Pith. sign in

REVIEW 2 major objections 5 minor 1 cited by

Near the boundary of large complex structure, the first worldsheet instanton can displace flux vacua significantly while higher instantons stay negligible, and such vacua are common in a bounded two-modulus scan.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · deepseek-v4-flash

2026-08-01 09:25 UTC pith:RUH7JJL7

load-bearing objection Concrete two-modulus vacua where the first instanton dominates — but the frequency claim rides on a proxy tail check and an underspecified scan. the 2 major comments →

arxiv 2607.20777 v1 pith:RUH7JJL7 submitted 2026-07-22 hep-th gr-qc

Flux Vacua Near the Boundary of Large Complex Structure

Aman Chauhan , Michele Cicoli , Anshuman Maharana , Pellegrino Piantadosi This is my paper
classification hep-th gr-qc
keywords complexinstantonpotentialstructurecontributionlargeperturbativevacua
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

In type IIB string compactifications, fluxes create a potential for the complex structure moduli. In the large complex structure region this potential is a polynomial piece plus an infinite series of exponentially small instanton corrections. Previous studies usually keep only the polynomial piece. This paper keeps the leading instanton terms and searches for flux choices whose vacuum moves to a region where the polynomial potential is accidentally small and the first instanton is comparable.

The authors work on a two-modulus Calabi-Yau orientifold, CP4[1,1,1,6,9], compute Gopakumar-Vafa invariants to high degree, solve the F-flatness equations with a truncated instanton series, and track how roots move as instanton terms are switched on. The simplest outcome is a large displacement of the perturbative minimum: even though the first correction to the prepotential is about three orders of magnitude smaller than the polynomial term, the minimum can shift by order-one distances because the relevant mass matrix has a small eigenvalue. They verify that higher-degree instantons do not accumulate: changing the truncation from degree 1 to degree 10 changes the minimum by roughly 10^-3 or less. They also find cases where instantons create or destroy minima, and a case where a minimum outside the fundamental domain is mapped back by monodromy.

A scan with small flux numbers produces a distribution of displacements; about 9.3% of the near-boundary vacua shift by more than 10% of their position. The paper is explicit that this number is conditional on the chosen scan region and on the small flux bound.

Core claim

The paper's central claim, from the abstract: "We present examples of vacua near the boundary of large complex structure, where the minimum of the potential is essentially determined by the perturbative contribution and the first instanton correction, while the effect of all higher instantons is negligible. Analysing an ensemble of flux vacua, we find that this phenomenon is statistically quite common." The supporting claim is that in explicit two-modulus examples (Tabs. 1-7) the shift from degree-1 to degree-10 truncation is tiny (~10^-3 or less), so the vacua are controlled by the perturbative term plus the first instanton.

Load-bearing premise

The selection protocol assumes that truncating the instanton series at d_max=10 and requiring |Delta F^{(d')}_inst|/|F^{(d)}| <= 10^-10 with d'=100 (Eq. 3.4), plus the individual degree-1 suppression check (Eq. 3.5), guarantees that all higher instantons are negligible for every reported vacuum. This is load-bearing for the 'higher instantons negligible' claim and is non-trivial: Appendix B exhibits a flux configuration (B.2) whose low-degree ratios (epsilon_ratio^(10) <= 10^-6) look convergent while the series loses control at d~50, so the safety of the reported vacua rests on the d'=100 check and the correctness of the degree-300 GV data. A second, distinct assumption is that vacua in the bounded scan with N_flux<=10 and Im(z_i) in [0.5,5] are representative enough to support the word 'common'.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 5 minor

Summary. The paper studies supersymmetric flux vacua in the large complex structure (LCS) patch of a two-modulus Calabi-Yau orientifold, including worldsheet instanton corrections to the prepotential. It constructs explicit examples in which the first instanton correction produces a large displacement of the perturbative minimum while higher instantons are claimed to be negligible, and it presents a statistical scan suggesting that such vacua are 'quite common'. It also reports examples with instanton-generated multiplicity, monodromy shifts, destabilization of perturbative minima near the LCS boundary, and instanton-induced minima. The main technical tools are a degree-10 truncated prepotential with degree-300 Gopakumar-Vafa data and convergence diagnostics based on high-degree ratios.

Significance. If the central claim holds, the paper provides a controlled exploration away from the deep LCS asymptotics, a regime usually avoided. The explicit construction with high-order GV invariants, the deformation-tracking method, and the honest Appendix B counterexample are valuable methodological contributions. The explicit examples in Tabs. 1-2 are convincing, with independent d=10 to d=20 convergence checks. However, the statistical analysis supports the 'quite common' claim only under a convergence proxy that is not fully validated, and the scan is heavily bounded; the abstract and conclusions overstate the result as it stands.

major comments (2)
  1. [Sec. 3.1 (Eq. 3.4), App. B] The selection criterion (3.4) bounds only |ΔF^(100)_inst|/|F^(d)|; it does not bound the tail sum S_tail = Σ_{d=11}^∞ |ΔF^(d)_inst|/|F^(10)|. Appendix B's counterexample (B.2) shows that ε_ratio^(10) ≤ 10^-6 can coexist with loss of control at d≈50, and no argument is given that d'=100 is a sufficient diagnostic for every selected vacuum, especially near the Im z ≈ 0.862 boundary from the exponential fit. The explicit Tabs. 1-2 have independent d=10 to d=20 convergence checks, but the ensemble claim in Sec. 4 inherits the unvalidated proxy. Please report actual tail estimates, e.g. ε_reference (B.1), for all selected vacua and exclude vacua in the non-convergent region of Fig. 7.
  2. [Sec. 4 and Abstract] The statement that the phenomenon is 'statistically quite common' is supported only by a scan with N_flux ≤ 10, Im(z_i) ∈ [0.5,5], further restricted to min{Im(z_i)}<1. The paper does not test how the 9.3% fraction depends on N_max or on the search region U, nor does it compare with any prior expectation. The abstract and conclusions present the claim without these qualifications. Please either weaken the wording to 'common within this bounded ensemble' or add robustness checks showing that the fraction is stable under reasonable variations of the scan parameters.
minor comments (5)
  1. [Sec. 3.1, Eq. (3.4)] The text defines d=0,d_max for the condition but the first condition is written with d=0; please clarify whether F^(0) denotes F_pert and define the notation explicitly.
  2. [Sec. 3.2.1, footnote 5] The stated validity condition δφ^T M δφ + b·δφ = 0 is not the standard quadratic-stationarity condition (which would be M δφ = -b); please correct or clarify this equation.
  3. [Sec. 4, Fig. 4 caption] The caption should explicitly state that the 9.3% and 1.2% fractions correspond to thresholds ||Δz||/||z_P|| ≥ 0.1 and ≥ 0.3; presently this is only given in the text.
  4. [Appendix A, Eq. (A.6)] The GV invariants grow extremely rapidly with degree; a brief note on the expected exponential growth and on how the invariants were cross-checked would aid reproducibility.
  5. [General] The Acknowledgements thank CYTools and JAXVacua, but no statement is made about availability of the scan data or code. A data/code availability statement would strengthen the paper.

Circularity Check

0 steps flagged

No significant circularity: the central vacua and statistics are obtained by direct numerical scanning and independent convergence checks, not by fitting the claimed outcome.

full rationale

The paper's claims are not reductions of outputs to inputs. The perturbative and non-perturbative minima in Tabs. 1-7 are obtained by solving the F-flatness conditions at successive instanton truncations, and the stability of each minimum is checked by comparing the d=1 and d=10 truncations (e.g., the shift in Im(z_i) is (0.00106,-0.00294) in Tab. 1) and by the d'=100 single-degree check in Eq. (3.4), Eq. (3.5), and the App. B estimators (B.1). Condition (3.4) is a hand-chosen convergence criterion rather than an output-defining fit; App. B itself demonstrates with configuration (B.2) that low-degree convergence can be misleading, which is a validation limitation, not a circular step, since the paper does not define 'higher instantons negligible' to be equivalent to (3.4). The linear-response vector v=-M^{-1}b in Eq. (3.7) is computed as an a posteriori diagnostic and compared with actual displacements in Fig. 6; it is a correlation check, not a parameter fitted to reproduce the observed shifts. Self-citations ([9], [52], [2], [46], [47]) are contextual and not load-bearing; the computational inputs are independent (CYTools [5,6], Hosono-Klemm-Theisen-Yau [17,21], and the GV invariants to degree 300 computed by the authors in App. A). No prediction is equivalent by construction to an input, so no circularity is found.

Axiom & Free-Parameter Ledger

4 free parameters · 5 axioms · 0 invented entities

The central claims rest on standard string-theory machinery (LCS prepotential, GV invariants, F-flatness) plus a set of computational control choices. No new particle, force, or conservation law is introduced. The main hidden cost is the convergence/truncation protocol and the representativeness of the small-flux scan region.

free parameters (4)
  • Tadpole scan bound N_max = 10
    The statistical scan restricts N_flux <= 10. The frequency of large-displacement vacua could change at larger flux, and this cutoff is arbitrary.
  • Search region U = Im z_i in [0.5,5], Re z_i in (-0.5,0.5], c0 in (-0.5,0.5], s in [sqrt(3)/2,20]
    The scan only searches this bounded box; 'no vacuum found' statements are relative to U, and the 9.3% statistic is conditional on vacua inside it.
  • Instanton truncation and convergence thresholds = d_max=10, d'=100, 10^-10 and 10^-3 thresholds (Eqs. 3.4-3.5)
    These thresholds define what counts as 'higher instantons negligible'. They are reasonable computational choices, not derived from physics, and the 'common' claim depends on them.
  • Exponential fit constants for max GW invariant growth = 5.4166 and -11.3748 in max(N_d) ~ exp(5.4166 d - 11.3748)
    Used in App. B to estimate the radius of convergence (Im ~ 0.862). This is a fit to degree>=100 GV invariants, used for diagnostics rather than to construct vacua.
axioms (5)
  • domain assumption The LCS prepotential with GV invariants (Eqs. 2.3-2.5) is the correct all-orders expansion in the LCS patch.
    The paper relies on mirror symmetry and CYTools computations of GV invariants. This is standard but not independently re-derived here.
  • domain assumption The complex-structure sector can be analyzed while remaining agnostic about Kähler moduli stabilization and other sectors.
    Section 2.1 states this explicitly. The conclusions describe complex-structure vacua, not full string vacua with all moduli stabilized.
  • ad hoc to paper Truncating the instanton series at d_max=10 and applying Eqs. (3.4)-(3.5) guarantees higher instantons are negligible.
    This is a numerical control assumption. Appendix B shows that low-order ratios alone can be misleading, so the full load rests on the d'=100 residual check and the degree-300 GV data.
  • ad hoc to paper The auxiliary deformation in Eq. (3.8) tracks the same root without unobserved branch crossing.
    The connection between perturbative and non-perturbative minima is established by numerical continuation; the paper does not provide a rigorous no-crossing proof.
  • ad hoc to paper The bounded scan with N_flux<=10 and Im(z_i) in [0.5,5] is representative enough for the statistical statement 'quite common'.
    The 9.3% fraction is computed only for vacua with min{Im z_i}<1 inside this box. This is the main load-bearing assumption for the statistical generalization.

pith-pipeline@v1.3.0-alltime-deepseek · 20412 in / 13942 out tokens · 123371 ms · 2026-08-01T09:25:08.804635+00:00 · methodology

0 comments
read the original abstract

Three-form fluxes generate a potential for the complex structure moduli in type IIB string compactifications on Calabi-Yau threefolds. In the large complex structure patch, the potential consists of a perturbative contribution and a convergent series of instanton corrections. We present examples of vacua near the boundary of large complex structure, where the minimum of the potential is essentially determined by the perturbative contribution and the first instanton correction, while the effect of all higher instantons is negligible. This phenomenon occurs when fluxes are such that the magnitude of the perturbative potential in certain directions in moduli space is of the same size as the first instanton contribution. Analysing an ensemble of flux vacua, we find that this phenomenon is statistically quite common. We also discover more subtle phenomena where instanton terms affect the multiplicity of the solutions and induce monodromy shifts.

discussion (0)

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

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Gravitational Waves from Multiple Cosmic Superstrings and the Overshoot Problem

    hep-th 2026-07 conditional novelty 6.0

    A string-theory model with three cosmic superstring species solves the modulus overshoot problem via gravitational-wave friction and predicts a high-frequency multi-peaked stochastic gravitational-wave spectrum.

Reference graph

Works this paper leans on

55 extracted references · 50 linked inside Pith · cited by 1 Pith paper

  1. [1]

    Is the Superstring Weakly Coupled?,

    M. Dine and N. Seiberg, “Is the Superstring Weakly Coupled?,”Phys. Lett. B162(1985) 299–302

    1985

  2. [2]

    String cosmology: From the early universe to today,

    M. Cicoli, J. P. Conlon, A. Maharana, S. Parameswaran, F. Quevedo, and I. Zavala, “String cosmology: From the early universe to today,”Phys. Rept.1059(2024) 1–155, arXiv:2303.04819 [hep-th]

    Pith/arXiv arXiv 2024

  3. [3]

    Moduli Stabilization in String Theory,

    L. McAllister and F. Quevedo, “Moduli Stabilization in String Theory,”arXiv:2310.20559 [hep-th]

    Pith/arXiv arXiv

  4. [4]

    Instanton

    A. Klemm and M. Kreuzer, “Instanton.” http://hep.itp.tuwien.ac.at/~kreuzer/CY/hep-th/0410018.html

    Pith/arXiv arXiv

  5. [5]

    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]

    Pith/arXiv arXiv

  6. [6]

    Computational Mirror Symmetry,

    M. Demirtas, M. Kim, L. McAllister, J. Moritz, and A. Rios-Tascon, “Computational Mirror Symmetry,”JHEP01(2024) 184,arXiv:2303.00757 [hep-th]

    Pith/arXiv arXiv 2024

  7. [7]

    Finding all flux vacua in an explicit example,

    D. Martinez-Pedrera, D. Mehta, M. Rummel, and A. Westphal, “Finding all flux vacua in an explicit example,”JHEP06(2013) 110,arXiv:1212.4530 [hep-th]

    Pith/arXiv arXiv 2013

  8. [8]

    JAXVacua — a framework for sampling string vacua,

    A. Dubey, S. Krippendorf, and A. Schachner, “JAXVacua — a framework for sampling string vacua,”JHEP12(2023) 146,arXiv:2306.06160 [hep-th]

    Pith/arXiv arXiv 2023

  9. [9]

    Deep observations of the Type IIB flux landscape,

    A. Chauhan, M. Cicoli, S. Krippendorf, A. Maharana, P. Piantadosi, and A. Schachner, “Deep observations of the Type IIB flux landscape,”arXiv:2501.03984 [hep-th]

    Pith/arXiv arXiv

  10. [10]

    Flux compactifications in string theory: A Comprehensive review,

    M. Grana, “Flux compactifications in string theory: A Comprehensive review,”Phys. Rept. 423(2006) 91–158,arXiv:hep-th/0509003

    Pith/arXiv arXiv 2006

  11. [11]

    Flux compactification,

    M. R. Douglas and S. Kachru, “Flux compactification,”Rev. Mod. Phys.79(2007) 733–796, arXiv:hep-th/0610102

    Pith/arXiv arXiv 2007

  12. [12]

    Orientifolding Kreuzer-Skarke,

    J. Moritz, “Orientifolding Kreuzer-Skarke,”arXiv:2305.06363 [hep-th]

    Pith/arXiv arXiv

  13. [13]

    On the intermediate Jacobian of M5-branes,

    P. Jefferson and M. Kim, “On the intermediate Jacobian of M5-branes,”JHEP05(2024) 180,arXiv:2211.00210 [hep-th]

    Pith/arXiv arXiv 2024

  14. [14]

    A Pair of Calabi-Yau manifolds as an exactly soluble superconformal theory,

    P. Candelas, X. C. De La Ossa, P. S. Green, and L. Parkes, “A Pair of Calabi-Yau manifolds as an exactly soluble superconformal theory,”Nucl. Phys. B359(1991) 21–74

    1991

  15. [15]

    Picard-Fuchs equations and special geometry,

    A. Ceresole, R. D’Auria, S. Ferrara, W. Lerche, and J. Louis, “Picard-Fuchs equations and special geometry,”Int. J. Mod. Phys. A8(1993) 79–114,arXiv:hep-th/9204035

    Pith/arXiv arXiv 1993

  16. [16]

    Mirror symmetry for two parameter models. 1.,

    P. Candelas, X. De La Ossa, A. Font, S. H. Katz, and D. R. Morrison, “Mirror symmetry for two parameter models. 1.,”Nucl. Phys. B416(1994) 481–538,arXiv:hep-th/9308083

    Pith/arXiv arXiv 1994

  17. [17]

    Mirror symmetry, mirror map and applications to Calabi-Yau hypersurfaces,

    S. Hosono, A. Klemm, S. Theisen, and S.-T. Yau, “Mirror symmetry, mirror map and applications to Calabi-Yau hypersurfaces,”Commun. Math. Phys.167(1995) 301–350, arXiv:hep-th/9308122

    Pith/arXiv arXiv 1995

  18. [18]

    Lectures on mirror symmetry,

    S. Hosono, A. Klemm, and S. Theisen, “Lectures on mirror symmetry,”Lect. Notes Phys. 436(1994) 235–280,arXiv:hep-th/9403096

    Pith/arXiv arXiv 1994

  19. [19]

    Mirror symmetry for two parameter models. 2.,

    P. Candelas, A. Font, S. H. Katz, and D. R. Morrison, “Mirror symmetry for two parameter models. 2.,”Nucl. Phys. B429(1994) 626–674,arXiv:hep-th/9403187. – 25 –

    Pith/arXiv arXiv 1994

  20. [20]

    Local mirror symmetry at higher genus,

    A. Klemm and E. Zaslow, “Local mirror symmetry at higher genus,”AMS/IP Stud. Adv. Math.23(2001) 183–207,arXiv:hep-th/9906046

    Pith/arXiv arXiv 2001

  21. [21]

    Mirror symmetry, mirror map and applications to complete intersection Calabi-Yau spaces,

    S. Hosono, A. Klemm, S. Theisen, and S.-T. Yau, “Mirror symmetry, mirror map and applications to complete intersection Calabi-Yau spaces,”Nucl. Phys. B433(1995) 501–554, arXiv:hep-th/9406055

    Pith/arXiv arXiv 1995

  22. [22]

    M theory and topological strings. 1.,

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

    Pith/arXiv arXiv

  23. [23]

    M theory and topological strings. 2.,

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

    Pith/arXiv arXiv

  24. [24]

    CFT’s from Calabi-Yau four folds,

    S. Gukov, C. Vafa, and E. Witten, “CFT’s from Calabi-Yau four folds,”Nucl. Phys. B584 (2000) 69–108,arXiv:hep-th/9906070. [Erratum: Nucl.Phys.B 608, 477–478 (2001)]

    Pith/arXiv arXiv 2000

  25. [25]

    Hierarchies from fluxes in string compactifications,

    S. B. Giddings, S. Kachru, and J. Polchinski, “Hierarchies from fluxes in string compactifications,”Phys. Rev. D66(2002) 106006,arXiv:hep-th/0105097

    Pith/arXiv arXiv 2002

  26. [26]

    Nonrenormalization of flux superpotentials in string theory,

    C. P. Burgess, C. Escoda, and F. Quevedo, “Nonrenormalization of flux superpotentials in string theory,”JHEP06(2006) 044,arXiv:hep-th/0510213

    Pith/arXiv arXiv 2006

  27. [27]

    Flux compactifications on Calabi-Yau threefolds,

    A. Giryavets, S. Kachru, P. K. Tripathy, and S. P. Trivedi, “Flux compactifications on Calabi-Yau threefolds,”JHEP04(2004) 003,arXiv:hep-th/0312104

    Pith/arXiv arXiv 2004

  28. [28]

    On the taxonomy of flux vacua,

    A. Giryavets, S. Kachru, and P. K. Tripathy, “On the taxonomy of flux vacua,”JHEP08 (2004) 002,arXiv:hep-th/0404243

    Pith/arXiv arXiv 2004

  29. [29]

    Enumerating flux vacua with enhanced symmetries,

    O. DeWolfe, A. Giryavets, S. Kachru, and W. Taylor, “Enumerating flux vacua with enhanced symmetries,”JHEP02(2005) 037,arXiv:hep-th/0411061

    Pith/arXiv arXiv 2005

  30. [30]

    Building a better racetrack,

    F. Denef, M. R. Douglas, and B. Florea, “Building a better racetrack,”JHEP06(2004) 034, arXiv:hep-th/0404257

    Pith/arXiv arXiv 2004

  31. [31]

    On the explicit construction and statistics of Calabi-Yau flux vacua,

    J. P. Conlon and F. Quevedo, “On the explicit construction and statistics of Calabi-Yau flux vacua,”JHEP10(2004) 039,arXiv:hep-th/0409215

    Pith/arXiv arXiv 2004

  32. [32]

    Distribution of flux vacua around singular points in Calabi-Yau moduli space,

    T. Eguchi and Y. Tachikawa, “Distribution of flux vacua around singular points in Calabi-Yau moduli space,”JHEP01(2006) 100,arXiv:hep-th/0510061

    Pith/arXiv arXiv 2006

  33. [33]

    Explicit de Sitter Flux Vacua for Global String Models with Chiral Matter,

    M. Cicoli, D. Klevers, S. Krippendorf, C. Mayrhofer, F. Quevedo, and R. Valandro, “Explicit de Sitter Flux Vacua for Global String Models with Chiral Matter,”JHEP05(2014) 001, arXiv:1312.0014 [hep-th]

    Pith/arXiv arXiv 2014

  34. [34]

    The Spectra of Type IIB Flux Compactifications at Large Complex Structure,

    C. Brodie and M. C. D. Marsh, “The Spectra of Type IIB Flux Compactifications at Large Complex Structure,”JHEP01(2016) 037,arXiv:1509.06761 [hep-th]

    Pith/arXiv arXiv 2016

  35. [35]

    Mirror quintic vacua: hierarchies and inflation,

    N. Cabo Bizet, O. Loaiza-Brito, and I. Zavala, “Mirror quintic vacua: hierarchies and inflation,”JHEP10(2016) 082,arXiv:1605.03974 [hep-th]

    Pith/arXiv arXiv 2016

  36. [36]

    Towards a complete mass spectrum of type-IIB flux vacua at large complex structure,

    J. J. Blanco-Pillado, K. Sousa, M. A. Urkiola, and J. M. Wachter, “Towards a complete mass spectrum of type-IIB flux vacua at large complex structure,”JHEP04(2021) 149, arXiv:2007.10381 [hep-th]

    Pith/arXiv arXiv 2021

  37. [37]

    Universal Class of Type-IIB Flux Vacua with Analytic Mass Spectrum,

    J. J. Blanco-Pillado, K. Sousa, M. A. Urkiola, and J. M. Wachter, “Universal Class of Type-IIB Flux Vacua with Analytic Mass Spectrum,”Phys. Rev. D103no. 10, (2021) 106006,arXiv:2011.13953 [hep-th]

    Pith/arXiv arXiv 2021

  38. [38]

    An index for flux vacua,

    S. L¨ ust, “An index for flux vacua,”arXiv:2405.04584 [hep-th]

    arXiv

  39. [39]

    Vacua with Small Flux Superpotential,

    M. Demirtas, M. Kim, L. Mcallister, and J. Moritz, “Vacua with Small Flux Superpotential,”Phys. Rev. Lett.124no. 21, (2020) 211603,arXiv:1912.10047 [hep-th]. – 26 –

    Pith/arXiv arXiv 2020

  40. [40]

    F-theory flux vacua at large complex structure,

    F. Marchesano, D. Prieto, and M. Wiesner, “F-theory flux vacua at large complex structure,”JHEP08(2021) 077,arXiv:2105.09326 [hep-th]

    Pith/arXiv arXiv 2021

  41. [41]

    Analytics of type IIB flux vacua and their mass spectra,

    T. Coudarchet, F. Marchesano, D. Prieto, and M. A. Urkiola, “Analytics of type IIB flux vacua and their mass spectra,”JHEP01(2023) 152,arXiv:2212.02533 [hep-th]

    Pith/arXiv arXiv 2023

  42. [42]

    The Statistics of string / M theory vacua,

    M. R. Douglas, “The Statistics of string / M theory vacua,”JHEP05(2003) 046, arXiv:hep-th/0303194

    Pith/arXiv arXiv 2003

  43. [43]

    Counting flux vacua,

    S. Ashok and M. R. Douglas, “Counting flux vacua,”JHEP01(2004) 060, arXiv:hep-th/0307049

    Pith/arXiv arXiv 2004

  44. [44]

    Basic results in vacuum statistics,

    M. R. Douglas, “Basic results in vacuum statistics,”Comptes Rendus Physique5(2004) 965–977,arXiv:hep-th/0409207

    Pith/arXiv arXiv 2004

  45. [45]

    Distributions of flux vacua,

    F. Denef and M. R. Douglas, “Distributions of flux vacua,”JHEP05(2004) 072, arXiv:hep-th/0404116

    Pith/arXiv arXiv 2004

  46. [46]

    Moduli Stabilisation and the Statistics of SUSY Breaking in the Landscape,

    I. Broeckel, M. Cicoli, A. Maharana, K. Singh, and K. Sinha, “Moduli Stabilisation and the Statistics of SUSY Breaking in the Landscape,”JHEP10(2020) 015,arXiv:2007.04327 [hep-th]

    Pith/arXiv arXiv 2020

  47. [47]

    Joint statistics of cosmological constant and SUSY breaking in flux vacua with nilpotent Goldstino,

    M. Cicoli, M. Licheri, A. Maharana, K. Singh, and K. Sinha, “Joint statistics of cosmological constant and SUSY breaking in flux vacua with nilpotent Goldstino,”JHEP01(2023) 013, arXiv:2211.07695 [hep-th]

    Pith/arXiv arXiv 2023

  48. [48]

    Moduli space holography and the finiteness of flux vacua,

    T. W. Grimm, “Moduli space holography and the finiteness of flux vacua,”JHEP10(2021) 153,arXiv:2010.15838 [hep-th]

    Pith/arXiv arXiv 2021

  49. [49]

    Finiteness for self-dual classes in integral variations of Hodge structure,

    B. Bakker, T. W. Grimm, C. Schnell, and J. Tsimerman, “Finiteness for self-dual classes in integral variations of Hodge structure,”arXiv:2112.06995 [math.AG]

    Pith/arXiv arXiv

  50. [50]

    Flux vacua of the mirror octic,

    E. Plauschinn and L. Schlechter, “Flux vacua of the mirror octic,”arXiv:2310.06040 [hep-th]

    Pith/arXiv arXiv

  51. [51]

    W0 sample = np.random.normal(0,1)?,

    J. Ebelt, S. Krippendorf, and A. Schachner, “W0 sample = np.random.normal(0,1)?,”Phys. Lett. B855(2024) 138786,arXiv:2307.15749 [hep-th]

    Pith/arXiv arXiv 2024

  52. [52]

    Parameter compression in the flux landscape,

    A. Chauhan, M. Cicoli, S. Krippendorf, A. Maharana, P. Piantadosi, and A. Schachner, “Parameter compression in the flux landscape,”arXiv:2603.04941 [hep-th]

    arXiv

  53. [53]

    Vacua with small flux superpotential,

    M. Demirtas, M. Kim, L. McAllister, and J. Moritz, “Vacua with small flux superpotential,” Physical Review Letters124no. 21, (May, 2020) . https://doi.org/10.1103%2Fphysrevlett.124.211603

    2020

  54. [54]

    Flux vacua with approximate flat directions,

    M. Cicoli, M. Licheri, R. Mahanta, and A. Maharana, “Flux vacua with approximate flat directions,”JHEP10(2022) 086,arXiv:2209.02720 [hep-th]

    Pith/arXiv arXiv 2022

  55. [55]

    On asymptotics and resurgent structures of enumerative Gromov–Witten invariants,

    R. Couso-Santamar ´ ıa, R. Schiappa, and R. Vaz, “On asymptotics and resurgent structures of enumerative Gromov–Witten invariants,”Commun. Num. Theor. Phys.11(2017) 707–790, arXiv:1605.07473 [math.AG]. – 27 –

    Pith/arXiv arXiv 2017