996) 506–524,hep-th/9510209

    work page Pith review arXiv 1996

  20. [20]

    Eleven-Dimensional Supergravity on a Manifold with Boundary

    P. Horava and E. Witten, “Eleven-dimensional supergravity on a manifold with boundary,”Nucl. Phys. B475(1996) 94–114,hep-th/9603142

    work page Pith review arXiv 1996

  21. [21]

    Symmetric vacua in heterotic M theory,

    A. Lukas and B. A. Ovrut, “Symmetric vacua in heterotic M theory,”Int. J. Mod. Phys. A15(2000) 5161,hep-th/9908100

    work page arXiv 2000

  22. [22]

    The Weak Gravity Conjecture and Emergence from an Ultraviolet Cutoff

    B. Heidenreich, M. Reece, and T. Rudelius, “The Weak Gravity Conjecture and Emergence from an Ultraviolet Cutoff,”Eur. Phys. J. C78(2018), no. 4, 337, 1712.01868

    work page Pith review arXiv 2018

  23. [23]

    Infinite Distances in Field Space and Massless Towers of States,

    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

  24. [24]

    Emergence and the Swampland Conjectures

    B. Heidenreich, M. Reece, and T. Rudelius, “Emergence of Weak Coupling at Large Distance in Quantum Gravity,”Phys. Rev. Lett.121(2018), no. 5, 051601, 1802.08698

    work page Pith review arXiv 2018

  25. [25]

    EFT strings and emergence,

    F. Marchesano and L. Melotti, “EFT strings and emergence,”JHEP02(2023) 112, 2211.01409

    work page arXiv 2023

  26. [26]

    The emergence proposal in quantum gravity and the species scale,

    A. Castellano, A. Herr´ aez, and L. E. Ib´ a˜ nez, “The emergence proposal in quantum gravity and the species scale,”JHEP06(2023) 047,2212.03908. 25

    work page arXiv 2023

  27. [27]

    The emergence proposal and the emergent string,

    R. Blumenhagen, A. Gligovic, and A. Paraskevopoulou, “The emergence proposal and the emergent string,”JHEP10(2023) 145,2305.10490

    work page arXiv 2023

  28. [28]

    On the particle picture of Emergence,

    J. Hattab and E. Palti, “On the particle picture of Emergence,”JHEP03(2024) 065, 2312.15440

    work page arXiv 2024

  29. [29]

    Emergence in string theory and Fermi gases,

    J. Hattab and E. Palti, “Emergence in string theory and Fermi gases,”JHEP07 (2024) 144,2404.05176

    work page arXiv 2024

  30. [30]

    Notes on integrating out M2 branes,

    J. Hattab and E. Palti, “Notes on integrating out M2 branes,”Eur. Phys. J. C85 (2025), no. 1, 107,2410.15809

    work page arXiv 2025

  31. [31]

    Demystifying the Emergence Proposal,

    R. Blumenhagen, N. Cribiori, A. Gligovic, and A. Paraskevopoulou, “Demystifying the Emergence Proposal,”JHEP04(2024) 053,2309.11551

    work page arXiv 2024

  32. [32]

    Emergent M-theory limit,

    R. Blumenhagen, N. Cribiori, A. Gligovic, and A. Paraskevopoulou, “Emergent M-theory limit,”Phys. Rev. D109(2024), no. 2, L021901,2309.11554

    work page arXiv 2024

  33. [33]

    Emergence of R4-terms in M-theory,

    R. Blumenhagen, N. Cribiori, A. Gligovic, and A. Paraskevopoulou, “Emergence of R4-terms in M-theory,”JHEP07(2024) 018,2404.01371

    work page arXiv 2024

  34. [34]

    Emergence ofF 4-couplings in heterotic/type IIA dual string theories,

    M. Artime, R. Blumenhagen, and A. Paraskevopoulou, “Emergence ofF 4-couplings in Heterotic/Type IIA Dual String Theories,”2504.05392

    work page arXiv

  35. [35]

    The Swampland Distance Conjecture for K¨ ahler moduli,

    P. Corvilain, T. W. Grimm, and I. Valenzuela, “The Swampland Distance Conjecture for K¨ ahler moduli,”JHEP08(2019) 075,1812.07548

    work page arXiv 2019

  36. [36]

    Reflections on an M-theoretic Emergence Proposal,

    R. Blumenhagen, N. Cribiori, A. Gligovic, and A. Paraskevopoulou, “Reflections on an M-theoretic Emergence Proposal,”PoSCORFU2023(2024) 238,2404.05801

    work page arXiv 2024

  37. [37]

    Aspects of (2,0) String Compactifications,

    J. Distler and B. R. Greene, “Aspects of (2,0) String Compactifications,”Nucl. Phys. B304(1988) 1–62

    work page 1988

  38. [38]

    Heterotic anomaly cancellation in five-dimensions,

    A. Lukas and K. S. Stelle, “Heterotic anomaly cancellation in five-dimensions,”JHEP 01(2000) 010,hep-th/9911156

    work page arXiv 2000

  39. [39]

    Loop-corrected compactifications of the heterotic string with line bundles,

    R. Blumenhagen, G. Honecker, and T. Weigand, “Loop-corrected compactifications of the heterotic string with line bundles,”JHEP06(2005) 020,hep-th/0504232

    work page arXiv 2005

  40. [40]

    Heterotic GUT and standard model vacua from simply connected Calabi-Yau manifolds,

    R. Blumenhagen, S. Moster, and T. Weigand, “Heterotic GUT and standard model vacua from simply connected Calabi-Yau manifolds,”Nucl. Phys. B751(2006) 186–221,hep-th/0603015. 26

    work page arXiv 2006

  41. [41]

    Two Hundred Heterotic Standard Models on Smooth Calabi-Yau Threefolds,

    L. B. Anderson, J. Gray, A. Lukas, and E. Palti, “Two Hundred Heterotic Standard Models on Smooth Calabi-Yau Threefolds,”Phys. Rev. D84(2011) 106005, 1106.4804

    work page arXiv 2011

  42. [42]

    Strong coupling expansion of Calabi-Yau compactification,

    E. Witten, “Strong coupling expansion of Calabi-Yau compactification,”Nucl. Phys. B 471(1996) 135–158,hep-th/9602070

    work page arXiv 1996

  43. [43]

    Cvetiˇ c and M

    M. Cvetiˇ c and M. Wiesner, “Nonperturbative resolution of strong coupling singularities in 4D N=1 heterotic M-theory,”Phys. Rev. D110(2024), no. 10, 106008,2408.12458

    work page arXiv 2024

  44. [44]

    Four flux and warped heterotic M theory compactifications,

    G. Curio and A. Krause, “Four flux and warped heterotic M theory compactifications,” Nucl. Phys. B602(2001) 172–200,hep-th/0012152

    work page arXiv 2001

  45. [45]

    The dark dimension, proton decay, and the length of the M-theory interval,

    M. Reig and I. Ruiz, “The dark dimension, proton decay, and the length of the M-theory interval,”2510.25832

    work page arXiv

  46. [46]

    Quantum obstructions for $N=1$ infinite distance limits -- Part I: $g_s$ obstructions

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

    work page internal anchor Pith review Pith/arXiv arXiv

  47. [47]

    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

    work page arXiv

  48. [48]

    On Quantum Obstructions in Type IIA Orientifolds

    L. Kaufmann, T. Weigand, and M. Wiesner, “On Quantum Obstructions in Type IIA Orientifolds,”2604.25988

    work page internal anchor Pith review Pith/arXiv arXiv

  49. [49]

    Beyond the standard embedding in M theory on S**1 / Z(2),

    Z. Lalak, S. Pokorski, and S. Thomas, “Beyond the standard embedding in M theory on S**1 / Z(2),”Nucl. Phys. B549(1999) 63–97,hep-ph/9807503

    work page arXiv 1999

  50. [50]

    Low-Energy Remnants of Superstring Anomaly Cancellation Terms,

    L. E. Ibanez and H. P. Nilles, “Low-Energy Remnants of Superstring Anomaly Cancellation Terms,”Phys. Lett. B169(1986) 354–358

    work page 1986

  51. [51]

    Couplings and Scales in Strongly Coupled Heterotic String Theory

    T. Banks and M. Dine, “Couplings and scales in strongly coupled heterotic string theory,”Nucl. Phys. B479(1996) 173–196,hep-th/9605136

    work page Pith review arXiv 1996

  52. [52]

    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,hep-th/0110129

    work page arXiv 2002

  53. [53]

    Black Holes and Large N Species Solution to the Hierarchy Problem

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

    work page Pith review arXiv 2010

  54. [54]

    On Gauge couplings in string theory,

    V. Kaplunovsky and J. Louis, “On Gauge couplings in string theory,”Nucl. Phys. B 444(1995) 191–244,hep-th/9502077

    work page arXiv 1995

  55. [55]

    Type I/heterotic duality and M-theory amplitudes,

    M. B. Green and A. Rudra, “Type I/heterotic duality and M-theory amplitudes,” JHEP12(2016) 060,1604.00324. 27

    work page arXiv 2016

  56. [56]

    Heterotic type I superstring duality and low-energy effective actions,

    A. A. Tseytlin, “Heterotic type I superstring duality and low-energy effective actions,” Nucl. Phys. B467(1996) 383–398,hep-th/9512081

    work page arXiv 1996

  57. [57]

    Gravitational Threshold Corrections in Non-Supersymmetric Heterotic Strings,

    I. Florakis, “Gravitational Threshold Corrections in Non-Supersymmetric Heterotic Strings,”Nucl. Phys. B916(2017) 484–509,1611.10323

    work page arXiv 2017

  58. [58]

    Dark dimension and the grand unification of forces,

    J. J. Heckman, C. Vafa, T. Weigand, and F. Xu, “Dark dimension and the grand unification of forces,”Phys. Rev. D111(2025), no. 4, 046014,2409.01405

    work page arXiv 2025

  59. [59]

    Grieco, I

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

    work page arXiv

  60. [60]

    The EFT stringy viewpoint on large distances,

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

    work page arXiv 2021

  61. [61]

    Large Field Distances from EFT strings,

    S. Lanza, F. Marchesano, L. Martucci, and I. Valenzuela, “Large Field Distances from EFT strings,”PoSCORFU2021(2022) 169,2205.04532

    work page arXiv 2022

  62. [62]

    Taxonomy of Instanton Corrections in Infinite Distance Limits

    M. Artime, R. Blumenhagen, and P. Leivadaros, “Taxonomy of Instanton Corrections in Infinite Distance Limits,”2605.03005

    work page internal anchor Pith review Pith/arXiv arXiv

  63. [63]

    Heterotic M theory in five-dimensions,

    A. Lukas, B. A. Ovrut, K. S. Stelle, and D. Waldram, “Heterotic M theory in five-dimensions,”Nucl. Phys. B552(1999) 246–290,hep-th/9806051

    work page arXiv 1999

  64. [64]

    M theory and topological strings. 1.,

    R. Gopakumar and C. Vafa, “M theory and topological strings. 1.,”hep-th/9809187

    work page arXiv

  65. [65]

    M theory and topological strings. 2.,

    R. Gopakumar and C. Vafa, “M theory and topological strings. 2.,”hep-th/9812127

    work page arXiv

  66. [66]

    On $R^4$ threshold corrections in IIB string theory and (p,q) string instantons

    E. Kiritsis and B. Pioline, “On R**4 threshold corrections in IIb string theory and (p, q) string instantons,”Nucl. Phys. B508(1997) 509–534,hep-th/9707018

    work page Pith review arXiv 1997

  67. [67]

    One Loop Threshold Effects in String Unification,

    V. S. Kaplunovsky, “One Loop Threshold Effects in String Unification,”Nucl. Phys. B 307(1988) 145–156,hep-th/9205068. [Erratum: Nucl.Phys.B 382, 436–438 (1992)]

    work page internal anchor Pith review arXiv 1988

  68. [68]

    Moduli dependence of string loop corrections to gauge coupling constants,

    L. J. Dixon, V. Kaplunovsky, and J. Louis, “Moduli dependence of string loop corrections to gauge coupling constants,”Nucl. Phys. B355(1991) 649–688

    work page 1991

  69. [69]

    Threshold corrections to gauge couplings in orbifold compactifications,

    P. Mayr and S. Stieberger, “Threshold corrections to gauge couplings in orbifold compactifications,”Nucl. Phys. B407(1993) 725–748,hep-th/9303017

    work page arXiv 1993

  70. [70]

    SUSY quivers, intersecting branes and the modest hierarchy problem,

    D. Cremades, L. E. Ibanez, and F. Marchesano, “SUSY quivers, intersecting branes and the modest hierarchy problem,”JHEP07(2002) 009,hep-th/0201205

    work page arXiv 2002

  71. [71]

    Hypercharge Flux in Heterotic Compactifications,

    L. B. Anderson, A. Constantin, S.-J. Lee, and A. Lukas, “Hypercharge Flux in Heterotic Compactifications,”Phys. Rev. D91(2015), no. 4, 046008,1411.0034. 28

    work page arXiv 2015