pith. sign in

arxiv: 2410.21372 · v2 · pith:UOK5J7QXnew · submitted 2024-10-28 · ✦ hep-th

Morse-Bott inequalities, Topology Change and Cobordisms to Nothing

Ignacio Ruiz This is my paper

Pith reviewed 2026-05-23 18:45 UTC · model grok-4.3

classification ✦ hep-th
keywords Cobordism ConjectureBubbles of NothingMorse-Bott theorytopology changevacuum decaycobordism defectsstring theory compactifications
0
0 comments X

The pith

Assuming a smooth description, Morse-Bott theory bounds the homology of generic compact manifolds in cobordisms to nothing and specifies their topology changes.

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

This paper applies Morse-Bott theory to cobordisms to nothing, configurations in which both spacetime and the compact manifold end. It assumes the mediating solution admits a homeomorphic smooth description and derives bounds on the homology of a generic compactification manifold C_n. These bounds then translate into constraints on the number and kinds of topology changes the manifold must experience while shrinking, as well as the locations of possible defects. The same method handles more involved cases such as colliding bubbles of nothing and intersecting end-of-the-world branes, with examples drawn from string theory constructions.

Core claim

Assuming the solution mediating such decay to nothing is homeomorphic to a smooth description, Morse-Bott inequalities supply topological bounds on the homology for generic C_n. Morse-Bott theory then converts these bounds into statements about the number and types of topology changes the compact manifold undergoes as one moves toward the tip of the bordism, together with the placement of possible cobordism defects. The framework also covers BoN collisions and intersections of End of the World branes and is illustrated with explicit string theory examples.

What carries the argument

Morse-Bott theory applied to the bordism, which converts homology bounds into counts and locations of critical points that mark topology changes.

If this is right

  • Topological bounds on homology hold for generic C_n in cobordisms to nothing.
  • The number and types of topology changes are constrained as the manifold shrinks toward the bordism tip.
  • Possible locations of cobordism defects are identified.
  • The same analysis extends to collisions of bubbles of nothing and intersections of End of the World branes.

Where Pith is reading between the lines

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

  • These homology bounds may exclude certain string-theory compactifications from admitting smooth decays to nothing.
  • The technique could be tested by constructing explicit bordisms for known Calabi-Yau or other manifolds and checking the predicted change sequences.
  • Similar Morse-Bott reasoning might apply to other topology-altering processes conjectured in quantum gravity.

Load-bearing premise

The solution mediating the decay to nothing is homeomorphic to a smooth manifold description.

What would settle it

An explicit smooth cobordism to nothing for a generic C_n whose homology violates the Morse-Bott-derived bounds would falsify the central claim.

read the original abstract

The Cobordism Conjecture predicts spacetime-ending configurations, such as Bubbles of Nothing (BoN), being commonplace. These correspond to vacuum decays in which the compactification manifold $\mathcal{C}_n$ shrinks to a point, with the instability expanding at the speed of light and leaving nothing (not even spacetime) behind. Most constructions of BoN or cobordisms to nothing found in the literature feature simple instances of $\mathcal{C}_n$ or singular cobordisms, which cannot be approached from the effective field theory. Assuming the solution mediating such decay to nothing is homeomorphic to a smooth description, we are able to go a step further, and obtain topological bounds on its homology for generic $\mathcal{C}_n$. Through the use of Morse-Bott theory we then translate this into information on the number and types of topology changes the compact manifold experiences as we move towards the tip of the bordism, as well as the location of possible cobordism defects. We illustrate our results with different detailed examples coming from String Theory. Furthermore, with this approach, we are able to study more complicated arrangements such as BoN collisions or intersection of End of the World branes.

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 / 3 minor

Summary. The paper claims that, assuming mediating solutions for cobordisms to nothing (such as Bubbles of Nothing) are homeomorphic to smooth manifolds, Morse-Bott theory yields topological bounds on the homology of generic compactification manifolds C_n. These bounds are then translated into statements about the number and types of topology changes experienced by the compact manifold toward the bordism tip, as well as the location of possible cobordism defects. The results are illustrated with string-theory examples and extended to more complex cases including BoN collisions and intersections of End-of-the-World branes.

Significance. If the derivations hold under the stated assumption, the work supplies a systematic topological toolkit for constraining vacuum-decay configurations in the Cobordism Conjecture beyond the simple or singular cases common in the literature. The translation from homology bounds to concrete counts of topology changes via Morse-Bott theory, together with the treatment of collisions and brane intersections, would constitute a useful advance for the swampland program.

major comments (2)
  1. [Abstract and §1] Abstract and §1: the central claims rest explicitly on the premise that the mediating solution is homeomorphic to a smooth manifold. The manuscript should provide a dedicated discussion (with references to the string-theory examples) of when and why this homeomorphism can be assumed, as any violation would render the Morse-Bott analysis inapplicable.
  2. [§3] §3 (Morse-Bott application): the translation from homology bounds to the number and types of topology changes must be checked for dependence on the choice of Morse-Bott function; if the counts are invariant only for generic choices, this should be stated explicitly with a supporting lemma.
minor comments (3)
  1. [§2] Notation for the compactification manifold C_n and the bordism should be introduced with a single consistent definition in §2 rather than piecemeal.
  2. Figure captions for the string-theory examples should include the specific compactification data (e.g., Calabi-Yau or orbifold) used in each case.
  3. [final section] The discussion of BoN collisions in the final section would benefit from a short comparison table listing the homology bounds before and after collision.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading, positive assessment, and constructive suggestions. We address each major comment below and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: [Abstract and §1] Abstract and §1: the central claims rest explicitly on the premise that the mediating solution is homeomorphic to a smooth manifold. The manuscript should provide a dedicated discussion (with references to the string-theory examples) of when and why this homeomorphism can be assumed, as any violation would render the Morse-Bott analysis inapplicable.

    Authors: We agree that an explicit discussion of this assumption strengthens the paper. In the revised manuscript we will insert a dedicated paragraph (or short subsection) immediately following the statement of the assumption in §1. This paragraph will summarize the conditions under which mediating solutions (e.g., Bubbles of Nothing) are expected to be homeomorphic to smooth manifolds, with references to the relevant string-theory literature (standard Kaluza-Klein BoN constructions, their generalizations to warped throats, and known cases where singularities are resolved or absent). We will also note the regimes in which the assumption may fail and the Morse-Bott analysis would not apply. revision: yes

  2. Referee: [§3] §3 (Morse-Bott application): the translation from homology bounds to the number and types of topology changes must be checked for dependence on the choice of Morse-Bott function; if the counts are invariant only for generic choices, this should be stated explicitly with a supporting lemma.

    Authors: The counts we extract are those furnished by the Morse-Bott inequalities for a generic choice of Morse-Bott function; this is the standard setting in which the inequalities yield sharp topological information. In the revised §3 we will add an explicit sentence stating that the derived bounds on the number and types of topology changes hold for generic Morse-Bott functions. We will also include a short supporting remark (or lemma) recalling that, for a fixed cobordism, the critical-point data of generic functions are related by handle cancellations that preserve the homology bounds, thereby making the counts invariant under generic perturbations. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation applies standard external theory under explicit assumption

full rationale

The paper's central derivation begins from the explicitly stated premise that the mediating solution is homeomorphic to a smooth manifold, then invokes standard Morse-Bott theory (an external topological tool) to obtain homology bounds and count topology changes for generic C_n. No step reduces a claimed prediction or first-principles result to a fitted parameter, self-citation chain, or definitional equivalence; the bounds are conditional outputs of the external theory applied to the assumed smooth structure. The argument structure is self-contained against external benchmarks and does not rely on load-bearing self-citations or ansatzes smuggled from prior work.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on one explicit domain assumption; no free parameters or invented entities are mentioned in the abstract.

axioms (1)
  • domain assumption The solution mediating such decay to nothing is homeomorphic to a smooth description
    Stated in the abstract as the premise enabling the Morse-Bott analysis for generic C_n.

pith-pipeline@v0.9.0 · 5731 in / 1227 out tokens · 19731 ms · 2026-05-23T18:45:53.863542+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 2 Pith papers

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

  1. A missing link: Brane networks and the Cobordism Conjecture

    hep-th 2026-05 unverdicted novelty 6.0

    Defects tied to discrete symmetries via bordism groups Ω^ξ_2(BG) and homology H_2(BG;Z) are codimension-two branes that participate in networks with junctions, expanding the Cobordism Conjecture's predictions in strin...

  2. Bordisms between 9d type IIB supergravities and commutator widths of duality groups

    hep-th 2026-05 unverdicted novelty 6.0

    Proposes a refinement of the Swampland Cobordism Conjecture for Ω1(BG) with duality bundle G, where diverging commutator width of G requires infinitely many duality defects to realize monodromies via gravitational solitons.

Reference graph

Works this paper leans on

143 extracted references · 143 canonical work pages · cited by 2 Pith papers · 58 internal anchors

  1. [1]

    Brane/Flux Annihilation and the String Dual of a Non-Supersymmetric Field Theory

    S. Kachru, J. Pearson and H. L. Verlinde, Brane / flux annihilation and the string dual of a nonsupersymmetric field theory, JHEP 06 (2002) 021 [ hep-th/0112197]

    work page internal anchor Pith review Pith/arXiv arXiv 2002

  2. [2]

    J. J. Blanco-Pillado, D. Schwartz-Perlov and A. Vilenkin, Quantum Tunneling in Flux Compactifications, JCAP 12 (2009) 006 [ 0904.3106]

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  3. [3]

    An M-theory Flop as a Large N Duality

    M. Atiyah, J. M. Maldacena and C. Vafa, An M theory flop as a large N duality , J. Math. Phys. 42 (2001) 3209 [ hep-th/0011256]

    work page internal anchor Pith review Pith/arXiv arXiv 2001

  4. [4]

    B. S. Acharya and S. Gukov, M theory and singularities of exceptional holonomy manifolds , Phys. Rept. 392 (2004) 121 [ hep-th/0409191]

    work page internal anchor Pith review Pith/arXiv arXiv 2004

  5. [5]

    P. S. Aspinwall, B. R. Greene and D. R. Morrison, Multiple mirror manifolds and topology change in string theory , Phys. Lett. B 303 (1993) 249 [ hep-th/9301043]

    work page internal anchor Pith review Pith/arXiv arXiv 1993

  6. [6]

    Phases of $N=2$ Theories In Two Dimensions

    E. Witten, Phases of N=2 theories in two-dimensions , Nucl. Phys. B 403 (1993) 159 [hep-th/9301042]

    work page internal anchor Pith review Pith/arXiv arXiv 1993

  7. [7]

    Massless Black Holes and Conifolds in String Theory

    A. Strominger, Massless black holes and conifolds in string theory , Nucl. Phys. B 451 (1995) 96 [hep-th/9504090]

    work page internal anchor Pith review Pith/arXiv arXiv 1995

  8. [8]

    B. R. Greene, D. R. Morrison and A. Strominger, Black hole condensation and the unification of string vacua , Nucl. Phys. B451 (1995) 109 [ hep-th/9504145]

    work page internal anchor Pith review Pith/arXiv arXiv 1995

  9. [9]

    S. B. Giddings and A. Strominger, Axion Induced Topology Change in Quantum Gravity and String Theory, Nucl. Phys. B 306 (1988) 890

    work page 1988

  10. [10]

    B. R. Greene and M. R. Plesser, Duality in Calabi-Yau Moduli Space , Nucl. Phys. B 338 (1990) 15

    work page 1990

  11. [11]

    Target Space Duality in String Theory

    A. Giveon, M. Porrati and E. Rabinovici, Target space duality in string theory , Phys. Rept. 244 (1994) 77 [ hep-th/9401139]

    work page internal anchor Pith review Pith/arXiv arXiv 1994

  12. [12]

    Anti-de Sitter Space, Thermal Phase Transition, And Confinement In Gauge Theories

    E. Witten, Anti-de Sitter space, thermal phase transition, and confinement in gauge theories , Adv. Theor. Math. Phys. 2 (1998) 505 [ hep-th/9803131]

    work page internal anchor Pith review Pith/arXiv arXiv 1998

  13. [13]

    I. n. Garc´ ıa-Etxebarria and M. Montero,Dai-Freed anomalies in particle physics , JHEP 08 (2019) 003 [ 1808.00009]

    work page arXiv 2019

  14. [14]

    Demulder, D

    S. Demulder, D. Lust and T. Raml, Topology change and non-geometry at infinite distance , JHEP 06 (2024) 079 [ 2312.07674]

    work page arXiv 2024

  15. [15]

    Witten, Instability of the Kaluza-Klein Vacuum , Nucl

    E. Witten, Instability of the Kaluza-Klein Vacuum , Nucl. Phys. B 195 (1982) 481

    work page 1982

  16. [16]

    Casimir Effect Between World-Branes in Heterotic M-Theory

    M. Fabinger and P. Horava, Casimir effect between world branes in heterotic M theory , Nucl. Phys. B 580 (2000) 243 [ hep-th/0002073]

    work page internal anchor Pith review Pith/arXiv arXiv 2000

  17. [17]

    M. Dine, P. J. Fox and E. Gorbatov, Catastrophic decays of compactified space-times, JHEP 09 (2004) 037 [ hep-th/0405190]

    work page internal anchor Pith review Pith/arXiv arXiv 2004

  18. [18]

    G. T. Horowitz, J. Orgera and J. Polchinski, Nonperturbative Instability of AdS(5) x S**5/Z(k), Phys. Rev. D 77 (2008) 024004 [ 0709.4262]

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  19. [19]

    Stretched extra dimensions and bubbles of nothing in a toy model landscape

    I.-S. Yang, Stretched extra dimensions and bubbles of nothing in a toy model landscape , Phys. Rev. D 81 (2010) 125020 [ 0910.1397]. – 49 –

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  20. [20]

    J. J. Blanco-Pillado and B. Shlaer, Bubbles of Nothing in Flux Compactifications , Phys. Rev. D 82 (2010) 086015 [ 1002.4408]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  21. [21]

    J. J. Blanco-Pillado, H. S. Ramadhan and B. Shlaer, Decay of flux vacua to nothing , JCAP 10 (2010) 029 [ 1009.0753]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  22. [22]

    A. R. Brown and A. Dahlen, Bubbles of Nothing and the Fastest Decay in the Landscape , Phys. Rev. D 84 (2011) 043518 [ 1010.5240]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  23. [23]

    J. J. Blanco-Pillado, H. S. Ramadhan and B. Shlaer, Bubbles from Nothing , JCAP 01 (2012) 045 [1104.5229]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  24. [24]

    A. R. Brown and A. Dahlen, On ’nothing’ as an infinitely negatively curved spacetime , Phys. Rev. D 85 (2012) 104026 [ 1111.0301]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  25. [25]

    Stability, Tunneling and Flux Changing de Sitter Transitions in the Large Volume String Scenario

    S. de Alwis, R. Gupta, E. Hatefi and F. Quevedo, Stability, Tunneling and Flux Changing de Sitter Transitions in the Large Volume String Scenario , JHEP 11 (2013) 179 [ 1308.1222]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  26. [26]

    A. R. Brown, Decay of hot Kaluza-Klein space , Phys. Rev. D 90 (2014) 104017 [ 1408.5903]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  27. [27]

    J. J. Blanco-Pillado, B. Shlaer, K. Sousa and J. Urrestilla, Bubbles of Nothing and Supersymmetric Compactifications, JCAP 10 (2016) 002 [ 1606.03095]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  28. [28]

    New Kaluza-Klein Instantons and Decay of AdS Vacua

    H. Ooguri and L. Spodyneiko, New Kaluza-Klein instantons and the decay of AdS vacua , Phys. Rev. D 96 (2017) 026016 [ 1703.03105]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  29. [29]

    Dibitetto, N

    G. Dibitetto, N. Petri and M. Schillo, Nothing really matters , JHEP 08 (2020) 040 [2002.01764]

    work page arXiv 2020

  30. [30]

    García Etxebarria, M

    I. Garc´ ıa Etxebarria, M. Montero, K. Sousa and I. Valenzuela, Nothing is certain in string compactifications, JHEP 12 (2020) 032 [ 2005.06494]

    work page arXiv 2020

  31. [31]

    Bomans, D

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

    work page arXiv 2022

  32. [32]

    Draper, I

    P. Draper, I. G. Garcia and B. Lillard, Bubble of nothing decays of unstable theories , Phys. Rev. D 104 (2021) L121701 [ 2105.08068]

    work page arXiv 2021

  33. [33]

    Draper, I

    P. Draper, I. Garcia Garcia and B. Lillard, De Sitter decays to infinity , JHEP 12 (2021) 154 [2105.10507]

    work page arXiv 2021

  34. [34]

    Petri, Bubbles of nothing and AdS instabilities , PoS CORFU2021 (2022) 170 [2205.00884]

    N. Petri, Bubbles of nothing and AdS instabilities , PoS CORFU2021 (2022) 170 [2205.00884]

    work page arXiv 2022

  35. [35]

    Bandos, J

    I. Bandos, J. J. Blanco-Pillado, K. Sousa and M. A. Urkiola, Brane nucleation in supersymmetric models, JHEP 10 (2023) 061 [ 2306.09412]

    work page arXiv 2023

  36. [36]

    Ookouchi, R

    Y. Ookouchi, R. Sato and S. Tsukahara, Decay of Kaluza-Klein Vacuum via Singular Instanton, 2404.13917

    work page arXiv

  37. [37]

    J. J. Heckman and M. H¨ ubner,Celestial Topology, Symmetry Theories, and Evidence for a Non-SUSY D3-Brane CFT , 2406.08485

    work page arXiv

  38. [38]

    Heterotic and Type I String Dynamics from Eleven Dimensions

    P. Horava and E. Witten, Heterotic and type I string dynamics from eleven-dimensions , Nucl. Phys. B 460 (1996) 506 [ hep-th/9510209]

    work page internal anchor Pith review Pith/arXiv arXiv 1996

  39. [39]

    Eleven-Dimensional Supergravity on a Manifold with Boundary

    P. Horava and E. Witten, Eleven-dimensional supergravity on a manifold with boundary , Nucl. Phys. B 475 (1996) 94 [ hep-th/9603142]. – 50 –

    work page internal anchor Pith review Pith/arXiv arXiv 1996

  40. [40]

    McNamara and C

    J. McNamara and C. Vafa, Cobordism Classes and the Swampland , 1909.10355

    work page arXiv 1909

  41. [41]

    The String Landscape and the Swampland

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

    work page internal anchor Pith review Pith/arXiv arXiv

  42. [42]

    T. D. Brennan, F. Carta and C. Vafa, The String Landscape, the Swampland, and the Missing Corner, PoS TASI2017 (2017) 015 [ 1711.00864]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  43. [43]

    The Swampland: Introduction and Review

    E. Palti, The Swampland: Introduction and Review , Fortsch. Phys. 67 (2019) 1900037 [1903.06239]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  44. [44]

    van Beest, J

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

    work page arXiv 2022

  45. [45]

    Gra˜ na and A

    M. Gra˜ na and A. Herr´ aez,The Swampland Conjectures: A Bridge from Quantum Gravity to Particle Physics, Universe 7 (2021) 273 [ 2107.00087]

    work page arXiv 2021

  46. [46]

    Harlow, B

    D. Harlow, B. Heidenreich, M. Reece and T. Rudelius, Weak gravity conjecture, Rev. Mod. Phys. 95 (2023) 035003 [ 2201.08380]

    work page arXiv 2023

  47. [47]

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

    work page arXiv

  48. [48]

    Banks and L

    T. Banks and L. J. Dixon, Constraints on String Vacua with Space-Time Supersymmetry , Nucl. Phys. B307 (1988) 93

    work page 1988

  49. [49]

    GRAVITY AND GLOBAL SYMMETRIES

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

    work page internal anchor Pith review Pith/arXiv arXiv 1995

  50. [50]

    Symmetries and Strings in Field Theory and Gravity

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

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  51. [51]

    Montero and C

    M. Montero and C. Vafa, Cobordism Conjecture, Anomalies, and the String Lamppost Principle, JHEP 01 (2021) 063 [ 2008.11729]

    work page arXiv 2021

  52. [52]

    Dierigl, J

    M. Dierigl, J. J. Heckman, M. Montero and E. Torres, IIB string theory explored: Reflection 7-branes, Phys. Rev. D 107 (2023) 086015 [ 2212.05077]

    work page arXiv 2023

  53. [53]

    S. R. Coleman, The Fate of the False Vacuum. 1. Semiclassical Theory , Phys. Rev. D 15 (1977) 2929

    work page 1977

  54. [54]

    Witten, Supersymmetry and Morse theory , J

    E. Witten, Supersymmetry and Morse theory , J. Diff. Geom. 17 (1982) 661

    work page 1982

  55. [55]

    R. D. Sorkin, CONSEQUENCES OF SPACE-TIME TOPOLOGY ,

    work page

  56. [56]

    Complex actions in two-dimensional topology change

    J. Louko and R. D. Sorkin, Complex actions in two-dimensional topology change , Class. Quant. Grav. 14 (1997) 179 [ gr-qc/9511023]

    work page internal anchor Pith review Pith/arXiv arXiv 1997

  57. [57]

    H. F. Dowker and R. S. Garcia, A Handlebody calculus for topology change , Class. Quant. Grav. 15 (1998) 1859 [ gr-qc/9711042]

    work page internal anchor Pith review Pith/arXiv arXiv 1998

  58. [58]

    Topology Change and Causal Continuity

    F. Dowker and S. Surya, Topology change and causal continuity , Phys. Rev. D 58 (1998) 124019 [gr-qc/9711070]

    work page internal anchor Pith review Pith/arXiv arXiv 1998

  59. [59]

    H. F. Dowker, R. S. Garcia and S. Surya, Morse index and causal continuity: A Criterion for topology change in quantum gravity , Class. Quant. Grav. 17 (2000) 697 [ gr-qc/9910034]

    work page internal anchor Pith review Pith/arXiv arXiv 2000

  60. [60]

    Garc´ ıa-Heveling,Topology change with Morse functions: progress on the Borde–Sorkin conjecture, Adv

    L. Garc´ ıa-Heveling,Topology change with Morse functions: progress on the Borde–Sorkin conjecture, Adv. Theor. Math. Phys. 27 (2023) 1159 [ 2202.09833]. – 51 –

    work page arXiv 2023

  61. [61]

    L¨ ust,An index for flux vacua , 2405.04584

    S. L¨ ust,An index for flux vacua , 2405.04584

    work page arXiv

  62. [62]

    Scherk and J

    J. Scherk and J. H. Schwarz, Spontaneous Breaking of Supersymmetry Through Dimensional Reduction, Phys. Lett. B 82 (1979) 60

    work page 1979

  63. [63]

    Scherk and J

    J. Scherk and J. H. Schwarz, How to Get Masses from Extra Dimensions , Nucl. Phys. B 153 (1979) 61

    work page 1979

  64. [64]

    Kounnas and B

    C. Kounnas and B. Rostand, Coordinate Dependent Compactifications and Discrete Symmetries, Nucl. Phys. B 341 (1990) 641

    work page 1990

  65. [65]

    Schon and S.-T

    R. Schon and S.-T. Yau, On the Proof of the positive mass conjecture in general relativity , Commun. Math. Phys. 65 (1979) 45

    work page 1979

  66. [66]

    Witten, A Simple Proof of the Positive Energy Theorem , Commun

    E. Witten, A Simple Proof of the Positive Energy Theorem , Commun. Math. Phys. 80 (1981) 381

    work page 1981

  67. [67]

    D. W. Anderson, E. H. Brown and F. P. Peterson, The structure of the spin cobordism ring , Annals of Mathematics 86 (1967) 271

    work page 1967

  68. [68]

    Closed tachyon solitons in type II string theory

    I. Garc´ ıa-Etxebarria, M. Montero and A. M. Uranga, Closed tachyon solitons in type II string theory, Fortsch. Phys. 63 (2015) 571 [ 1505.05510]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  69. [69]

    18, 26 [Xio18] Charles Zhaoxi Xiong

    Z. Wan and J. Wang, Higher anomalies, higher symmetries, and cobordisms I: classification of higher-symmetry-protected topological states and their boundary fermionic/bosonic anomalies via a generalized cobordism theory, Ann. Math. Sci. Appl. 4 (2019) 107 [ 1812.11967]

    work page arXiv 2019

  70. [70]

    Negative Energy Density in Calabi-Yau Compactifications

    T. Hertog, G. T. Horowitz and K. Maeda, Negative energy density in Calabi-Yau compactifications, JHEP 05 (2003) 060 [ hep-th/0304199]

    work page internal anchor Pith review Pith/arXiv arXiv 2003

  71. [71]

    Negative Energy in String Theory and Cosmic Censorship Violation

    T. Hertog, G. T. Horowitz and K. Maeda, Negative energy in string theory and cosmic censorship violation, Phys. Rev. D 69 (2004) 105001 [ hep-th/0310054]

    work page internal anchor Pith review Pith/arXiv arXiv 2004

  72. [72]

    Curiel, A Primer on Energy Conditions , Einstein Stud

    E. Curiel, A Primer on Energy Conditions , Einstein Stud. 13 (2017) 43 [ 1405.0403]

    work page arXiv 2017

  73. [73]

    Draper, B

    P. Draper, B. Lillard and C. Skye, Neutralizing topological obstructions to bubbles of nothing , JHEP 10 (2023) 049 [ 2305.17838]

    work page arXiv 2023

  74. [74]

    J. J. Blanco-Pillado, J. R. Espinosa, J. Huertas and K. Sousa, Tunneling potentials to nothing , Phys. Rev. D 109 (2024) 084057 [ 2311.18821]

    work page arXiv 2024

  75. [75]

    J. J. Blanco-Pillado, J. R. Espinosa, J. Huertas and K. Sousa, Bubbles of nothing: the tunneling potential approach, JCAP 03 (2024) 029 [ 2312.00133]

    work page arXiv 2024

  76. [76]

    Delgado, The bubble of nothing under T-duality , JHEP 05 (2024) 333 [ 2312.09291]

    M. Delgado, The bubble of nothing under T-duality , JHEP 05 (2024) 333 [ 2312.09291]

    work page arXiv 2024

  77. [77]

    Friedrich and A

    B. Friedrich and A. Hebecker, The boundary proposal, Phys. Lett. B 856 (2024) 138946 [2403.18892]

    work page arXiv 2024

  78. [78]

    Angius, J

    R. Angius, J. Calder´ on-Infante, M. Delgado, J. Huertas and A. M. Uranga, At the end of the world: Local Dynamical Cobordism, JHEP 06 (2022) 142 [ 2203.11240]

    work page arXiv 2022

  79. [79]

    Friedrich, A

    B. Friedrich, A. Hebecker and J. Walcher, Cobordism and bubbles of anything in the string landscape, JHEP 02 (2024) 127 [ 2310.06021]

    work page arXiv 2024

  80. [80]

    Vilenkin, Cosmic Strings and Domain Walls , Phys

    A. Vilenkin, Cosmic Strings and Domain Walls , Phys. Rept. 121 (1985) 263

    work page 1985

Showing first 80 references.