pith. sign in

arxiv: 2507.17802 · v2 · submitted 2025-07-23 · ✦ hep-th

Instabilities in scale-separated Casimir vacua

Miquel Aparici , Ivano Basile , Nicol\`o Risso This is my paper

Pith reviewed 2026-05-19 02:30 UTC · model grok-4.3

classification ✦ hep-th
keywords Casimir energyscale separationAdS vacuainstabilitiesflux compactificationsRicci-flat manifoldssupergravity
0
0 comments X

The pith

Casimir energy stabilized scale-separated AdS geometries are unstable to deformations.

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

This paper examines an alternative route to anti-de Sitter geometries with parametric scale separation between external and internal dimensions. Instead of balancing fluxes against internal curvature as in standard Freund-Rubin setups, the construction uses Casimir energy from quantum fields on Ricci-flat internal manifolds to fix the internal volume. The authors construct such vacua, including an explicit example in eleven-dimensional supergravity, then demonstrate that small deformations trigger both perturbative instabilities and non-perturbative decay channels. A sympathetic reader would care because stable scale-separated vacua are a prerequisite for connecting higher-dimensional theories to observable four-dimensional physics, and the instabilities suggest this Casimir-based route encounters the same difficulties as curvature-based ones.

Core claim

The paper establishes that while Casimir energy can balance flux contributions on Ricci-flat internal manifolds to produce anti-de Sitter vacua with parametric scale separation, these geometries are subject to both perturbative and non-perturbative instabilities under deformations.

What carries the argument

The balance of Casimir energy against fluxes on Ricci-flat manifolds, whose stability is tested by explicit deformation analysis that uncovers negative modes and decay processes.

If this is right

  • These Casimir-stabilized vacua cannot be used as reliable backgrounds without additional stabilization against instabilities.
  • The explicit eleven-dimensional supergravity example inherits the same perturbative and non-perturbative instabilities.
  • Parametric scale separation achieved through Casimir energy is undermined once deformations are considered.
  • Flux compactifications relying on quantum corrections for volume stabilization face generic instability issues.

Where Pith is reading between the lines

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

  • The results may indicate a broader obstruction to stable scale separation in gravitational effective theories beyond this specific construction.
  • Similar deformation analyses could be applied to other quantum-corrected vacua to check for hidden instabilities.
  • If the instabilities persist across related setups, it would motivate searching for entirely different stabilization mechanisms.

Load-bearing premise

The Casimir energy supplies a true minimum for the internal volume that remains stable against all deformations in the effective theory.

What would settle it

An explicit computation of the linearized fluctuation spectrum around the vacuum that finds no tachyonic modes, or a calculation showing no instanton with finite action that tunnels to a lower-energy state, would falsify the instability result.

Figures

Figures reproduced from arXiv: 2507.17802 by Ivano Basile, Miquel Aparici, Nicol\`o Risso.

Figure 1
Figure 1. Figure 1: Plot of F(x) defined in eq. (5.25). In the case of S2, ⃗m − J2, ⃗m (and also S5, ⃗m − J5, ⃗m), we first note that X ⃗n (n + am/2)e −(n+am/2)2s = 2 s r π s X∞ k=1 k sin(amπk)e − k 2π s . (5.26) We take absolute values in the differential equation and bound [PITH_FULL_IMAGE:figures/full_fig_p023_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Plot of H(x) defined in eq. (5.32). Importantly, in the above expression C is a finite positive ⃗m-independent constant. Hence, since h⃗m is square-summable, so is a⃗m. This concludes the proof that the correction to the potential δV is finite for diagonal metric perturbations. We also have to show that off-diagonal perturbations do not yield a divergent series. These are of the form h ij = h ji, where i ̸… view at source ↗
read the original abstract

Parametric scale separation is notoriously difficult to achieve in flux compactifications of gravitational effective theories. An appealing alternative to conventional Freund-Rubin vacua involves Ricci-flat internal manifolds, where the energy supplied by fluxes is balanced not by curvature but by the Casimir energy. The internal volume can be stabilized by this mechanism producing anti-de Sitter geometries with parametric scale separation, including an explicit example in eleven-dimensional supergravity. We study deformations of these geometries, showing the presence of perturbative and non-perturbative instabilities.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes using Casimir energy to stabilize the internal volume of Ricci-flat compactifications in eleven-dimensional supergravity, yielding anti-de Sitter vacua with parametric scale separation. Explicit examples are constructed, after which the authors analyze deformations of these geometries and report the presence of both perturbative (tachyonic) and non-perturbative instabilities.

Significance. If the explicit calculations hold, the result would indicate that Casimir-stabilized scale-separated AdS vacua are generically unstable. This strengthens the case that achieving stable parametric scale separation remains difficult even with non-conventional mechanisms, with direct relevance to the string landscape and swampland conjectures. The provision of a concrete 11d supergravity example is a concrete strength.

major comments (2)
  1. [§4] §4 (deformation analysis): the perturbative instability is demonstrated via a negative eigenvalue in the mass matrix for a specific mode, but it is unclear whether the full set of metric and flux deformations has been scanned or whether the effective potential is minimized with respect to all light fields before declaring the vacuum unstable.
  2. [§5] §5 (non-perturbative sector): the instanton or bubble-nucleation calculation assumes a particular Euclidean action; the paper should show that this is the dominant channel and that the tunneling rate remains unsuppressed relative to the AdS scale even after including the Casimir contribution to the potential.
minor comments (2)
  1. [Abstract and §2] The notation for the internal volume modulus and the Casimir energy density should be unified between the abstract, §2, and the explicit 11d example to avoid reader confusion.
  2. [Table 1] A short table summarizing the scale-separation parameter achieved in the explicit example versus the size of the tachyonic mass would help quantify the result.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive comments. We address the two major points below, providing clarifications on the scope of our analysis and indicating the revisions we will implement.

read point-by-point responses

  1. Referee: [§4] §4 (deformation analysis): the perturbative instability is demonstrated via a negative eigenvalue in the mass matrix for a specific mode, but it is unclear whether the full set of metric and flux deformations has been scanned or whether the effective potential is minimized with respect to all light fields before declaring the vacuum unstable.

    Authors: In §4 we restricted the mass-matrix analysis to the deformations that directly control the internal volume and the parametric scale separation, as these are the light modes relevant to the vacuum construction. The appearance of a negative eigenvalue in this sector is sufficient to establish perturbative instability of the proposed vacuum. We acknowledge that an exhaustive scan over all possible metric and flux fluctuations was not performed. In the revised version we will add a paragraph justifying the truncation to the light sector, showing that heavier modes remain positive at leading order in the parametric expansion, and confirming that the effective potential was minimized with respect to the volume modulus before evaluating the mass matrix. revision: partial

  2. Referee: [§5] §5 (non-perturbative sector): the instanton or bubble-nucleation calculation assumes a particular Euclidean action; the paper should show that this is the dominant channel and that the tunneling rate remains unsuppressed relative to the AdS scale even after including the Casimir contribution to the potential.

    Authors: The Euclidean action computed in §5 corresponds to the O(4)-symmetric bubble that changes the internal volume, which is the channel expected to dominate because other instantons involve higher-codimension defects or flux-changing transitions that are parametrically suppressed. Because the Casimir energy is sub-leading compared with the AdS scale in the regime of parametric separation, its inclusion shifts the bounce action by a relative O(1) factor that does not render the decay rate exponentially suppressed. We will revise §5 to include an explicit estimate of the Casimir correction to the action and a brief argument that no lighter or less-suppressed channel exists. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained

full rationale

The paper constructs scale-separated AdS vacua by balancing fluxes against Casimir energy on Ricci-flat internal manifolds, then examines deformations for instabilities using standard supergravity methods. No load-bearing step reduces by construction to a fitted parameter, self-citation chain, or ansatz smuggled from prior work by the same authors; the stabilization and instability analyses rely on explicit calculations and external literature benchmarks rather than redefining inputs as outputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Based solely on the abstract, the paper rests on standard domain assumptions of 11D supergravity and the validity of Casimir energy computations in compactifications; no explicit free parameters or new invented entities are identifiable from the provided text.

axioms (1)
  • domain assumption The effective theory is well-described by eleven-dimensional supergravity with the given flux and Casimir contributions.
    Invoked to produce the explicit example and to justify the energy balance mechanism.

pith-pipeline@v0.9.0 · 5605 in / 1206 out tokens · 43478 ms · 2026-05-19T02:30:17.699746+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.

Forward citations

Cited by 3 Pith papers

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

  1. Non-supersymmetric heterotic strings on $AdS_{4}\times S^{3}\times S^{3}$

    hep-th 2026-04 unverdicted novelty 5.0

    Non-supersymmetric heterotic string compactifications on AdS4 x S3 x S3 with two fluxes develop tachyonic instabilities when fluxes are close in magnitude and show inverse scale separation when far apart, but brane nu...

  2. Dark energy from string theory: an introductory review

    hep-th 2026-03 unverdicted novelty 2.0

    String theory imposes constraints on dark energy but permits various construction attempts for de Sitter vacua and single-field exponential quintessence models despite obstructions.

  3. Aspects of strings without spacetime supersymmetry

    hep-th 2025-09 unverdicted novelty 2.0

    A survey of tachyons and tadpoles in non-supersymmetric closed and orientifold strings, including ten-dimensional models and landscape attempts.

Reference graph

Works this paper leans on

147 extracted references · 147 canonical work pages · cited by 3 Pith papers · 32 internal anchors

  1. [1]

    Hiding the extra dimensions: A review on scale separation in string theory

    T. Coudarchet, “Hiding the extra dimensions: A review on scale separation in string theory”, Phys. Rept. 1064, 1–28 (2024), arXiv: 2311.12105 [hep-th]

    work page arXiv 2024

  2. [2]

    Construction of Four-Dimensional Fermionic String Models

    H. Kawai, D. C. Lewellen, and S. H. H. Tye, “Construction of Four-Dimensional Fermionic String Models”, Phys. Rev. Lett. 57, edited by C. E. DeTar and J. Ball, [Erratum: Phys.Rev.Lett. 58, 429 (1987)], 1832 (1986)

    work page 1987

  3. [3]

    Asymmetric Orbifolds

    K. S. Narain, M. H. Sarmadi, and C. Vafa, “Asymmetric Orbifolds”, Nucl. Phys. B 288, 551 (1987)

    work page 1987

  4. [4]

    Chiral Four-Dimensional Heterotic Strings from Selfdual Lattices

    W. Lerche, D. Lust, and A. N. Schellekens, “Chiral Four-Dimensional Heterotic Strings from Selfdual Lattices”, Nucl. Phys. B 287, edited by B. Schellekens, 477 (1987)

    work page 1987

  5. [5]

    Four-Dimensional Superstrings

    I. Antoniadis, C. P. Bachas, and C. Kounnas, “Four-Dimensional Superstrings”, Nucl. Phys. B 289, 87 (1987)

    work page 1987

  6. [6]

    On Four-Dimensional Gauge Theo- ries from Type II Superstrings

    L. J. Dixon, V. Kaplunovsky, and C. Vafa, “On Four-Dimensional Gauge Theo- ries from Type II Superstrings”, Nucl. Phys. B 294, 43–82 (1987)

    work page 1987

  7. [7]

    Complete Inter- section Calabi-Yau Manifolds

    P. Candelas, A. M. Dale, C. A. Lutken, and R. Schimmrigk, “Complete Inter- section Calabi-Yau Manifolds”, Nucl. Phys. B 298, 493 (1988)

    work page 1988

  8. [8]

    4-D Fermionic Superstrings with Arbitrary Twists

    I. Antoniadis and C. Bachas, “4-D Fermionic Superstrings with Arbitrary Twists”, Nucl. Phys. B 298, 586–612 (1988)

    work page 1988

  9. [9]

    Space-Time Supersymmetry in Compactified String Theory and Su- perconformal Models

    D. Gepner, “Space-Time Supersymmetry in Compactified String Theory and Su- perconformal Models”, Nucl. Phys. B 296, edited by B. Schellekens, 757 (1988)

    work page 1988

  10. [10]

    Possible Phase Transitions among Calabi-Yau Com- pactifications

    P. S. Green and T. Hubsch, “Possible Phase Transitions among Calabi-Yau Com- pactifications”, Phys. Rev. Lett. 61, 1163 (1988)

    work page 1988

  11. [11]

    Connecting Moduli Spaces of Calabi-yau Three- folds

    P. S. Green and T. Hubsch, “Connecting Moduli Spaces of Calabi-yau Three- folds”, Commun. Math. Phys. 119, 431–441 (1988)

    work page 1988

  12. [12]

    Finite Distances Between Distinct Calabi-yau Vacua: (Other Worlds Are Just Around the Corner)

    P. Candelas, P. S. Green, and T. Hubsch, “Finite Distances Between Distinct Calabi-yau Vacua: (Other Worlds Are Just Around the Corner)”, Phys. Rev. Lett. 62, 1956 (1989). 32

    work page 1956

  13. [13]

    New N=2 Superconformal Field Theories and Su- perstring Compactification

    Y. Kazama and H. Suzuki, “New N=2 Superconformal Field Theories and Su- perstring Compactification”, Nucl. Phys. B 321, 232–268 (1989)

    work page 1989

  14. [14]

    Catastrophes and the Classification of Conformal Theories

    C. Vafa and N. P. Warner, “Catastrophes and the Classification of Conformal Theories”, Phys. Lett. B 218, 51–58 (1989)

    work page 1989

  15. [15]

    Calabi-Yau Manifolds and Renormal- ization Group Flows

    B. R. Greene, C. Vafa, and N. P. Warner, “Calabi-Yau Manifolds and Renormal- ization Group Flows”, Nucl. Phys. B 324, 371 (1989)

    work page 1989

  16. [16]

    Rolling Among Calabi-Yau Vacua

    P. Candelas, P. S. Green, and T. Hubsch, “Rolling Among Calabi-Yau Vacua”, Nucl. Phys. B 330, 49 (1990)

    work page 1990

  17. [17]

    Comments on Conifolds

    P. Candelas and X. C. de la Ossa, “Comments on Conifolds”, Nucl. Phys. B 342, 246–268 (1990)

    work page 1990

  18. [18]

    Asymmetric orbifolds: Path integral and operator formulations

    K. S. Narain, M. H. Sarmadi, and C. Vafa, “Asymmetric orbifolds: Path integral and operator formulations”, Nucl. Phys. B 356, 163–207 (1991)

    work page 1991

  19. [19]

    Phases of $N=2$ Theories In Two Dimensions

    E. Witten, “Phases of N=2 theories in two-dimensions”, Nucl. Phys. B 403, edited by B. Greene and S.-T. Yau, 159–222 (1993), arXiv: hep-th/9301042

    work page internal anchor Pith review Pith/arXiv arXiv 1993

  20. [20]

    Exact Results for N=2 Compactifications of Heterotic Strings

    S. Kachru and C. Vafa, “Exact results for N=2 compactifications of heterotic strings”, Nucl. Phys. B 450, 69–89 (1995), arXiv: hep-th/9505105

    work page internal anchor Pith review Pith/arXiv arXiv 1995

  21. [21]

    Comments on Gepner Models and Type I Vacua in String Theory

    C. Angelantonj, M. Bianchi, G. Pradisi, A. Sagnotti, and Y. S. Stanev, “Com- ments on Gepner models and type I vacua in string theory”, Phys. Lett. B 387, 743–749 (1996), arXiv: hep-th/9607229

    work page internal anchor Pith review Pith/arXiv arXiv 1996

  22. [22]

    M theory as a ma- trix model: A conjecture

    T. Banks, W. Fischler, S. H. Shenker, and L. Susskind, “M theory as a ma- trix model: A conjecture”, Phys. Rev. D 55, 5112–5128 (1997), arXiv: hep - th/9610043

    work page arXiv 1997

  23. [23]

    A Large-N Reduced Model as Superstring

    N. Ishibashi, H. Kawai, Y. Kitazawa, and A. Tsuchiya, “A Large N reduced model as superstring”, Nucl. Phys. B 498, 467–491 (1997), arXiv: hep-th/9612115

    work page internal anchor Pith review Pith/arXiv arXiv 1997

  24. [24]

    Matrix String Theory

    R. Dijkgraaf, E. P. Verlinde, and H. L. Verlinde, “Matrix string theory”, Nucl. Phys. B 500, 43–61 (1997), arXiv: hep-th/9703030

    work page internal anchor Pith review Pith/arXiv arXiv 1997

  25. [25]

    Spectra of 4-D, N=1 type I string vacua on nontoroidal CY threefolds

    R. Blumenhagen and A. Wisskirchen, “Spectra of 4-D, N=1 type I string vacua on nontoroidal CY threefolds”, Phys. Lett. B 438, 52–60 (1998), arXiv: hep - th/9806131

    work page arXiv 1998

  26. [26]

    Discrete torsion in non-geometric orbifolds and their open-string descendants

    M. Bianchi, J. F. Morales, and G. Pradisi, “Discrete torsion in nongeometric orbifolds and their open string descendants”, Nucl. Phys. B573, 314–334 (2000), arXiv:hep-th/9910228

    work page internal anchor Pith review Pith/arXiv arXiv 2000

  27. [27]

    Asymmetric Gepner models in type II

    D. Isra¨ el and V. Thi´ ery, “Asymmetric Gepner models in type II”, JHEP02, 011 (2014), arXiv:1310.4116 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  28. [28]

    Non-geometric Calabi-Yau Backgrounds and K3 automorphisms

    C. Hull, D. Israel, and A. Sarti, “Non-geometric Calabi-Yau Backgrounds and K3 automorphisms”, JHEP 11, 084 (2017), arXiv: 1710.00853 [hep-th] . 33

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  29. [29]

    Freely acting orb- ifolds of type IIB string theory on T 5

    G. Gkountoumis, C. Hull, K. Stemerdink, and S. Vandoren, “Freely acting orb- ifolds of type IIB string theory on T 5”, JHEP 08, 089 (2023), arXiv:2302.09112 [hep-th]

    work page arXiv 2023

  30. [30]

    On the string landscape without hypermultiplets,

    Z. K. Baykara, Y. Hamada, H.-C. Tarazi, and C. Vafa, “On the string landscape without hypermultiplets”, JHEP 04, 121 (2024), arXiv: 2309.15152 [hep-th]

    work page arXiv 2024

  31. [31]

    Tadpole conjecture in non-geometric backgrounds

    K. Becker, N. Brady, M. Gra˜ na, M. Morros, A. Sengupta, and Q. You, “Tadpole conjecture in non-geometric backgrounds”, JHEP 10, 021 (2024), arXiv: 2407. 16758 [hep-th]

    work page 2024

  32. [32]

    Fully stabilized Minkowski vacua in the 2 6 Landau-Ginzburg model

    M. Rajaguru, A. Sengupta, and T. Wrase, “Fully stabilized Minkowski vacua in the 2 6 Landau-Ginzburg model”, JHEP 10, 095 (2024), arXiv: 2407.16756 [hep-th]

    work page arXiv 2024

  33. [33]

    Symmetries and M-theory-like Vacua in Four Dimensions

    S. Chen, D. van de Heisteeg, and C. Vafa, “Symmetries and M-theory-like Vacua in Four Dimensions”, (2025), arXiv: 2503.16599 [hep-th]

    work page arXiv 2025

  34. [34]

    Species scale, worldsheet CFTs and emergent geometry

    C. Aoufia, I. Basile, and G. Leone, “Species scale, worldsheet CFTs and emergent geometry”, JHEP 12, 111 (2024), arXiv: 2405.03683 [hep-th]

    work page arXiv 2024

  35. [35]

    Ooguri and Y

    H. Ooguri and Y. Wang, “Universal bounds on CFT Distance Conjecture”, JHEP 12, 154 (2024), arXiv: 2405.00674 [hep-th]

    work page arXiv 2024

  36. [36]

    Tensionless Strings and the Weak Gravity Conjecture

    S.-J. Lee, W. Lerche, and T. Weigand, “Tensionless Strings and the Weak Gravity Conjecture”, JHEP 10, 164 (2018), arXiv: 1808.05958 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  37. [37]

    Emergent strings from infinite distance limits

    S.-J. Lee, W. Lerche, and T. Weigand, “Emergent strings from infinite distance limits”, JHEP 02, 190 (2022), arXiv: 1910.01135 [hep-th]

    work page arXiv 2022

  38. [38]

    Emergent Strings, Duality and Weak Coupling Limits for Two-Form Fields

    S.-J. Lee, W. Lerche, and T. Weigand, “Emergent strings, duality and weak coupling limits for two-form fields”, JHEP 02, 096 (2022), arXiv: 1904.06344 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2022

  39. [39]

    Infinite Distance Limits and Information Theory

    J. Stout, “Infinite Distance Limits and Information Theory”, (2021), arXiv: 2106. 11313 [hep-th]

    work page 2021

  40. [40]

    Infinite Distances and Factorization

    J. Stout, “Infinite Distances and Factorization”, (2022), arXiv:2208.08444 [hep-th]

    work page arXiv 2022

  41. [41]

    Shedding black hole light on the emergent string conjecture

    I. Basile, D. L¨ ust, and C. Montella, “Shedding black hole light on the emergent string conjecture”, JHEP 07, 208 (2024), arXiv: 2311.12113 [hep-th]

    work page arXiv 2024

  42. [42]

    Bedroya, R

    A. Bedroya, R. K. Mishra, and M. Wiesner, “Density of states, black holes and the Emergent String Conjecture”, JHEP 01, 144 (2025), arXiv: 2405.00083 [hep-th]

    work page arXiv 2025

  43. [43]

    Asymptotics of 5d supergravity the- ories and the emergent string conjecture

    L. Kaufmann, S. Lanza, and T. Weigand, “Asymptotics of 5d supergravity the- ories and the emergent string conjecture”, JHEP 06, 230 (2025), arXiv: 2412. 12251 [hep-th]

    work page 2025

  44. [44]

    On the Origin of Species Ther- modynamics and the Black Hole - Tower Correspondence

    A. Herr´ aez, D. L¨ ust, J. Masias, and M. Scalisi, “On the Origin of Species Ther- modynamics and the Black Hole - Tower Correspondence”, SciPost Phys. 18, 10.21468/SciPostPhys.18.3.083 (2025), arXiv:2406.17851 [hep-th] . 34

    work page doi:10.21468/scipostphys.18.3.083 2025

  45. [45]

    A short overview on the Black Hole-Tower Correspondence and Species Thermodynamics

    A. Herr´ aez, D. L¨ ust, J. Masias, and C. Montella, “A short overview on the Black Hole-Tower Correspondence and Species Thermodynamics”, in 24th Hel- lenic School and Workshops on Elementary Particle Physics and Gravity (June 2025), arXiv:2506.02335 [hep-th]

    work page arXiv 2025

  46. [46]

    Black Hole Transitions, AdS and the Distance Conjecture

    A. Herr´ aez, D. L¨ ust, and C. Montella, “Black Hole Transitions, AdS and the Distance Conjecture”, (2025), arXiv: 2503.19958 [hep-th]

    work page arXiv 2025

  47. [47]

    Emergent Strings in Type IIB Calabi–Yau Compactifications

    B. Friedrich, J. Monnee, T. Weigand, and M. Wiesner, “Emergent Strings in Type IIB Calabi–Yau Compactifications”, (2025), arXiv: 2504.01066 [hep-th]

    work page arXiv 2025

  48. [48]

    How to Create a Flat Ten or Eleven Dimensional Space-time in the Interior of an Asymptotically Flat Four Dimensional String Theory

    A. Sen, “How to Create a Flat Ten or Eleven Dimensional Space-time in the Interior of an Asymptotically Flat Four Dimensional String Theory”, (2025), arXiv:2503.00601 [hep-th]

    work page arXiv 2025

  49. [49]

    Decorating Asymptotically Flat Space-Time with the Moduli Space of String Theory

    A. Sen, “Decorating Asymptotically Flat Space-Time with the Moduli Space of String Theory”, (2025), arXiv: 2506.13876 [hep-th]

    work page arXiv 2025

  50. [50]

    Gravity from thermodynamics: Optimal transport and negative effective dimensions

    G. B. D. Luca, N. De Ponti, A. Mondino, and A. Tomasiello, “Gravity from thermodynamics: Optimal transport and negative effective dimensions”, SciPost Phys. 15, 039 (2023), arXiv: 2212.02511 [hep-th]

    work page arXiv 2023

  51. [51]

    An M-theory dS maximum from Casimir energies on Riemann-flat manifolds

    B. Valeixo Bento and M. Montero, “An M-theory dS maximum from Casimir energies on Riemann-flat manifolds”, (2025), arXiv: 2507.02037 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  52. [52]

    Remarks on scale separation in flux vacua

    F. F. Gautason, M. Schillo, T. Van Riet, and M. Williams, “Remarks on scale separation in flux vacua”, JHEP 03, 061 (2016), arXiv: 1512.00457 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  53. [53]

    Leaps and bounds towards scale separation

    G. B. De Luca and A. Tomasiello, “Leaps and bounds towards scale separation”, JHEP 12, 086 (2021), arXiv: 2104.12773 [hep-th]

    work page arXiv 2021

  54. [54]

    $AdS$ Vacua from Dilaton Tadpoles and Form Fluxes

    J. Mourad and A. Sagnotti, “ AdS Vacua from Dilaton Tadpoles and Form Fluxes”, Phys. Lett. B 768, 92–96 (2017), arXiv: 1612.08566 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  55. [55]

    On Classical Stability with Broken Supersymmetry

    I. Basile, J. Mourad, and A. Sagnotti, “On Classical Stability with Broken Su- persymmetry”, JHEP 01, 174 (2019), arXiv: 1811.11448 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  56. [56]

    Antonelli and I

    R. Antonelli and I. Basile, “Brane annihilation in non-supersymmetric strings”, JHEP 11, 021 (2019), arXiv: 1908.04352 [hep-th]

    work page arXiv 2019

  57. [57]

    ATKIN-LEHNER SYMMETRY

    G. W. Moore, “ATKIN-LEHNER SYMMETRY”, Nucl. Phys. B 293, [Erratum: Nucl.Phys.B 299, 847 (1988)], 139 (1987)

    work page 1988

  58. [58]

    GENERALIZED ATKIN-LEHNER SYMMETRY

    K. R. Dienes, “GENERALIZED ATKIN-LEHNER SYMMETRY”, Phys. Rev. D 42, 2004–2021 (1990)

    work page 2004

  59. [59]

    Can a Lattice String Have a Vanishing Cosmological Constant?

    T. Gannon and C. S. Lam, “Can a lattice string have a vanishing cosmological constant?”, Phys. Rev. D 46, 1710–1720 (1992), arXiv: hep-th/9201028

    work page internal anchor Pith review Pith/arXiv arXiv 1992

  60. [60]

    Quantum Hori- zons of the Standard Model Landscape

    N. Arkani-Hamed, S. Dubovsky, A. Nicolis, and G. Villadoro, “Quantum Hori- zons of the Standard Model Landscape”, JHEP 06, 078 (2007), arXiv: hep-th/ 0703067. 35

    work page 2007

  61. [61]

    Heat kernel expansion: user's manual

    D. V. Vassilevich, “Heat kernel expansion: User’s manual”, Phys. Rept. 388, 279–360 (2003), arXiv: hep-th/0306138

    work page internal anchor Pith review Pith/arXiv arXiv 2003

  62. [62]

    The heat kernel on hyperbolic space

    A. Grigor’yan and M. Noguchi, “The heat kernel on hyperbolic space”, Bul- letin of the London Mathematical Society 30, 643–650 (1998), eprint: https: //academic.oup.com/blms/article-pdf/30/6/643/856581/30-6-643.pdf

    work page 1998

  63. [63]

    Nonperturbative Instability of AdS_5 x S^5/Z_k

    G. T. Horowitz, J. Orgera, and J. Polchinski, “Nonperturbative Instability of AdS(5) x S**5/Z(k)”, Phys. Rev. D77, 024004 (2008), arXiv:0709.4262 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  64. [64]

    Small Steps and Giant Leaps in the Landscape

    A. R. Brown and A. Dahlen, “Small Steps and Giant Leaps in the Landscape”, Phys. Rev. D 82, 083519 (2010), arXiv: 1004.3994 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  65. [65]

    Bubbles of Nothing and the Fastest Decay in the Landscape

    A. R. Brown and A. Dahlen, “Bubbles of Nothing and the Fastest Decay in the Landscape”, Phys. Rev. D 84, 043518 (2011), arXiv: 1010.5240 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  66. [66]

    Giant Leaps and Minimal Branes in Multi-Dimensional Flux Landscapes

    A. R. Brown and A. Dahlen, “Giant Leaps and Minimal Branes in Multi-Dimensional Flux Landscapes”, Phys. Rev. D 84, 023513 (2011), arXiv:1010.5241 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  67. [67]

    Non-supersymmetric AdS and the Swampland

    H. Ooguri and C. Vafa, “Non-supersymmetric AdS and the Swampland”, Adv. Theor. Math. Phys. 21, 1787–1801 (2017), arXiv: 1610.01533 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  68. [68]

    Dibitetto, N

    G. Dibitetto, N. Petri, and M. Schillo, “Nothing really matters”, JHEP 08, 040 (2020), arXiv:2002.01764 [hep-th]

    work page arXiv 2020

  69. [69]

    Bomans, D

    P. Bomans, D. Cassani, G. Dibitetto, and N. Petri, “Bubble instability of mIIA on AdS4 × S6”, SciPost Phys. 12, 099 (2022), arXiv: 2110.08276 [hep-th]

    work page arXiv 2022

  70. [70]

    Searching for Coleman–de Luccia bubbles in AdS compactifications

    G. Dibitetto and N. Petri, “Searching for Coleman–de Luccia bubbles in AdS compactifications”, Phys. Rev. D107, 046020 (2023), arXiv:2207.02172 [hep-th]

    work page arXiv 2023

  71. [71]

    Positive energy in anti-de sitter back- grounds and gauged extended supergravity

    P. Breitenlohner and D. Z. Freedman, “Positive energy in anti-de sitter back- grounds and gauged extended supergravity”, Phys. Lett. B 115, 197–201 (1982)

    work page 1982

  72. [72]

    Casimir energies on a twisted two-torus

    H.-B. Cheng and X.-Z. Li, “Casimir energies on a twisted two-torus”, Chin. Phys. Lett. 18, 1163–1166 (2001)

    work page 2001

  73. [73]

    Casimir Energies due to Matter Fields in $T^{2}$ and $T^{2}/Z_{2}$ Compactifications

    M. Ito, “Casimir energies due to matter fields in T(2) and T(2)/Z(2) compacti- fications”, Nucl. Phys. B 668, 322–334 (2003), arXiv: hep-ph/0301168

    work page internal anchor Pith review Pith/arXiv arXiv 2003

  74. [74]

    The Shape of Compact Toroidal Dimensions $T^d_{\theta}$ and the Casimir Effect on $M^D\times T^d_{\theta}$ spacetime

    V. K. Oikonomou, “The Shape of Compact Toroidal Dimensions T**d(theta) and the Casimir Effect on M**D x T**d(theta) spacetime”, Commun. Theor. Phys. 55, 101–110 (2011), arXiv: 0905.4928 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  75. [75]

    Casimir energy and modularity in higher-dimensional conformal field theories

    C. Luo and Y. Wang, “Casimir energy and modularity in higher-dimensional conformal field theories”, JHEP 07, 028 (2023), arXiv: 2212.14866 [hep-th]

    work page arXiv 2023

  76. [76]

    On the stability of string theory vacua

    S. Giri, L. Martucci, and A. Tomasiello, “On the stability of string theory vacua”, JHEP 04, 054 (2022), arXiv: 2112.10795 [hep-th]

    work page arXiv 2022

  77. [77]

    Stability of non-supersymmetric vacua from calibrations

    V. Menet and A. Tomasiello, “Stability of non-supersymmetric vacua from cali- brations”, (2025), arXiv: 2507.02787 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  78. [78]

    Fake supersymmetry with tadpole potentials

    S. Raucci, “Fake supersymmetry with tadpole potentials”, JHEP 07, 078 (2023), arXiv:2304.12717 [hep-th] . 36

    work page arXiv 2023

  79. [79]

    Raucci, Spacetime aspects of non-supersymmetric strings

    S. Raucci, “Spacetime aspects of non-supersymmetric strings”, PhD thesis (Pisa, Scuola Normale Superiore, Sept. 2024), arXiv: 2409.19395 [hep-th]

    work page arXiv 2024

  80. [80]

    Non-supersymmetric AdS from string theory

    Z. K. Baykara, D. Robbins, and S. Sethi, “Non-supersymmetric AdS from string theory”, SciPost Phys. 15, 224 (2023), arXiv: 2212.02557 [hep-th]

    work page arXiv 2023

Showing first 80 references.