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Aspects of strings without spacetime supersymmetry

T0 review · 1 major / 2 minor · reviewed 2026-05-18 · grok-4.3

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Pith's one-line read Tachyons and worldsheet tadpoles challenge stable vacua in non-supersymmetric strings.

desk verdict This is a review that organizes the tachyon and tadpole issues in non-supersymmetric strings without adding new results or frameworks. read the letter →

arxiv 2509.24703 v2 submitted 2025-09-29 hep-th

Giorgio Leone , Salvatore Raucci This is my paper · ORCID
classification hep-th
keywords non-supersymmetricstringstachyonsworldsheettadpolesorientifoldprojectionsstringlandscapeten-dimensionalmodelsoff-shellapproaches
checked against alexander_duality_circle_linking
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

This review examines the main obstacles to finding stable string theory vacua when spacetime supersymmetry is absent. It explains the origin of tachyons in closed string spectra and their orientifold projections, along with off-shell techniques that can address these instabilities. The survey then focuses on tachyon-free ten-dimensional models and shows how tadpoles create additional constraints whose cancellation shapes the resulting spacetime physics. It closes by outlining recent efforts to chart the wider landscape of such models.

What carries the argument

Tachyons in closed strings and orientifold projections, together with worldsheet tadpoles whose cancellation is required in tachyon-free ten-dimensional models.

What would settle it

An explicit worldsheet computation for a specific orientifold projection that fails to reproduce the tachyon spectrum or tadpole structure described would test the characterizations in the survey.

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Extended reading notes

Core claim

In non-supersymmetric string constructions, tachyons appear in the spectra of closed strings and orientifold projections, and can be characterized through their worldsheet properties. Off-shell approaches provide tools to handle them beyond conventional on-shell methods. For tachyon-free ten-dimensional models, worldsheet tadpoles introduce further issues, and their cancellation produces concrete spacetime consequences for the field content and stability of the vacuum. The review synthesizes these elements and surveys ongoing attempts to explore the non-supersymmetric string landscape.

Load-bearing premise

The review assumes that the ten-dimensional models and recent landscape attempts it selects are representative of the main challenges in non-supersymmetric strings.

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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

1 major / 2 minor

Summary. The manuscript surveys aspects of string theory without spacetime supersymmetry. It covers the appearance and characterization of tachyons in closed strings and their orientifold projections, off-shell approaches to tackle tachyons, the simplest ten-dimensional tachyon-free non-supersymmetric models, the additional issues from tadpoles and spacetime consequences of their cancellation, and recent attempts to explore the non-supersymmetric string landscape.

Significance. The review is significant for providing a coherent structure to discuss key challenges in non-supersymmetric strings. It synthesizes literature on tachyons, tadpoles, and model building, which can aid researchers in navigating this area. No new derivations are presented, but the survey of prior work is a useful contribution if comprehensive.

major comments (1)
  1. [Ten-dimensional models section] The introduction of the simplest ten-dimensional models would benefit from an explicit statement of the selection criteria used, as this is central to assessing the generality of the tadpole cancellation consequences discussed.
minor comments (2)
  1. [Abstract] The abstract provides a good overview but could briefly indicate the main open questions or conclusions drawn from the survey.
  2. The paper should ensure that all technical terms, such as those related to orientifold projections, are defined at their first use for readers less familiar with the subfield.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the positive recommendation of minor revision. We address the single major comment below.

read point-by-point responses

  1. Referee: [Ten-dimensional models section] The introduction of the simplest ten-dimensional models would benefit from an explicit statement of the selection criteria used, as this is central to assessing the generality of the tadpole cancellation consequences discussed.

    Authors: We agree that an explicit statement of the selection criteria will improve clarity and help readers assess the generality of the tadpole cancellation results. In the revised manuscript we will add a brief paragraph in the relevant section stating that the models considered are the simplest tachyon-free, non-supersymmetric ten-dimensional string theories obtained from consistent heterotic constructions or orientifold projections that satisfy world-sheet modular invariance and level-matching conditions. This addition will directly address the referee's concern without altering the overall scope of the survey. revision: yes

Circularity Check

0 steps flagged · score 0.0 of 10

Review paper surveys prior literature with no new derivations or predictions

full rationale

This is a review article that describes existing results on tachyons in closed strings, orientifold projections, off-shell methods, and tachyon-free 10d models from the literature. No original derivation chain, quantitative prediction, or load-bearing assumption is advanced within the paper itself. All technical content is attributed to external citations, so no step reduces by construction to the paper's own inputs or self-citations. The presentation is self-contained as a survey.

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

As a review, the paper does not introduce new free parameters, axioms, or invented entities; it discusses concepts from the existing string theory literature.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Aspects of strings without spacetime supersymmetry." pith.science (2026). https://pith.science/paper/2509.24703

@misc{pith2026250924703,
  author       = {Pith},
  title        = {Pith review of: Aspects of strings without spacetime supersymmetry},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2509.24703}},
  note         = {Machine review of arXiv:2509.24703}
}
read the original abstract

String theory relies on spacetime supersymmetry to guarantee the existence of stable vacua. In this review, we survey two features of non-supersymmetric strings that challenge both aspects: the appearance of tachyons and worldsheet tadpoles. We describe how tachyons arise, how to characterise their presence in closed strings and in their orientifold projections, and how off-shell approaches can be used to tackle them. We then turn to tachyon-free, non-supersymmetric strings. After introducing the simplest ten-dimensional models, we address the additional issues raised by tadpoles and the spacetime consequences of their cancellation. Finally, we discuss recent attempts to explore the non-supersymmetric string landscape.

Discussion (0). Continue with ORCID to comment.

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Reference graph

Works this paper leans on

266 extracted references · 266 canonical work pages · cited by 9 Pith papers

  1. [1]

    Construction of a crossing - symmetric, Regge behaved amplitude for linearly rising trajectories

    Veneziano, G.: Construction of a crossing - symmetric, Regge behaved amplitude for linearly rising trajectories. Nuovo Cim. A 57, 190–197 (1968) https://doi. org/10.1007/BF02824451

    work page doi:10.1007/bf02824451 1968

  2. [2]

    PhD thesis, Universit` a degli Studi di Torino, Italy, Turin U

    Leone, G.: Aspects of Stability, Rigidity and Unitarity in String Vacua. PhD thesis, Universit` a degli Studi di Torino, Italy, Turin U. (2024)

    work page 2024

  3. [3]

    PhD thesis, Pisa, Scuola Normale Superiore (September 2024)

    Raucci, S.: Spacetime aspects of non-supersymmetric strings. PhD thesis, Pisa, Scuola Normale Superiore (September 2024)

    work page 2024

  4. [4]

    Schwarz, J.H.: Superstring Theory. Phys. Rept. 89, 223–322 (1982) https://doi. org/10.1016/0370-1573(82)90087-4

    work page doi:10.1016/0370-1573(82)90087-4 1982

  5. [5]

    Green, M.B., Schwarz, J.H., Witten, E.: Superstirng Theory. Vol. 1: Introduc- tion. Cambridge Monographs on Mathematical Physics, (1988)

    work page 1988

  6. [6]

    Green, M.B., Schwarz, J.H., Witten, E.: Superstring Theory. Vol. 2: Loop Amplitudes, Anomalies and Phenomenology, (1988)

    work page 1988

  7. [7]

    D’Hoker, E., Phong, D.H.: The Geometry of String Perturbation Theory. Rev. Mod. Phys. 60, 917 (1988) https://doi.org/10.1103/RevModPhys.60.917

    work page doi:10.1103/revmodphys.60.917 1988

  8. [8]

    In: Theoretical Advanced Study Insti- tute in Elementary Particle Physics (TASI 96): Fields, Strings, and Duality, pp

    Polchinski, J.: Tasi lectures on D-branes. In: Theoretical Advanced Study Insti- tute in Elementary Particle Physics (TASI 96): Fields, Strings, and Duality, pp. 293–356 (1996)

    work page 1996

Show all 266 references
  1. [9]

    In: NATO Advanced Study Institute: Les Houches Summer School on Theoretical Physics, Session 64: Quantum Symmetries, pp

    Dijkgraaf, R.: Les Houches lectures on fields, strings and duality. In: NATO Advanced Study Institute: Les Houches Summer School on Theoretical Physics, Session 64: Quantum Symmetries, pp. 3–147 (1997)

    1997

  2. [10]

    Polchinski, J.: String Theory. Vol. 1: An Introduction to the Bosonic String. Cambridge Monographs on Mathematical Physics, (1998). https://doi.org/10. 1017/CBO9780511816079

    1998

  3. [11]

    Polchinski, J.: String Theory. Vol. 2: Superstring Theory and Beyond. Cam- bridge Monographs on Mathematical Physics, (1998). https://doi.org/10.1017/ CBO9780511618123

    1998

  4. [12]

    In: A Newton Insti- tute Euroconference on Duality and Supersymmetric Theories, pp

    Sen, A.: An Introduction to nonperturbative string theory. In: A Newton Insti- tute Euroconference on Duality and Supersymmetric Theories, pp. 297–413 (1998)

    1998

  5. [13]

    Angelantonj, C., Sagnotti, A.: Open strings. Phys. Rept. 371, 1–150 (2002) https://doi.org/10.1016/S0370-1573(02)00273-9 arXiv:hep-th/0204089. [Erra- tum: Phys.Rept. 376, 407 (2003)] 50

    2002 doi arXiv

  6. [14]

    Witten, E.: Superstring Perturbation Theory Revisited (2012) arXiv:1209.5461 [hep-th]

    2012

  7. [15]

    Mourad, J., Sagnotti, A.: An Update on Brane Supersymmetry Breaking (2017) arXiv:1711.11494 [hep-th]

    2017 arXiv

  8. [16]

    PhD thesis, Pisa, Scuola Normale Superiore (2020)

    Basile, I.: On String Vacua without Supersymmetry: brane dynamics, bubbles and holography. PhD thesis, Pisa, Scuola Normale Superiore (2020)

    2020

  9. [17]

    Basile, I.: Supersymmetry breaking and stability in string vacua: Brane dynam- ics, bubbles and the swampland. Riv. Nuovo Cim. 44(10), 499–596 (2021) https://doi.org/10.1007/s40766-021-00024-9 arXiv:2107.02814 [hep-th]

    2021 doi

  10. [18]

    https://doi.org/10.1007/978-981-19-3079-9 53-1

    Angelantonj, C., Florakis, I.: A Lightning Introduction to String Theory, (2024). https://doi.org/10.1007/978-981-19-3079-9 53-1

    2024 doi

  11. [19]

    JHEP 10, 226 (2019) https: //doi.org/10.1007/JHEP10(2019)226 arXiv:1812.09714 [hep-th]

    Abel, S., Dudas, E., Lewis, D., Partouche, H.: Stability and vacuum energy in open string models with broken supersymmetry. JHEP 10, 226 (2019) https: //doi.org/10.1007/JHEP10(2019)226 arXiv:1812.09714 [hep-th]

    2019 doi

  12. [20]

    Itoyama, H., Nakajima, S.: Stability, enhanced gauge symmetry and sup- pressed cosmological constant in 9D heterotic interpolating models. Nucl. Phys. B 958, 115111 (2020) https://doi.org/10.1016/j.nuclphysb.2020.115111 arXiv:2003.11217 [hep-th]

    2020 doi

  13. [21]

    JHEP 11, 125 (2020) https://doi.org/10.1007/ JHEP11(2020)125 arXiv:2007.12722 [hep-th]

    Angelantonj, C., Bonnefoy, Q., Condeescu, C., Dudas, E.: String Defects, Super- symmetry and the Swampland. JHEP 11, 125 (2020) https://doi.org/10.1007/ JHEP11(2020)125 arXiv:2007.12722 [hep-th]

    2020

  14. [22]

    Faraggi, A.E., Matyas, V.G., Percival, B.: Type ¯0 heterotic string orbifolds. Phys. Lett. B 814, 136080 (2021) https://doi.org/10.1016/j.physletb.2021. 136080 arXiv:2011.12630 [hep-th]

    2021 doi

  15. [23]

    Itoyama, H., Nakajima, S.: Marginal deformations of heterotic interpolat- ing models and exponential suppression of the cosmological constant. Phys. Lett. B 816, 136195 (2021) https://doi.org/10.1016/j.physletb.2021.136195 arXiv:2101.10619 [hep-th]

    2021 doi

  16. [24]

    Itoyama, H., Koga, Y., Nakajima, S.: Target space duality of non- supersymmetric string theory. Nucl. Phys. B 975, 115667 (2022) https://doi. org/10.1016/j.nuclphysb.2022.115667 arXiv:2110.09762 [hep-th]

    2022 doi

  17. [25]

    Avalos, A.R.D., Faraggi, A.E., Matyas, V.G., Percival, B.: Fayet–Iliopoulos D- term in non-supersymmetric heterotic string orbifolds. Eur. Phys. J. C 83(10), 926 (2023) https://doi.org/10.1140/epjc/s10052-023-12059-9 arXiv:2302.10075 [hep-th] 51

    2023 doi

  18. [26]

    Nakajima, S.: New non-supersymmetric heterotic string theory with reduced rank and exponential suppression of the cosmological constant (2023) arXiv:2303.04489 [hep-th]

    2023

  19. [27]

    Avalos, A.R.D., Faraggi, A.E., Matyas, V.G., Percival, B.: D-term uplifts in nonsupersymmetric heterotic string models. Phys. Rev. D108(8), 086007 (2023) https://doi.org/10.1103/PhysRevD.108.086007 arXiv:2306.16878 [hep-th]

    2023 doi

  20. [28]

    JHEP 09, 056 (2024) https://doi.org/ 10.1007/JHEP09(2024)056 arXiv:2405.19409 [hep-th]

    Saxena, V.: A T-duality of non-supersymmetric heterotic strings and an impli- cation for Topological Modular Forms. JHEP 09, 056 (2024) https://doi.org/ 10.1007/JHEP09(2024)056 arXiv:2405.19409 [hep-th]

    2024 doi

  21. [29]

    Basaad, E., Detraux, L.A., Avalos, A.R.D., Faraggi, A.E., Percival, B.: Vac- uum energy in non-supersymmetric quasi-realistic heterotic-string vacua with fixed moduli. Eur. Phys. J. C 85(2), 209 (2025) https://doi.org/10.1140/epjc/ s10052-024-13733-2 arXiv:2408.03928 [hep-th]

    2025 doi

  22. [30]

    JHEP 04, 107 (2025) https://doi.org/10.1007/JHEP04(2025)107 arXiv:2412.01914 [hep-th]

    Abel, S., Basile, I., Matyas, V.G.: Banks-Zaks stabilisation of non-SUSY strings. JHEP 04, 107 (2025) https://doi.org/10.1007/JHEP04(2025)107 arXiv:2412.01914 [hep-th]

    2025 doi

  23. [31]

    JHEP 06, 136 (2025) https://doi.org/10.1007/ JHEP06(2025)136 arXiv:2412.17894 [hep-th]

    Larotonda, V., Lin, L.: Anomaly inflow and gauge group topology in the 10d Sugimoto string theory. JHEP 06, 136 (2025) https://doi.org/10.1007/ JHEP06(2025)136 arXiv:2412.17894 [hep-th]

    2025

  24. [32]

    JHEP 07, 090 (2025) https://doi.org/10.1007/JHEP07(2025)090 arXiv:2504.06985 [hep-th]

    Montero, M., Zapata, L.: M-theory boundaries beyond supersymmetry. JHEP 07, 090 (2025) https://doi.org/10.1007/JHEP07(2025)090 arXiv:2504.06985 [hep-th]

    2025 doi

  25. [33]

    Basile, I., Larotonda, V.: Non-supersymmetric branes and discrete topological terms (2025) arXiv:2507.11610 [hep-th]

    2025

  26. [34]

    In: Eotvos Summer School in Physics: Nonperturbative QFT Methods and Their Applications, pp

    Schweigert, C., Fuchs, J., Walcher, J.: Conformal field theory, boundary condi- tions and applications to string theory. In: Eotvos Summer School in Physics: Nonperturbative QFT Methods and Their Applications, pp. 37–93 (2000). https://doi.org/10.1142/9789812799968 0002

    2000 doi

  27. [35]

    Fields Inst

    Schweigert, C., Fuchs, J.: The World sheet revisited. Fields Inst. Commun. 39, 241–249 (2003) arXiv:hep-th/0105266

    2003 arXiv

  28. [36]

    Polyakov, A.M.: Quantum Geometry of Bosonic Strings. Phys. Lett. B 103, 207–210 (1981) https://doi.org/10.1016/0370-2693(81)90743-7

    1981 doi

  29. [37]

    Polyakov, A.M.: Quantum Geometry of Fermionic Strings. Phys. Lett. B 103, 211–213 (1981) https://doi.org/10.1016/0370-2693(81)90744-9

    1981 doi

  30. [38]

    Pure Appl

    Witten, E.: Notes On Supermanifolds and Integration. Pure Appl. Math. 52 Quart. 15(1), 3–56 (2019) https://doi.org/10.4310/PAMQ.2019.v15.n1.a1 arXiv:1209.2199 [hep-th]

    2019 doi arXiv

  31. [39]

    Pure Appl

    Witten, E.: Notes On Super Riemann Surfaces And Their Moduli. Pure Appl. Math. Quart. 15(1), 57–211 (2019) https://doi.org/10.4310/PAMQ.2019.v15. n1.a2 arXiv:1209.2459 [hep-th]

    2019 doi arXiv

  32. [40]

    JHEP 07, 023 (1998) https://doi.org/10.1088/1126-6708/1998/07/023 arXiv:hep-th/9806087

    Henningson, M., Skenderis, K.: The Holographic Weyl anomaly. JHEP 07, 023 (1998) https://doi.org/10.1088/1126-6708/1998/07/023 arXiv:hep-th/9806087

    1998 doi arXiv

  33. [41]

    Sci- Post Phys

    Eberhardt, L., Pal, S.: Holographic Weyl anomaly in string theory. Sci- Post Phys. 16(1), 027 (2024) https://doi.org/10.21468/SciPostPhys.16.1.027 arXiv:2307.03000 [hep-th]

    2024 doi

  34. [42]

    Liu, J., Polchinski, J.: Renormalization of the Mobius Volume. Phys. Lett. B 203, 39–43 (1988) https://doi.org/10.1016/0370-2693(88)91566-3

    1988 doi

  35. [43]

    Troost, J.: The AdS3 central charge in string theory. Phys. Lett. B705, 260–263 (2011) https://doi.org/10.1016/j.physletb.2011.10.007 arXiv:1109.1923 [hep-th]

    2011 doi arXiv

  36. [44]

    Distler, J., Kawai, H.: Conformal Field Theory and 2D Quantum Gravity. Nucl. Phys. B 321, 509–527 (1989) https://doi.org/10.1016/0550-3213(89)90354-4

    1989 doi

  37. [45]

    JHEP 01, 151 (2013) https://doi.org/10.1007/JHEP01(2013)151 arXiv:1210.2398 [hep-th]

    Maltz, J.: Gauge Invariant Computable Quantities In Timelike Liouville Theory. JHEP 01, 151 (2013) https://doi.org/10.1007/JHEP01(2013)151 arXiv:1210.2398 [hep-th]

    2013 doi arXiv

  38. [46]

    JHEP 09, 116 (2021) https://doi.org/10

    Anninos, D., Bautista, T., M¨ uhlmann, B.: The two-sphere partition function in two-dimensional quantum gravity. JHEP 09, 116 (2021) https://doi.org/10. 1007/JHEP09(2021)116 arXiv:2106.01665 [hep-th]

    2021

  39. [47]

    JHEP07, 132 (2022) https://doi.org/10.1007/ JHEP07(2022)132 arXiv:2107.01172 [hep-th]

    Mahajan, R., Stanford, D., Yan, C.: Sphere and disk partition functions in Liouville and in matrix integrals. JHEP07, 132 (2022) https://doi.org/10.1007/ JHEP07(2022)132 arXiv:2107.01172 [hep-th]

    2022

  40. [48]

    JHEP 07, 139 (2019) https://doi.org/10.1007/JHEP07(2019)139 arXiv:1906.06051 [hep- th]

    Erbin, H., Maldacena, J., Skliros, D.: Two-Point String Amplitudes. JHEP 07, 139 (2019) https://doi.org/10.1007/JHEP07(2019)139 arXiv:1906.06051 [hep- th]

    2019 doi

  41. [49]

    Gibbons, G.W., Hawking, S.W.: Action Integrals and Partition Functions in Quantum Gravity. Phys. Rev. D15, 2752–2756 (1977) https://doi.org/10.1103/ PhysRevD.15.2752

    1977

  42. [50]

    Shapiro, J.A.: On the Renormalization of Dual Models. Phys. Rev. D 11, 2937 (1975) https://doi.org/10.1103/PhysRevD.11.2937

    1975 doi

  43. [51]

    Ademollo, M., D’Adda, A., D’Auria, R., Gliozzi, F., Napolitano, E., Sciuto, S., Di Vecchia, P.: Soft Dilations and Scale Renormalization in Dual Theories. Nucl. 53 Phys. B 94, 221–259 (1975) https://doi.org/10.1016/0550-3213(75)90491-5

    1975 doi

  44. [52]

    In: NATO Advanced Summer Institute on Nonperturbative Quantum Field Theory (Cargese Summer Institute) (1987)

    Sagnotti, A.: Open Strings and their Symmetry Groups. In: NATO Advanced Summer Institute on Nonperturbative Quantum Field Theory (Cargese Summer Institute) (1987)

    1987

  45. [53]

    Pradisi, G., Sagnotti, A.: Open String Orbifolds. Phys. Lett. B216, 59–67 (1989) https://doi.org/10.1016/0370-2693(89)91369-5

    1989 doi

  46. [54]

    Bianchi, M., Sagnotti, A.: On the systematics of open string theories. Phys. Lett. B 247, 517–524 (1990) https://doi.org/10.1016/0370-2693(90)91894-H

    1990 doi

  47. [55]

    Bianchi, M., Pradisi, G., Sagnotti, A.: Toroidal compactification and symmetry breaking in open string theories. Nucl. Phys. B 376, 365–386 (1992) https: //doi.org/10.1016/0550-3213(92)90129-Y

    1992 doi

  48. [56]

    Polchinski, J.: Dirichlet Branes and Ramond-Ramond charges. Phys. Rev. Lett. 75, 4724–4727 (1995) https://doi.org/10.1103/PhysRevLett.75.4724 arXiv:hep- th/9510017

    1995 doi

  49. [57]

    JHEP 08, 026 (2021) https://doi.org/10.1007/JHEP08(2021)026 arXiv:2105.08726 [hep- th]

    Eberhardt, L., Pal, S.: The disk partition function in string theory. JHEP 08, 026 (2021) https://doi.org/10.1007/JHEP08(2021)026 arXiv:2105.08726 [hep- th]

    2021 doi

  50. [58]

    Gliozzi, F., Scherk, J., Olive, D.I.: Supergravity and the Spinor Dual Model. Phys. Lett. B 65, 282–286 (1976) https://doi.org/10.1016/0370-2693(76) 90183-0

    1976 doi

  51. [59]

    Gliozzi, F., Scherk, J., Olive, D.I.: Supersymmetry, Supergravity Theories and the Dual Spinor Model. Nucl. Phys. B 122, 253–290 (1977) https://doi.org/10. 1016/0550-3213(77)90206-1

    1977

  52. [60]

    Seiberg, N., Witten, E.: Spin Structures in String Theory. Nucl. Phys. B 276, 272 (1986) https://doi.org/10.1016/0550-3213(86)90297-X

    1986 doi

  53. [61]

    Kutasov, D., Seiberg, N.: Number of degrees of freedom, density of states and tachyons in string theory and CFT. Nucl. Phys. B 358, 600–618 (1991) https: //doi.org/10.1016/0550-3213(91)90426-X

    1991 doi

  54. [62]

    Horava, P.: Strings on World Sheet Orbifolds. Nucl. Phys. B327, 461–484 (1989) https://doi.org/10.1016/0550-3213(89)90279-4

    1989 doi

  55. [63]

    Bianchi, M., Sagnotti, A.: Twist symmetry and open string Wilson lines. Nucl. Phys. B 361, 519–538 (1991) https://doi.org/10.1016/0550-3213(91)90271-X

    1991 doi

  56. [64]

    Dudas, E.: Theory and phenomenology of type I strings and M theory. Class. Quant. Grav. 17, 41–116 (2000) https://doi.org/10.1088/0264-9381/17/22/201 arXiv:hep-ph/0006190 54

    2000 doi arXiv

  57. [65]

    Fioravanti, D., Pradisi, G., Sagnotti, A.: Sewing constraints and nonorientable open strings. Phys. Lett. B 321, 349–354 (1994) https://doi.org/10.1016/ 0370-2693(94)90255-0 arXiv:hep-th/9311183

    1994 arXiv

  58. [66]

    Paton, J.E., Chan, H.-M.: Generalized veneziano model with isospin. Nucl. Phys. B 10, 516–520 (1969) https://doi.org/10.1016/0550-3213(69)90038-8

    1969 doi

  59. [67]

    Sonoda, H.: Sewing Conformal Field Theories. Nucl. Phys. B 311, 401–416 (1988) https://doi.org/10.1016/0550-3213(88)90066-1

    1988 doi

  60. [68]

    Sonoda, H.: Sewing Conformal Field Theories, 2. Nucl. Phys. B 311, 417–432 (1988) https://doi.org/10.1016/0550-3213(88)90067-3

    1988 doi

  61. [69]

    Moore, G.W., Seiberg, N.: Polynomial Equations for Rational Conformal Field Theories. Phys. Lett. B 212, 451–460 (1988) https://doi.org/10.1016/ 0370-2693(88)91796-0

    1988

  62. [70]

    Moore, G.W., Seiberg, N.: Classical and Quantum Conformal Field Theory. Commun. Math. Phys. 123, 177 (1989) https://doi.org/10.1007/BF01238857

    1989 doi

  63. [71]

    Schellekens, A.N., Warner, N.P.: Anomalies, Characters and Strings. Nucl. Phys. B 287, 317 (1987) https://doi.org/10.1016/0550-3213(87)90108-8

    1987 doi

  64. [72]

    Schellekens, A.N., Warner, N.P.: Anomalies and Modular Invariance in String Theory. Phys. Lett. B 177, 317–323 (1986) https://doi.org/10.1016/ 0370-2693(86)90760-4

    1986

  65. [73]

    Green, M.B., Schwarz, J.H.: Anomaly Cancellation in Supersymmetric D=10 Gauge Theory and Superstring Theory. Phys. Lett. B 149, 117–122 (1984) https://doi.org/10.1016/0370-2693(84)91565-X

    1984 doi

  66. [74]

    Green, M.B., Schwarz, J.H., West, P.C.: Anomaly Free Chiral Theories in Six-Dimensions. Nucl. Phys. B 254, 327–348 (1985) https://doi.org/10.1016/ 0550-3213(85)90222-6

    1985

  67. [75]

    Sagnotti, A.: A Note on the Green-Schwarz mechanism in open string theo- ries. Phys. Lett. B 294, 196–203 (1992) https://doi.org/10.1016/0370-2693(92) 90682-T arXiv:hep-th/9210127

    1992 doi arXiv

  68. [76]

    JHEP 08, 003 (2019) https://doi.org/10.1007/JHEP08(2019)003 arXiv:1808.00009 [hep-th]

    Garc´ ıa-Etxebarria, I., Montero, M.: Dai-Freed anomalies in particle physics. JHEP 08, 003 (2019) https://doi.org/10.1007/JHEP08(2019)003 arXiv:1808.00009 [hep-th]

    2019 doi

  69. [77]

    Tachikawa, Y., Yamashita, M.: Topological Modular Forms and the Absence of All Heterotic Global Anomalies. Commun. Math. Phys. 402(2), 1585–1620 (2023) https://doi.org/10.1007/s00220-023-04761-2 arXiv:2108.13542 [hep-th]. [Erratum: Commun.Math.Phys. 402, 2131 (2023)] 55

    2023 doi

  70. [78]

    PTEP 2022(4), 04–107 (2022) https://doi.org/10.1093/ptep/ptab060 arXiv:2103.12211 [hep-th]

    Tachikawa, Y.: Topological modular forms and the absence of a heterotic global anomaly. PTEP 2022(4), 04–107 (2022) https://doi.org/10.1093/ptep/ptab060 arXiv:2103.12211 [hep-th]

    2022 doi

  71. [79]

    Debray, A., Dierigl, M., Heckman, J.J., Montero, M.: The anomaly that was not meant IIB. Fortsch. Phys. 70(1), 2100168 (2022) https://doi.org/10.1002/prop. 202100168 arXiv:2107.14227 [hep-th]

    2022 doi

  72. [80]

    Debray, A., Dierigl, M., Heckman, J.J., Montero, M.: The Chronicles of IIBordia: Dualities, Bordisms, and the Swampland (2023) arXiv:2302.00007 [hep-th]

    2023

  73. [81]

    JHEP 02, 092 (2024) https://doi.org/10.1007/ JHEP02(2024)092 arXiv:2310.06895 [hep-th]

    Basile, I., Debray, A., Delgado, M., Montero, M.: Global anomalies & bordism of non-supersymmetric strings. JHEP 02, 092 (2024) https://doi.org/10.1007/ JHEP02(2024)092 arXiv:2310.06895 [hep-th]

    2024

  74. [82]

    JHEP 04, 067 (2024) https://doi.org/10.1007/JHEP04(2024) 067 arXiv:2310.20480 [hep-th]

    Basile, I., Leone, G.: Anomaly constraints for heterotic strings and supergravity in six dimensions. JHEP 04, 067 (2024) https://doi.org/10.1007/JHEP04(2024) 067 arXiv:2310.20480 [hep-th]

    2024 doi

  75. [83]

    Pradisi, G., Sagnotti, A., Stanev, Y.S.: Completeness conditions for boundary operators in 2-D conformal field theory. Phys. Lett. B381, 97–104 (1996) https: //doi.org/10.1016/0370-2693(96)00578-3 arXiv:hep-th/9603097

    1996 doi arXiv

  76. [84]

    Stanev, Y.S.: Two-dimensional conformal field theory on open and unoriented surfaces. In: 4th SIGRAV Graduate School on Contemporary Relativity and Gravitational Physics and 2001 School on Algebraic Geometry and Physics: Geometry and Physics of Branes (SAGP 2001), pp. 39–85 (2001)

    2001

  77. [85]

    Gava, E., Jengo, R., Jayaraman, T., Ramachandran, R.: Multiloop Divergences in the Closed Bosonic String Theory. Phys. Lett. B 168, 207–211 (1986) https: //doi.org/10.1016/0370-2693(86)90964-0

    1986 doi

  78. [86]

    JHEP 03, 030 (2000) https: //doi.org/10.1088/1126-6708/2000/03/030 arXiv:hep-th/0002149

    Bianchi, M., Morales, J.F.: Anomalies \& tadpoles. JHEP 03, 030 (2000) https: //doi.org/10.1088/1126-6708/2000/03/030 arXiv:hep-th/0002149

    2000 doi arXiv

  79. [87]

    JHEP 06, 031 (1999) https://doi.org/10.1088/1126-6708/1999/06/031 arXiv:hep-th/9904071

    Aldazabal, G., Badagnani, D., Ibanez, L.E., Uranga, A.M.: Tadpole versus anomaly cancellation in D = 4, D = 6 compact IIB orientifolds. JHEP 06, 031 (1999) https://doi.org/10.1088/1126-6708/1999/06/031 arXiv:hep-th/9904071

    1999 doi arXiv

  80. [88]

    JHEP 04, 055 (2015) https: //doi.org/10.1007/JHEP04(2015)055 arXiv:1307.5124 [hep-th]

    Witten, E.: The Feynman iϵin String Theory. JHEP 04, 055 (2015) https: //doi.org/10.1007/JHEP04(2015)055 arXiv:1307.5124 [hep-th]

    2015 doi arXiv

  81. [89]

    SciPost Phys

    Eberhardt, L., Mizera, S.: Unitarity cuts of the worldsheet. SciPost Phys. 14(2), 015 (2023) https://doi.org/10.21468/SciPostPhys.14.2.015 arXiv:2208.12233 [hep-th]

    2023 doi

  82. [90]

    Marcus, N.: Unitarity and regularized divergences in string amplitudes. Phys. 56 Lett. B 219, 265–272 (1989) https://doi.org/10.1016/0370-2693(89)90389-4

    1989 doi

  83. [91]

    Baccianti, M.M., Chandra, J., Eberhardt, L., Hartman, T., Mizera, S.: Rademacher expansion of modular integrals (2025) arXiv:2501.13827 [hep-th]

    2025

  84. [92]

    Fradkin, E.S., Tseytlin, A.A.: Effective Field Theory from Quantized Strings. Phys. Lett. B 158, 316–322 (1985) https://doi.org/10.1016/0370-2693(85) 91190-6

    1985 doi

  85. [93]

    Fradkin, E.S., Tseytlin, A.A.: Quantum String Theory Effective Action. Nucl. Phys. B 261, 1–27 (1985) https://doi.org/10.1016/0550-3213(85)90559-0 . [Erratum: Nucl.Phys.B 269, 745–745 (1986)]

    1985 doi

  86. [94]

    Tseytlin, A.A.: Vector Field Effective Action in the Open Superstring Theory. Nucl. Phys. B 276, 391 (1986) https://doi.org/10.1016/0550-3213(86)90303-2 . [Erratum: Nucl.Phys.B 291, 876 (1987)]

    1986 doi

  87. [95]

    Metsaev, R.R., Tseytlin, A.A.: On Loop Corrections To String Theory Effec- tive Actions. Nucl. Phys. B 298, 109–132 (1988) https://doi.org/10.1016/ 0550-3213(88)90306-9

    1988

  88. [96]

    Tseytlin, A.A.: Sigma Model Approach To String Theory. Int. J. Mod. Phys. A 4, 1257 (1989) https://doi.org/10.1142/S0217751X8900056X

    1989 doi

  89. [97]

    Tseytlin, A.A.: STRING THEORY EFFECTIVE ACTION: STRING LOOP CORRECTIONS. Int. J. Mod. Phys. A 3, 365–395 (1988) https://doi.org/10. 1142/S0217751X88000138

    1988

  90. [98]

    Sci- Post Phys

    Ahmadain, A., Wall, A.C.: Off-shell strings I: S-matrix and action. Sci- Post Phys. 17(1), 005 (2024) https://doi.org/10.21468/SciPostPhys.17.1.005 arXiv:2211.08607 [hep-th]

    2024 doi

  91. [99]

    Ahmadain, A., Frenkel, A., Wall, A.C.: A Background-Independent Closed String Action at Tree Level (2024) arXiv:2410.11938 [hep-th]

    2024

  92. [100]

    Sen, A., Zwiebach, B.: String Field Theory: A Review (2024) arXiv:2405.19421 [hep-th]

    2024

  93. [101]

    Tseytlin, A.A.: Renormalization of Mobius Infinities and Partition Function Representation for String Theory Effective Action. Phys. Lett. B 202, 81–88 (1988) https://doi.org/10.1016/0370-2693(88)90857-X

    1988 doi

  94. [102]

    Tseytlin, A.A.: Mobius Infinity Subtraction and Effective Action in σModel Approach to Closed String Theory. Phys. Lett. B 208, 221–227 (1988) https: //doi.org/10.1016/0370-2693(88)90421-2

    1988 doi

  95. [103]

    Tseytlin, A.A.: On field redefinitions and exact solutions in string theory. Phys. Lett. B 317, 559–564 (1993) https://doi.org/10.1016/0370-2693(93)91372-T 57 arXiv:hep-th/9308042

    1993 doi arXiv

  96. [104]

    Banks, T.: The Tachyon potential in string theory. Nucl. Phys. B 361, 166–172 (1991) https://doi.org/10.1016/0550-3213(91)90620-D

    1991 doi

  97. [105]

    Tseytlin, A.A.: On the tachyonic terms in the string effective action. Phys. Lett. B 264, 311–318 (1991) https://doi.org/10.1016/0370-2693(91)90355-T

    1991 doi

  98. [106]

    Tseytlin, A.A.: Sigma model approach to string theory effective actions with tachyons. J. Math. Phys. 42, 2854–2871 (2001) https://doi.org/10.1063/1. 1376129 arXiv:hep-th/0011033

    2001 doi arXiv

  99. [107]

    Witten, E.: On background independent open string field theory. Phys. Rev. D 46, 5467–5473 (1992) https://doi.org/10.1103/PhysRevD.46.5467 arXiv:hep- th/9208027

    1992 doi

  100. [108]

    Witten, E.: Some computations in background independent off-shell string the- ory. Phys. Rev. D 47, 3405–3410 (1993) https://doi.org/10.1103/PhysRevD.47. 3405 arXiv:hep-th/9210065

    1993 doi arXiv

  101. [109]

    Shatashvili, S.L.: Comment on the background independent open string theory. Phys. Lett. B311, 83–86 (1993) https://doi.org/10.1016/0370-2693(93)90537-R arXiv:hep-th/9303143

    1993 doi arXiv

  102. [110]

    Shatashvili, S.L.: On the problems with background independence in string theory. Alg. Anal. 6, 215–226 (1994) https://doi.org/10.1007/3-540-58453-6 12 arXiv:hep-th/9311177

    1994 doi arXiv

  103. [111]

    JHEP 10, 045 (2000) https://doi.org/10.1088/ 1126-6708/2000/10/045 arXiv:hep-th/0009148

    Kutasov, D., Marino, M., Moore, G.W.: Some exact results on tachyon con- densation in string field theory. JHEP 10, 045 (2000) https://doi.org/10.1088/ 1126-6708/2000/10/045 arXiv:hep-th/0009148

    2000 arXiv

  104. [112]

    Harvey, J.A., Kutasov, D., Martinec, E.J.: On the relevance of tachyons (2000) arXiv:hep-th/0003101

    2000 arXiv

  105. [113]

    JHEP 08, 010 (1998) https://doi.org/10.1088/1126-6708/1998/08/010 arXiv:hep-th/9805019

    Sen, A.: Stable nonBPS bound states of BPS D-branes. JHEP 08, 010 (1998) https://doi.org/10.1088/1126-6708/1998/08/010 arXiv:hep-th/9805019

    1998 doi arXiv

  106. [114]

    JHEP 08, 012 (1998) https://doi.org/10.1088/1126-6708/1998/08/012 arXiv:hep-th/9805170

    Sen, A.: Tachyon condensation on the brane anti-brane system. JHEP 08, 012 (1998) https://doi.org/10.1088/1126-6708/1998/08/012 arXiv:hep-th/9805170

    1998 doi arXiv

  107. [115]

    JHEP03, 002 (2000) https://doi.org/10.1088/1126-6708/2000/03/002 arXiv:hep-th/9912249

    Sen, A., Zwiebach, B.: Tachyon condensation in string field theory. JHEP03, 002 (2000) https://doi.org/10.1088/1126-6708/2000/03/002 arXiv:hep-th/9912249

    2000 doi arXiv

  108. [116]

    Schnabl, M.: Analytic solution for tachyon condensation in open string field the- ory. Adv. Theor. Math. Phys. 10(4), 433–501 (2006) https://doi.org/10.4310/ ATMP.2006.v10.n4.a1 arXiv:hep-th/0511286 58

    2006 arXiv

  109. [117]

    Hellerman, S., Swanson, I.: A Stable vacuum of the tachyonic E8 string (2007) arXiv:0710.1628 [hep-th]

    2007 arXiv

  110. [118]

    Kaidi, J.: Stable Vacua for Tachyonic Strings. Phys. Rev. D 103(10), 106026 (2021) https://doi.org/10.1103/PhysRevD.103.106026 arXiv:2010.10521 [hep- th]

    2021 doi

  111. [119]

    Kaidi, J., Ohmori, K., Tachikawa, Y., Yonekura, K.: Nonsupersymmetric Het- erotic Branes. Phys. Rev. Lett.131(12), 121601 (2023) https://doi.org/10.1103/ PhysRevLett.131.121601 arXiv:2303.17623 [hep-th]

    2023

  112. [120]

    JHEP 03, 211 (2025) https://doi.org/10.1007/JHEP03(2025)211 arXiv:2411.04344 [hep-th]

    Kaidi, J., Tachikawa, Y., Yonekura, K.: On non-supersymmetric het- erotic branes. JHEP 03, 211 (2025) https://doi.org/10.1007/JHEP03(2025)211 arXiv:2411.04344 [hep-th]

    2025 doi

  113. [121]

    Dienes, K.R.: Modular invariance, finiteness, and misaligned supersymmetry: New constraints on the numbers of physical string states. Nucl. Phys. B 429, 533–588 (1994) https://doi.org/10.1016/0550-3213(94)90153-8 arXiv:hep- th/9402006

    1994 doi

  114. [122]

    Rademacher, H.: A Convergent Series for the Partition Function p(n). Proc. Natl. Acad. Sci. 23, 78 (1937)

    1937

  115. [123]

    Rademacher, H.: On the Partition Function p(n). Proc. Lond. Math. Soc. 43, 241 (1937)

    1937

  116. [124]

    Rademacher, H.: The Fourier Coefficients of the Modular Invariant J(τ). Am. J. Math. 60, 501 (1938)

    1938

  117. [125]

    Dijkgraaf, R., Maldacena, J.M., Moore, G.W., Verlinde, E.P.: A Black hole Farey tail (2000) arXiv:hep-th/0005003

    2000 arXiv

  118. [126]

    Manschot, J., Moore, G.W.: A Modern Farey Tail. Commun. Num. Theor. Phys. 4, 103–159 (2010) https://doi.org/10.4310/CNTP.2010.v4.n1.a3 arXiv:0712.0573 [hep-th]

    2010 doi arXiv

  119. [127]

    Hardy, G.H., Ramanujan, S.: Asymptotic Formulaæ in Combinatory Analysis. Proc. Lond. Math. Soc. 17, 75 (1918)

    1918

  120. [128]

    Kani, I., Vafa, C.: Asymptotic Mass Degeneracies in Conformal Field The- ories. Commun. Math. Phys. 130, 529–580 (1990) https://doi.org/10.1007/ BF02096934

    1990

  121. [129]

    JHEP 04, 099 (2021) https://doi.org/10.1007/ JHEP04(2021)099 arXiv:2012.04677 [hep-th] 59

    Cribiori, N., Parameswaran, S., Tonioni, F., Wrase, T.: Misaligned Super- symmetry and Open Strings. JHEP 04, 099 (2021) https://doi.org/10.1007/ JHEP04(2021)099 arXiv:2012.04677 [hep-th] 59

    2021

  122. [130]

    JHEP 06, 174 (2023) https://doi.org/10.1007/ JHEP06(2023)174 arXiv:2301.13702 [hep-th]

    Angelantonj, C., Florakis, I., Leone, G.: Tachyons and misaligned supersym- metry in closed string vacua. JHEP 06, 174 (2023) https://doi.org/10.1007/ JHEP06(2023)174 arXiv:2301.13702 [hep-th]

    2023

  123. [131]

    Cardy, J.L.: Duality and the Theta Parameter in Abelian Lattice Models. Nucl. Phys. B 205, 17–26 (1982) https://doi.org/10.1016/0550-3213(82)90464-3

    1982 doi

  124. [132]

    JHEP 11, 066 (2023) https://doi.org/10.1007/JHEP11(2023)066 arXiv:2308.09757 [hep-th]

    Leone, G.: Tachyons and Misaligned Supersymmetry in orientifold vacua. JHEP 11, 066 (2023) https://doi.org/10.1007/JHEP11(2023)066 arXiv:2308.09757 [hep-th]

    2023 doi

  125. [133]

    Sagnotti, A.: Surprises in open string perturbation theory. Nucl. Phys. B Proc. Suppl. 56, 332–343 (1997) https://doi.org/10.1016/S0920-5632(97) 00344-7 arXiv:hep-th/9702093

    1997 doi arXiv

  126. [134]

    Lerche, W., Lust, D., Schellekens, A.N.: Ten-dimensional Heterotic Strings From Niemeier Lattices. Phys. Lett. B 181, 71 (1986) https://doi.org/10.1016/ 0370-2693(86)91257-8

    1986

  127. [135]

    Niemeier, H.V.: Definite quadratische Formen der Dimension 24 und Diskrimi- nante 1,. J. Number Theory 5, 142–178 (1973)

    1973

  128. [136]

    779, (2009)

    Blumenhagen, R., Plauschinn, E.: Introduction to Conformal Field Theory : with Applications to String Theory vol. 779, (2009). https://doi.org/10.1007/ 978-3-642-00450-6

    2009

  129. [137]

    JHEP12, 055 (2023) https://doi.org/10.1007/JHEP12(2023)055 arXiv:2309.15988 [hep-th]

    Markou, C., Skvortsov, E.: An excursion into the string spectrum. JHEP12, 055 (2023) https://doi.org/10.1007/JHEP12(2023)055 arXiv:2309.15988 [hep-th]

    2023 doi

  130. [138]

    JHEP 07, 184 (2024) https://doi.org/10.1007/JHEP07(2024)184 arXiv:2405.18467 [hep-th]

    Basile, T., Markou, C.: On the deep superstring spectrum. JHEP 07, 184 (2024) https://doi.org/10.1007/JHEP07(2024)184 arXiv:2405.18467 [hep-th]

    2024 doi

  131. [139]

    Alvarez-Gaume, L., Ginsparg, P.H., Moore, G.W., Vafa, C.: An O(16) x O(16) Heterotic String. Phys. Lett. B 171, 155–162 (1986) https://doi.org/10.1016/ 0370-2693(86)91524-8

    1986

  132. [140]

    Kawai, H., Lewellen, D.C., Tye, S.H.H.: Classification of Closed Fermionic String Models. Phys. Rev. D 34, 3794 (1986) https://doi.org/10.1103/PhysRevD.34. 3794

    1986 doi

  133. [141]

    Dixon, L.J., Harvey, J.A.: String Theories in Ten-Dimensions Without Space- Time Supersymmetry. Nucl. Phys. B 274, 93–105 (1986) https://doi.org/10. 1016/0550-3213(86)90619-X

    1986

  134. [142]

    Com- mun

    Schellekens, A.N.: Meromorphic C = 24 conformal field theories. Com- mun. Math. Phys. 153, 159–186 (1993) https://doi.org/10.1007/BF02099044 arXiv:hep-th/9205072 60

    1993 doi arXiv

  135. [143]

    SciPost Phys

    Boyle Smith, P., Lin, Y.-H., Tachikawa, Y., Zheng, Y.: Classification of chiral fermionic CFTs of central charge ≤16. SciPost Phys. 16(2), 058 (2024) https: //doi.org/10.21468/SciPostPhys.16.2.058 arXiv:2303.16917 [hep-th]

    2024 doi

  136. [144]

    Ginsparg, P.H., Vafa, C.: Toroidal Compactification of Nonsupersymmetric Heterotic Strings. Nucl. Phys. B 289, 414 (1987) https://doi.org/10.1016/ 0550-3213(87)90387-7

    1987

  137. [145]

    Narain, K.S., Sarmadi, M.H., Vafa, C.: Asymmetric Orbifolds. Nucl. Phys. B 288, 551 (1987) https://doi.org/10.1016/0550-3213(87)90228-8

    1987 doi

  138. [146]

    Narain, K.S., Sarmadi, M.H., Vafa, C.: Asymmetric orbifolds: Path integral and operator formulations. Nucl. Phys. B 356, 163–207 (1991) https://doi.org/10. 1016/0550-3213(91)90145-N

    1991

  139. [147]

    Aldazabal, G., Andr´ es, E., Font, A., Narain, K., Zadeh, I.G.: Asymmet- ric Orbifolds, Rank Reduction and Heterotic Islands (2025) arXiv:2501.17228 [hep-th]

    2025

  140. [148]

    Harvey, J.A., Moore, G.W., Vafa, C.: Quasirystalline Compactification. Nucl. Phys. B 304, 269–290 (1988) https://doi.org/10.1016/0550-3213(88)90627-X

    1988 doi

  141. [149]

    Baykara, Z.K., Tarazi, H.-C., Vafa, C.: New Non-Supersymmetric Tachyon-Free Strings (2024) arXiv:2406.00185 [hep-th]

    2024

  142. [150]

    Baykara, Z.K., Tarazi, H.-C., Vafa, C.: Quasicrystalline string landscape. Phys. Rev. D 111(8), 086025 (2025) https://doi.org/10.1103/PhysRevD.111.086025 arXiv:2406.00129 [hep-th]

    2025 doi

  143. [151]

    JHEP 10, 216 (2024) https://doi.org/10.1007/JHEP10(2024)216 arXiv:2407.09597 [hep- th]

    Angelantonj, C., Florakis, I., Leone, G., Perugini, D.: Non-supersymmetric non- tachyonic heterotic vacua with reduced rank in various dimensions. JHEP 10, 216 (2024) https://doi.org/10.1007/JHEP10(2024)216 arXiv:2407.09597 [hep- th]

    2024 doi

  144. [152]

    JHEP 01, 174 (2019) https://doi.org/10.1007/JHEP01(2019)174 arXiv:1811.11448 [hep-th]

    Basile, I., Mourad, J., Sagnotti, A.: On Classical Stability with Broken Super- symmetry. JHEP 01, 174 (2019) https://doi.org/10.1007/JHEP01(2019)174 arXiv:1811.11448 [hep-th]

    2019 doi arXiv

  145. [153]

    SciPost Phys

    Baykara, Z.K., Robbins, D., Sethi, S.: Non-supersymmetric AdS from string theory. SciPost Phys. 15(6), 224 (2023) https://doi.org/10.21468/SciPostPhys. 15.6.224 arXiv:2212.02557 [hep-th]

    2023 doi

  146. [154]

    Sugimoto, S.: Anomaly cancellations in type I D-9 - anti-D-9 system and the USp(32) string theory. Prog. Theor. Phys.102, 685–699 (1999) https://doi.org/ 10.1143/PTP.102.685 arXiv:hep-th/9905159 61

    1999 doi arXiv

  147. [155]

    Dudas, E., Mourad, J.: Consistent gravitino couplings in nonsupersymmet- ric strings. Phys. Lett. B 514, 173–182 (2001) https://doi.org/10.1016/ S0370-2693(01)00777-8 arXiv:hep-th/0012071

    2001 arXiv

  148. [156]

    JETP Lett

    Volkov, D.V., Akulov, V.P.: Possible universal neutrino interaction. JETP Lett. 16, 438–440 (1972)

    1972

  149. [157]

    Antoniadis, I., Dudas, E., Sagnotti, A.: Brane supersymmetry breaking. Phys. Lett. B 464, 38–45 (1999) https://doi.org/10.1016/S0370-2693(99)01023-0 arXiv:hep-th/9908023

    1999 doi arXiv

  150. [158]

    JHEP 10, 024 (1999) https://doi.org/ 10.1088/1126-6708/1999/10/024 arXiv:hep-th/9908072

    Aldazabal, G., Uranga, A.M.: Tachyon free nonsupersymmetric type IIB orien- tifolds via Brane - anti-brane systems. JHEP 10, 024 (1999) https://doi.org/ 10.1088/1126-6708/1999/10/024 arXiv:hep-th/9908072

    1999 doi arXiv

  151. [159]

    JHEP 04, 103 (2024) https://doi.org/10.1007/ JHEP04(2024)103 arXiv:2403.02392 [hep-th]

    Angelantonj, C., Condeescu, C., Dudas, E., Leone, G.: Rigid vacua with Brane Supersymmetry Breaking. JHEP 04, 103 (2024) https://doi.org/10.1007/ JHEP04(2024)103 arXiv:2403.02392 [hep-th]

    2024

  152. [160]

    JHEP 06, 062 (2025) https://doi.org/10.1007/ JHEP06(2025)062 arXiv:2412.19185 [hep-th]

    Leone, G.: New comments on six-dimensional orientifold vacua with reduced rank and unitarity constraints. JHEP 06, 062 (2025) https://doi.org/10.1007/ JHEP06(2025)062 arXiv:2412.19185 [hep-th]

    2025

  153. [161]

    Klebanov, I.R., Tseytlin, A.A.: D-branes and dual gauge theories in type 0 strings. Nucl. Phys. B 546, 155–181 (1999) https://doi.org/10.1016/ S0550-3213(99)00041-3 arXiv:hep-th/9811035

    1999 arXiv

  154. [162]

    Dudas, E., Mourad, J., Sagnotti, A.: Charged and uncharged D-branes in various string theories. Nucl. Phys. B 620, 109–151 (2002) https://doi.org/10.1016/ S0550-3213(01)00552-1 arXiv:hep-th/0107081

    2002 arXiv

  155. [163]

    In: International Workshop on Supersymmetry and Unification of Fundamental Interactions (SUSY 95), pp

    Sagnotti, A.: Some properties of open string theories. In: International Workshop on Supersymmetry and Unification of Fundamental Interactions (SUSY 95), pp. 473–484 (1995)

    1995

  156. [164]

    JHEP 12, 082 (2024) https://doi.org/10.1007/ JHEP12(2024)082 arXiv:2307.13745 [hep-th]

    Fraiman, B., Gra˜ na, M., Parra De Freitas, H., Sethi, S.: Non-supersymmetric heterotic strings on a circle. JHEP 12, 082 (2024) https://doi.org/10.1007/ JHEP12(2024)082 arXiv:2307.13745 [hep-th]

    2024

  157. [165]

    JHEP 11, 002 (2024) https://doi.org/10.1007/JHEP11(2024)002 arXiv:2402.15562 [hep-th]

    De Freitas, H.P.: Non-supersymmetric heterotic strings and chiral CFTs. JHEP 11, 002 (2024) https://doi.org/10.1007/JHEP11(2024)002 arXiv:2402.15562 [hep-th]

    2024 doi

  158. [166]

    Antoniadis, I., Avalos, A.R.D., Faraggi, A.E.: A Perturbatively Stable Non- Supersymmetric String Model with AdS Vacuum (2025) arXiv:2504.19364 [hep- th] 62

    2025

  159. [167]

    Angelantonj, C.: Comments on open string orbifolds with a nonvanishing B(ab). Nucl. Phys. B 566, 126–150 (2000) https://doi.org/10.1016/S0550-3213(99) 00662-8 arXiv:hep-th/9908064

    2000 doi arXiv

  160. [168]

    Angelantonj, C., Antoniadis, I., D’Appollonio, G., Dudas, E., Sagnotti, A.: Type I vacua with brane supersymmetry breaking. Nucl. Phys. B 572, 36–70 (2000) https://doi.org/10.1016/S0550-3213(00)00052-3 arXiv:hep-th/9911081

    2000 doi arXiv

  161. [169]

    Pradisi, G., Riccioni, F.: Geometric couplings and brane supersymmetry break- ing. Nucl. Phys. B 615, 33–60 (2001) https://doi.org/10.1016/S0550-3213(01) 00441-2 arXiv:hep-th/0107090

    2001 doi arXiv

  162. [170]

    JHEP 04, 081 (2018) https://doi.org/10.1007/JHEP04(2018)081 arXiv:1802.03088 [hep-th]

    Kitazawa, N.: Brane SUSY Breaking and the Gravitino Mass. JHEP 04, 081 (2018) https://doi.org/10.1007/JHEP04(2018)081 arXiv:1802.03088 [hep-th]

    2018 doi arXiv

  163. [171]

    Polchinski, J.: Factorization of Bosonic String Amplitudes. Nucl. Phys. B 307, 61–92 (1988) https://doi.org/10.1016/0550-3213(88)90522-6

    1988 doi

  164. [172]

    Belavin, A.A., Knizhnik, V.G.: Algebraic Geometry and the Geometry of Quantum Strings. Phys. Lett. B 168, 201–206 (1986) https://doi.org/10.1016/ 0370-2693(86)90963-9

    1986

  165. [173]

    Moore, G.W.: Modular Forms and Two Loop String Physics. Phys. Lett. B 176, 369–379 (1986) https://doi.org/10.1016/0370-2693(86)90180-2

    1986 doi

  166. [174]

    Kato, A., Matsuo, Y., Odake, S.: Modular Invariance and Two Loop Bosonic String Vacuum Amplitude. Phys. Lett. B 179, 241–246 (1986) https://doi.org/ 10.1016/0370-2693(86)90573-3

    1986 doi

  167. [175]

    Alvarez-Gaume, L., Moore, G.W., Vafa, C.: Theta Functions, Modular Invari- ance and Strings. Commun. Math. Phys. 106, 1–40 (1986) https://doi.org/10. 1007/BF01210925

    1986

  168. [176]

    Martinec, E.J.: Nonrenormalization Theorems and Fermionic String Finiteness. Phys. Lett. B 171, 189 (1986) https://doi.org/10.1016/0370-2693(86)91529-7

    1986 doi

  169. [177]

    Friedan, D., Martinec, E.J., Shenker, S.H.: Conformal invariance, supersymme- try and string theory. Nucl. Phys. B 271, 93–165 (1986) https://doi.org/10. 1016/S0550-3213(86)80006-2

    1986

  170. [178]

    Fischler, W., Susskind, L.: Dilaton Tadpoles, String Condensates and Scale Invariance. Phys. Lett. B 171, 383–389 (1986) https://doi.org/10.1016/ 0370-2693(86)91425-5

    1986

  171. [179]

    Fischler, W., Susskind, L.: Dilaton Tadpoles, String Condensates and Scale Invariance. 2. Phys. Lett. B 173, 262–264 (1986) https://doi.org/10.1016/ 0370-2693(86)90514-9 63

    1986

  172. [180]

    Lovelace, C.: Stability of String Vacua. 1. A New Picture of the Renormal- ization Group. Nucl. Phys. B 273, 413–467 (1986) https://doi.org/10.1016/ 0550-3213(86)90253-1

    1986

  173. [181]

    Jr., Lovelace, C., Nappi, C.R., Yost, S.A.: String Loop Corrections to beta Functions

    Callan, C.G. Jr., Lovelace, C., Nappi, C.R., Yost, S.A.: String Loop Corrections to beta Functions. Nucl. Phys. B 288, 525–550 (1987) https://doi.org/10.1016/ 0550-3213(87)90227-6

    1987

  174. [182]

    Das, S.R., Rey, S.-J.: Dilaton Condensates and Loop Effects in Open and Closed Bosonic Strings. Phys. Lett. B 186, 328–338 (1987) https://doi.org/10.1016/ 0370-2693(87)90303-0

    1987

  175. [183]

    Jr., Lovelace, C., Nappi, C.R., Yost, S.A.: Loop Corrections to Conformal Invariance for Type 1 Superstrings

    Callan, C.G. Jr., Lovelace, C., Nappi, C.R., Yost, S.A.: Loop Corrections to Conformal Invariance for Type 1 Superstrings. Phys. Lett. B 206, 41–46 (1988) https://doi.org/10.1016/0370-2693(88)91259-2

    1988 doi

  176. [184]

    Jr., Lovelace, C., Nappi, C.R., Yost, S.A.: Loop Corrections to Superstring Equations of Motion

    Callan, C.G. Jr., Lovelace, C., Nappi, C.R., Yost, S.A.: Loop Corrections to Superstring Equations of Motion. Nucl. Phys. B 308, 221–284 (1988) https: //doi.org/10.1016/0550-3213(88)90565-2

    1988 doi

  177. [185]

    Russo, J., Tseytlin, A.A.: RENORMALIZATION OF MULTIPLE INFINITIES AND RENORMALIZATION GROUP IN STRING LOOPS. Nucl. Phys. B340, 113–147 (1990) https://doi.org/10.1016/0550-3213(90)90159-B

    1990 doi

  178. [186]

    Tseytlin, A.A.: Renormalization group and string loops. Int. J. Mod. Phys. A 5, 589–658 (1990) https://doi.org/10.1142/S0217751X90000301

    1990 doi

  179. [187]

    Dudas, E., Pradisi, G., Nicolosi, M., Sagnotti, A.: On tadpoles and vacuum redefinitions in string theory. Nucl. Phys. B 708, 3–44 (2005) https://doi.org/ 10.1016/j.nuclphysb.2004.11.028 arXiv:hep-th/0410101

    2005 doi arXiv

  180. [188]

    JHEP 10, 070 (2014) https://doi.org/10.1007/JHEP10(2014) 070 arXiv:1404.6254 [hep-th]

    Pius, R., Rudra, A., Sen, A.: String Perturbation Theory Around Dynamically Shifted Vacuum. JHEP 10, 070 (2014) https://doi.org/10.1007/JHEP10(2014) 070 arXiv:1404.6254 [hep-th]

    2014 doi arXiv

  181. [189]

    JHEP 12, 075 (2015) https://doi.org/10.1007/JHEP12(2015)075 arXiv:1508.02481 [hep-th]

    Sen, A.: Supersymmetry Restoration in Superstring Perturbation Theory. JHEP 12, 075 (2015) https://doi.org/10.1007/JHEP12(2015)075 arXiv:1508.02481 [hep-th]

    2015 doi arXiv

  182. [190]

    Kitazawa, N.: Tadpole Resummations in String Theory. Phys. Lett. B 660, 415–421 (2008) https://doi.org/10.1016/j.physletb.2008.01.028 arXiv:0801.1702 [hep-th]

    2008 doi arXiv

  183. [191]

    Dudas, E., Mourad, J.: Brane solutions in strings with broken supersymmetry and dilaton tadpoles. Phys. Lett. B 486, 172–178 (2000) https://doi.org/10. 1016/S0370-2693(00)00734-6 arXiv:hep-th/0004165 64

    2000 arXiv

  184. [192]

    Universe 8(10), 544 (2022) https://doi.org/10.3390/universe8100544 arXiv:2209.10553 [hep-th]

    Basile, I., Raucci, S., Thom´ ee, S.: Revisiting Dudas-Mourad Compactifi- cations. Universe 8(10), 544 (2022) https://doi.org/10.3390/universe8100544 arXiv:2209.10553 [hep-th]

    2022 doi

  185. [193]

    Blumenhagen, R., Font, A.: Dilaton tadpoles, warped geometries and large extra dimensions for nonsupersymmetric strings. Nucl. Phys. B 599, 241–254 (2001) https://doi.org/10.1016/S0550-3213(01)00028-1 arXiv:hep-th/0011269

    2001 doi arXiv

  186. [194]

    Dudas, E., Mourad, J., Timirgaziu, C.: Time and space dependent backgrounds from nonsupersymmetric strings. Nucl. Phys. B 660, 3–24 (2003) https://doi. org/10.1016/S0550-3213(03)00248-7 arXiv:hep-th/0209176

    2003 doi arXiv

  187. [195]

    Pelliconi, P., Sagnotti, A.: Integrable Models and Supersymmetry Breaking. Nucl. Phys. B 965, 115363 (2021) https://doi.org/10.1016/j.nuclphysb.2021. 115363 arXiv:2102.06184 [hep-th]

    2021 doi

  188. [196]

    Mourad, J., Sagnotti, A.: On warped string vacuum profiles and cosmologies. Part I. Supersymmetric strings. JHEP 12, 137 (2021) https://doi.org/10.1007/ JHEP12(2021)137 arXiv:2109.06852 [hep-th]

    2021

  189. [197]

    Mourad, J., Sagnotti, A.: On warped string vacuum profiles and cosmologies. Part II. Non-supersymmetric strings. JHEP 12, 138 (2021) https://doi.org/10. 1007/JHEP12(2021)138 arXiv:2109.12328 [hep-th]

    2021

  190. [198]

    Mourad, J., Sagnotti, A.: A 4D IIB flux vacuum and supersymmetry break- ing. Part I. Fermionic spectrum. JHEP 08, 301 (2022) https://doi.org/10.1007/ JHEP08(2022)301 arXiv:2206.03340 [hep-th]

    2022

  191. [199]

    Mourad, J., Sagnotti, A.: A 4D IIB flux vacuum and supersymmetry breaking. Part II. Bosonic spectrum and stability. JHEP 11, 061 (2023) https://doi.org/ 10.1007/JHEP11(2023)061 arXiv:2309.04026 [hep-th]

    2023 doi

  192. [200]

    Mourad, J., Sagnotti, A.: Effective orientifolds from broken supersymmetry. J. Phys. A 57(3), 035401 (2024) https://doi.org/10.1088/1751-8121/ad16f8 arXiv:2309.05268 [hep-th]

    2024 doi

  193. [201]

    JHEP 10, 054 (2024) https://doi.org/10.1007/ JHEP10(2024)054 arXiv:2406.14926 [hep-th]

    Mourad, J., Raucci, S., Sagnotti, A.: Brane-like solutions and other non-supersymmetric vacua. JHEP 10, 054 (2024) https://doi.org/10.1007/ JHEP10(2024)054 arXiv:2406.14926 [hep-th]

    2024

  194. [202]

    Mourad, J., Sagnotti, A.: On boundaries, charges and Fermi fields. Phys. Lett. B 804, 135368 (2020) https://doi.org/10.1016/j.physletb.2020.135368 arXiv:2002.05372 [hep-th]

    2020 doi

  195. [203]

    Raucci, S.: On codimension-one vacua and string theory. Nucl. Phys. B 985, 116002 (2022) https://doi.org/10.1016/j.nuclphysb.2022.116002 arXiv:2206.06399 [hep-th] 65

    2022 doi

  196. [204]

    JHEP 08, 041 (2023) https://doi.org/10.1007/JHEP08(2023)041 arXiv:2305.09587 [hep-th]

    Mourad, J., Sagnotti, A.: Non-supersymmetric vacua and self-adjoint extensions. JHEP 08, 041 (2023) https://doi.org/10.1007/JHEP08(2023)041 arXiv:2305.09587 [hep-th]

    2023 doi

  197. [205]

    McNamara, J., Vafa, C.: Cobordism Classes and the Swampland (2019) arXiv:1909.10355 [hep-th]

    2019

  198. [206]

    JHEP 11, 021 (2019) https://doi.org/10.1007/JHEP11(2019)021 arXiv:1908.04352 [hep-th]

    Antonelli, R., Basile, I.: Brane annihilation in non-supersymmetric strings. JHEP 11, 021 (2019) https://doi.org/10.1007/JHEP11(2019)021 arXiv:1908.04352 [hep-th]

    2019 doi

  199. [207]

    JHEP 06, 170 (2021) https: //doi.org/10.1007/JHEP06(2021)170 arXiv:2104.02091 [hep-th]

    Buratti, G., Delgado, M., Uranga, A.M.: Dynamical tadpoles, stringy cobordism, and the SM from spontaneous compactification. JHEP 06, 170 (2021) https: //doi.org/10.1007/JHEP06(2021)170 arXiv:2104.02091 [hep-th]

    2021 doi

  200. [208]

    JHEP 10, 037 (2021) https: //doi.org/10.1007/JHEP10(2021)037 arXiv:2107.09098 [hep-th]

    Buratti, G., Calder´ on-Infante, J., Delgado, M., Uranga, A.M.: Dynamical Cobordism and Swampland Distance Conjectures. JHEP 10, 037 (2021) https: //doi.org/10.1007/JHEP10(2021)037 arXiv:2107.09098 [hep-th]

    2021 doi

  201. [209]

    JHEP 06, 142 (2022) https: //doi.org/10.1007/JHEP06(2022)142 arXiv:2203.11240 [hep-th]

    Angius, R., Calder´ on-Infante, J., Delgado, M., Huertas, J., Uranga, A.M.: At the end of the world: Local Dynamical Cobordism. JHEP 06, 142 (2022) https: //doi.org/10.1007/JHEP06(2022)142 arXiv:2203.11240 [hep-th]

    2022 doi

  202. [210]

    JHEP 08, 204 (2022) https: //doi.org/10.1007/JHEP08(2022)204 arXiv:2205.09782 [hep-th]

    Blumenhagen, R., Cribiori, N., Kneissl, C., Makridou, A.: Dynamical cobordism of a domain wall and its companion defect 7-brane. JHEP 08, 204 (2022) https: //doi.org/10.1007/JHEP08(2022)204 arXiv:2205.09782 [hep-th]

    2022 doi

  203. [211]

    JHEP 08, 285 (2022) https://doi.org/10.1007/JHEP08(2022)285 arXiv:2207.13108 [hep-th]

    Angius, R., Delgado, M., Uranga, A.M.: Dynamical Cobordism and the begin- ning of time: supercritical strings and tachyon condensation. JHEP 08, 285 (2022) https://doi.org/10.1007/JHEP08(2022)285 arXiv:2207.13108 [hep-th]

    2022 doi

  204. [212]

    JHEP 05, 123 (2023) https://doi.org/10

    Blumenhagen, R., Kneissl, C., Wang, C.: Dynamical Cobordism Conjecture: solutions for end-of-the-world branes. JHEP 05, 123 (2023) https://doi.org/10. 1007/JHEP05(2023)123 arXiv:2303.03423 [hep-th]

    2023

  205. [213]

    JHEP 06, 070 (2023) https://doi.org/10.1007/JHEP06(2023)070 arXiv:2303.15903 [hep- th]

    Angius, R., Huertas, J., Uranga, A.M.: Small black hole explosions. JHEP 06, 070 (2023) https://doi.org/10.1007/JHEP06(2023)070 arXiv:2303.15903 [hep- th]

    2023 doi

  206. [214]

    JHEP 08, 140 (2023) https://doi.org/10.1007/JHEP08(2023)140 arXiv:2306.07335 [hep-th]

    Huertas, J., Uranga, A.M.: Aspects of dynamical cobordism in AdS/CFT. JHEP 08, 140 (2023) https://doi.org/10.1007/JHEP08(2023)140 arXiv:2306.07335 [hep-th]

    2023 doi

  207. [215]

    JHEP 03, 110 (2024) https://doi.org/10.1007/JHEP03(2024)110 arXiv:2312.16286 [hep-th] 66

    Angius, R., Makridou, A., Uranga, A.M.: Intersecting end of the world branes. JHEP 03, 110 (2024) https://doi.org/10.1007/JHEP03(2024)110 arXiv:2312.16286 [hep-th] 66

    2024 doi

  208. [216]

    JHEP 09, 178 (2024) https://doi.org/10.1007/JHEP09(2024)178 arXiv:2404.14486 [hep-th]

    Angius, R.: End of the world brane networks for infinite distance limits in CY moduli space. JHEP 09, 178 (2024) https://doi.org/10.1007/JHEP09(2024)178 arXiv:2404.14486 [hep-th]

    2024 doi

  209. [217]

    JHEP 25(6), 30 (2020) https://doi.org/10.1007/JHEP06(2025)030 arXiv:2410.21372 [hep-th]

    Ruiz, I.: Morse-Bott inequalities, topology change and cobordisms to nothing. JHEP 25(6), 30 (2020) https://doi.org/10.1007/JHEP06(2025)030 arXiv:2410.21372 [hep-th]

    2020 doi

  210. [218]

    JHEP 01, 002 (2025) https://doi.org/10.1007/JHEP01(2025)002 arXiv:2410.05368 [hep-th]

    Huertas, J., Uranga, A.M.: End of the world brane dynamics in holographic 4dN = 4 SU(N) with 3d N = 2 boundary conditions. JHEP 01, 002 (2025) https://doi.org/10.1007/JHEP01(2025)002 arXiv:2410.05368 [hep-th]

    2025 doi

  211. [219]

    JHEP 03, 064 (2025) https://doi.org/10.1007/ JHEP03(2025)064 arXiv:2410.07322 [hep-th]

    Angius, R., Uranga, A.M., Wang, C.: End of the world boundaries for chi- ral quantum gravity theories. JHEP 03, 064 (2025) https://doi.org/10.1007/ JHEP03(2025)064 arXiv:2410.07322 [hep-th]

    2025

  212. [220]

    Wald, R.M.: DYNAMICS IN NONGLOBALLY HYPERBOLIC, STATIC SPACE-TIMES. J. Math. Phys. 21, 2802–2805 (1980) https://doi.org/10.1063/ 1.524403

    1980

  213. [221]

    Horowitz, G.T., Marolf, D.: Quantum probes of space-time singularities. Phys. Rev. D 52, 5670–5675 (1995) https://doi.org/10.1103/PhysRevD.52.5670 arXiv:gr-qc/9504028

    1995 doi arXiv

  214. [222]

    Gubser, S.S.: Curvature singularities: The Good, the bad, and the naked. Adv. Theor. Math. Phys. 4, 679–745 (2000) https://doi.org/10.4310/ATMP.2000.v4. n3.a6 arXiv:hep-th/0002160

    2000 doi arXiv

  215. [223]

    JHEP 09, 019 (2024) https://doi.org/10.1007/JHEP09(2024)019 arXiv:2406.16327 [hep-th]

    Mourad, J., Raucci, S., Sagnotti, A.: Brane profiles of non-supersymmetric strings. JHEP 09, 019 (2024) https://doi.org/10.1007/JHEP09(2024)019 arXiv:2406.16327 [hep-th]

    2024 doi

  216. [224]

    Dudas, E., Mourad, J.: D-branes in nontachyonic 0B orientifolds. Nucl. Phys. B 598, 189–224 (2001) https://doi.org/10.1016/S0550-3213(00)00781-1 arXiv:hep-th/0010179

    2001 doi arXiv

  217. [225]

    Dudas, E., Kitazawa, N., Sagnotti, A.: On Climbing Scalars in String Theory. Phys. Lett. B 694, 80–88 (2011) https://doi.org/10.1016/j.physletb.2010.09.040 arXiv:1009.0874 [hep-th]

    2011 doi arXiv

  218. [226]

    JCAP08, 013 (2013) https://doi.org/10.1088/1475-7516/2013/08/013 arXiv:1306.0911 [hep-th]

    Condeescu, C., Dudas, E.: Kasner solutions, climbing scalars and big-bang sin- gularity. JCAP08, 013 (2013) https://doi.org/10.1088/1475-7516/2013/08/013 arXiv:1306.0911 [hep-th]

    2013 doi arXiv

  219. [227]

    JCAP 05, 012 (2012) https://doi.org/10.1088/ 1475-7516/2012/05/012 arXiv:1202.6630 [hep-th] 67

    Dudas, E., Kitazawa, N., Patil, S.P., Sagnotti, A.: CMB Imprints of a Pre- Inflationary Climbing Phase. JCAP 05, 012 (2012) https://doi.org/10.1088/ 1475-7516/2012/05/012 arXiv:1202.6630 [hep-th] 67

    2012 arXiv

  220. [228]

    Sagnotti, A.: Brane SUSY breaking and inflation: implications for scalar fields and CMB distortion, 465–473 (2013) https://doi.org/10.1134/ S1547477114070395 arXiv:1303.6685 [hep-th]

    2013 arXiv

  221. [229]

    Kitazawa, N., Sagnotti, A.: Pre-inflationary clues from String The- ory? JCAP 04, 017 (2014) https://doi.org/10.1088/1475-7516/2014/04/017 arXiv:1402.1418 [hep-th]

    2014 doi arXiv

  222. [230]

    95, 03031 (2015) https://doi.org/10.1051/epjconf/20159503031 arXiv:1411.6396 [hep-th]

    Kitazawa, N., Sagnotti, A.: String theory clues for the low– ℓCMB ? EPJ Web Conf. 95, 03031 (2015) https://doi.org/10.1051/epjconf/20159503031 arXiv:1411.6396 [hep-th]

    2015 doi

  223. [231]

    Kitazawa, N., Sagnotti, A.: A string-inspired model for the low- ℓCMB. Mod. Phys. Lett. A 30(28), 1550137 (2015) https://doi.org/10.1142/ S0217732315501370 arXiv:1503.04483 [hep-th]

    2015 arXiv

  224. [232]

    Angelantonj, C., Armoni, A.: Nontachyonic type 0B orientifolds, nonsupersym- metric gauge theories and cosmological RG flow. Nucl. Phys. B 578, 239–258 (2000) https://doi.org/10.1016/S0550-3213(00)00136-X arXiv:hep-th/9912257

    2000 doi arXiv

  225. [233]

    Angelantonj, C., Armoni, A.: RG flow, Wilson loops and the dilaton tadpole. Phys. Lett. B 482, 329–336 (2000) https://doi.org/10.1016/S0370-2693(00) 00475-5 arXiv:hep-th/0003050

    2000 doi arXiv

  226. [234]

    JHEP 10, 080 (2021) https://doi.org/10.1007/JHEP10(2021)080 arXiv:2106.04574 [hep-th]

    Basile, I.: Supersymmetry breaking, brane dynamics and Swampland con- jectures. JHEP 10, 080 (2021) https://doi.org/10.1007/JHEP10(2021)080 arXiv:2106.04574 [hep-th]

    2021 doi

  227. [235]

    Basile, I., Borys, A., Masias, J.: Dynamical dark energy in 0’B braneworlds (2025) arXiv:2502.20438 [hep-th]

    2025

  228. [236]

    JHEP 07, 044 (2002) https://doi.org/10.1088/1126-6708/ 2002/07/044 arXiv:hep-th/0108239

    Gubser, S.S., Mitra, I.: Some interesting violations of the Breitenlohner- Freedman bound. JHEP 07, 044 (2002) https://doi.org/10.1088/1126-6708/ 2002/07/044 arXiv:hep-th/0108239

    2002 doi arXiv

  229. [237]

    Mourad, J., Sagnotti, A.: AdS Vacua from Dilaton Tadpoles and Form Fluxes. Phys. Lett. B 768, 92–96 (2017) https://doi.org/10.1016/j.physletb.2017.02.053 arXiv:1612.08566 [hep-th]

    2017 doi arXiv

  230. [238]

    Raucci, S.: On new vacua of non-supersymmetric strings. Phys. Lett. B 837, 137663 (2023) https://doi.org/10.1016/j.physletb.2022.137663 arXiv:2209.06537 [hep-th]

    2023 doi

  231. [239]

    Astronomy 2(3), 206–225 (2023) https://doi.org/10.3390/astronomy2030015 arXiv:2201.08851 [hep-th] 68

    Basile, I.: Emergent Strings at an Infinite Distance with Broken Supersymmetry. Astronomy 2(3), 206–225 (2023) https://doi.org/10.3390/astronomy2030015 arXiv:2201.08851 [hep-th] 68

    2023 doi

  232. [240]

    SciPost Phys

    De Luca, G.B., Silverstein, E., Torroba, G.: Hyperbolic compactification of M- theory and de Sitter quantum gravity. SciPost Phys. 12(3), 083 (2022) https: //doi.org/10.21468/SciPostPhys.12.3.083 arXiv:2104.13380 [hep-th]

    2022 doi

  233. [241]

    Sci- Post Phys

    Luca, G.B.D., De Ponti, N., Mondino, A., Tomasiello, A.: Gravity from thermodynamics: Optimal transport and negative effective dimensions. Sci- Post Phys. 15(2), 039 (2023) https://doi.org/10.21468/SciPostPhys.15.2.039 arXiv:2212.02511 [hep-th]

    2023 doi

  234. [242]

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

    2025 arXiv

  235. [243]

    Dall’Agata, G., Zwirner, F.: Supersymmetry-breaking compactifications on Riemann-flat manifolds (2025) arXiv:2507.02339 [hep-th]

    2025

  236. [244]

    Aparici, M., Basile, I., Risso, N.: Instabilities in scale-separated Casimir vacua (2025) arXiv:2507.17802 [hep-th]

    2025 arXiv

  237. [245]

    JHEP 10, 108 (2020) https://doi.org/10.1007/ JHEP10(2020)108 arXiv:2007.13757 [hep-th]

    Basile, I., Lanza, S.: de Sitter in non-supersymmetric string theories: no-go theorems and brane-worlds. JHEP 10, 108 (2020) https://doi.org/10.1007/ JHEP10(2020)108 arXiv:2007.13757 [hep-th]

    2020

  238. [246]

    Maldacena, J.M., Nunez, C.: Supergravity description of field theories on curved manifolds and a no go theorem. Int. J. Mod. Phys. A 16, 822–855 (2001) https: //doi.org/10.1142/S0217751X01003937 arXiv:hep-th/0007018

    2001 doi arXiv

  239. [247]

    Fabinger, M., Horava, P.: Casimir effect between world branes in het- erotic M theory. Nucl. Phys. B 580, 243–263 (2000) https://doi.org/10.1016/ S0550-3213(00)00255-8 arXiv:hep-th/0002073

    2000 arXiv

  240. [248]

    JHEP 08, 090 (2005) https://doi.org/10.1088/1126-6708/2005/08/090 arXiv:hep- th/0506130

    McGreevy, J., Silverstein, E.: The Tachyon at the end of the universe. JHEP 08, 090 (2005) https://doi.org/10.1088/1126-6708/2005/08/090 arXiv:hep- th/0506130

    2005 doi

  241. [249]

    JHEP 10, 033 (2005) https://doi.org/ 10.1088/1126-6708/2005/10/033 arXiv:hep-th/0502021

    Adams, A., Liu, X., McGreevy, J., Saltman, A., Silverstein, E.: Things fall apart: Topology change from winding tachyons. JHEP 10, 033 (2005) https://doi.org/ 10.1088/1126-6708/2005/10/033 arXiv:hep-th/0502021

    2005 doi arXiv

  242. [250]

    JHEP 05, 333 (2024) https://doi.org/10.1007/JHEP05(2024)333 arXiv:2312.09291 [hep-th]

    Delgado, M.: The bubble of nothing under T-duality. JHEP 05, 333 (2024) https://doi.org/10.1007/JHEP05(2024)333 arXiv:2312.09291 [hep-th]

    2024 doi

  243. [251]

    Witten, E.: Instability of the Kaluza-Klein Vacuum. Nucl. Phys. B195, 481–492 (1982) https://doi.org/10.1016/0550-3213(82)90007-4

    1982 doi

  244. [252]

    JHEP 12, 032 (2020) https://doi.org/10.1007/ JHEP12(2020)032 arXiv:2005.06494 [hep-th] 69

    Garc´ ıa Etxebarria, I., Montero, M., Sousa, K., Valenzuela, I.: Nothing is cer- tain in string compactifications. JHEP 12, 032 (2020) https://doi.org/10.1007/ JHEP12(2020)032 arXiv:2005.06494 [hep-th] 69

    2020

  245. [253]

    Witten, E.: A Simple Proof of the Positive Energy Theorem. Commun. Math. Phys. 80, 381 (1981) https://doi.org/10.1007/BF01208277

    1981 doi

  246. [254]

    Nester, J.A.: A New gravitational energy expression with a simple positiv- ity proof. Phys. Lett. A 83, 241 (1981) https://doi.org/10.1016/0375-9601(81) 90972-5

    1981 doi

  247. [255]

    Boucher, W.: POSITIVE ENERGY WITHOUT SUPERSYMMETRY. Nucl. Phys. B 242, 282–296 (1984) https://doi.org/10.1016/0550-3213(84)90394-8

    1984 doi

  248. [256]

    Townsend, P.K.: Positive Energy and the Scalar Potential in Higher Dimensional (Super)gravity Theories. Phys. Lett. B 148, 55–59 (1984) https://doi.org/10. 1016/0370-2693(84)91610-1

    1984

  249. [257]

    Skenderis, K., Townsend, P.K.: Gravitational stability and renormaliza- tion group flow. Phys. Lett. B 468, 46–51 (1999) https://doi.org/10.1016/ S0370-2693(99)01212-5 arXiv:hep-th/9909070

    1999 arXiv

  250. [258]

    Freedman, D.Z., Nunez, C., Schnabl, M., Skenderis, K.: Fake supergravity and domain wall stability. Phys. Rev. D 69, 104027 (2004) https://doi.org/10.1103/ PhysRevD.69.104027 arXiv:hep-th/0312055

    2004 arXiv

  251. [259]

    Townsend, P.K.: Hamilton-Jacobi mechanics from pseudo-supersymmetry. Class. Quant. Grav. 25, 045017 (2008) https://doi.org/10.1088/0264-9381/25/ 4/045017 arXiv:0710.5178 [hep-th]

    2008 doi arXiv

  252. [260]

    JHEP 05, 078 (2012) https://doi.org/10.1007/JHEP05(2012) 078 arXiv:1203.3194 [hep-th]

    Trigiante, M., Van Riet, T., Vercnocke, B.: Fake supersymmetry versus Hamilton-Jacobi. JHEP 05, 078 (2012) https://doi.org/10.1007/JHEP05(2012) 078 arXiv:1203.3194 [hep-th]

    2012 doi arXiv

  253. [261]

    Danielsson, U.H., Dibitetto, G., Vargas, S.C.: Universal isolation in the AdS landscape. Phys. Rev. D 94(12), 126002 (2016) https://doi.org/10.1103/ PhysRevD.94.126002 arXiv:1605.09289 [hep-th]

    2016 arXiv

  254. [262]

    JHEP 07, 078 (2023) https://doi.org/10.1007/JHEP07(2023)078 arXiv:2304.12717 [hep-th]

    Raucci, S.: Fake supersymmetry with tadpole potentials. JHEP 07, 078 (2023) https://doi.org/10.1007/JHEP07(2023)078 arXiv:2304.12717 [hep-th]

    2023 doi

  255. [263]

    JHEP 04, 054 (2022) https://doi.org/10.1007/JHEP04(2022)054 arXiv:2112.10795 [hep-th]

    Giri, S., Martucci, L., Tomasiello, A.: On the stability of string the- ory vacua. JHEP 04, 054 (2022) https://doi.org/10.1007/JHEP04(2022)054 arXiv:2112.10795 [hep-th]

    2022 doi

  256. [264]

    JHEP 05, 100 (2024) https://doi.org/10.1007/JHEP05(2024)100 arXiv:2311.12115 [hep-th]

    Menet, V.: New non-supersymmetric flux vacua from generalised cali- brations. JHEP 05, 100 (2024) https://doi.org/10.1007/JHEP05(2024)100 arXiv:2311.12115 [hep-th]

    2024 doi

  257. [265]

    JHEP 07, 071 (2024) https://doi.org/10.1007/JHEP07(2024)071 arXiv:2312.04517 [hep-th] 70

    Menet, V.: D-terms in generalised complex geometry. JHEP 07, 071 (2024) https://doi.org/10.1007/JHEP07(2024)071 arXiv:2312.04517 [hep-th] 70

    2024 doi

  258. [266]

    Menet, V., Tomasiello, A.: Stability of non-supersymmetric vacua from calibra- tions (2025) arXiv:2507.02787 [hep-th] 71

    2025 arXiv

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