Abstract
We study bubble of nothing decays and their reverse processes, the creation of vacua through ‘bubbles of something’, in models of the Universe based on string theory. From the four-dimensional perspective, the corresponding gravitational instantons contain an end-of-the-world (ETW) boundary or brane, realized by the internal manifold shrinking to zero size. The existence of such ETW branes is predicted by the Cobordism Conjecture. We develop the 4d EFT description of such boundaries at three levels: first, by generalizing the Witten bubble through an additional defect. Second, by replacing the compact S1 with a Calabi-Yau orientifold and allowing it to shrink and disappear through a postulated defect. Third, we describe an ETW brane construction for type IIB Calabi-Yau orientifold compactifications with O3/O7 planes through an appropriate additional O5 orientifolding. Our 4d EFT formalism allows us to compute the decay/creation rates for bubbles of anything depending on two parameters: the size of the relevant defect and its tension a.k.a. the induced (generalized) deficit angle.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S.R. Coleman and F. De Luccia, Gravitational Effects on and of Vacuum Decay, Phys. Rev. D 21 (1980) 3305 [INSPIRE].
S.W. Hawking and I.G. Moss, Supercooled Phase Transitions in the Very Early Universe, Phys. Lett. B 110 (1982) 35 [INSPIRE].
E. Witten, Instability of the Kaluza-Klein Vacuum, Nucl. Phys. B 195 (1982) 481 [INSPIRE].
J.J. Blanco-Pillado and B. Shlaer, Bubbles of Nothing in Flux Compactifications, Phys. Rev. D 82 (2010) 086015 [arXiv:1002.4408] [INSPIRE].
J.J. Blanco-Pillado, B. Shlaer, K. Sousa and J. Urrestilla, Bubbles of Nothing and Supersymmetric Compactifications, JCAP 10 (2016) 002 [arXiv:1606.03095] [INSPIRE].
A.R. Brown and A. Dahlen, Bubbles of Nothing and the Fastest Decay in the Landscape, Phys. Rev. D 84 (2011) 043518 [arXiv:1010.5240] [INSPIRE].
A.R. Brown and A. Dahlen, On ‘nothing’ as an infinitely negatively curved spacetime, Phys. Rev. D 85 (2012) 104026 [arXiv:1111.0301] [INSPIRE].
J.J. Blanco-Pillado, H.S. Ramadhan and B. Shlaer, Decay of flux vacua to nothing, JCAP 10 (2010) 029 [arXiv:1009.0753] [INSPIRE].
G. Dibitetto, N. Petri and M. Schillo, Nothing really matters, JHEP 08 (2020) 040 [arXiv:2002.01764] [INSPIRE].
P. Draper, I. Garcia Garcia and B. Lillard, De Sitter decays to infinity, JHEP 12 (2021) 154 [arXiv:2105.10507] [INSPIRE].
P. Draper, I.G. Garcia and B. Lillard, Bubble of nothing decays of unstable theories, Phys. Rev. D 104 (2021) L121701 [arXiv:2105.08068] [INSPIRE].
P. Draper, B. Lillard and C. Skye, Neutralizing topological obstructions to bubbles of nothing, JHEP 10 (2023) 049 [arXiv:2305.17838] [INSPIRE].
D. Brill and G.T. Horowitz, Negative energy in string theory, Phys. Lett. B 262 (1991) 437 [INSPIRE].
M. Fabinger and P. Horava, Casimir effect between world branes in heterotic M theory, Nucl. Phys. B 580 (2000) 243 [hep-th/0002073] [INSPIRE].
G.T. Horowitz, J. Orgera and J. Polchinski, Nonperturbative Instability of AdS5 × S5/Z(k), Phys. Rev. D 77 (2008) 024004 [arXiv:0709.4262] [INSPIRE].
H. Ooguri and L. Spodyneiko, New Kaluza-Klein instantons and the decay of AdS vacua, Phys. Rev. D 96 (2017) 026016 [arXiv:1703.03105] [INSPIRE].
B.S. Acharya, Supersymmetry, Ricci Flat Manifolds and the String Landscape, JHEP 08 (2020) 128 [arXiv:1906.06886] [INSPIRE].
I. García Etxebarria, M. Montero, K. Sousa and I. Valenzuela, Nothing is certain in string compactifications, JHEP 12 (2020) 032 [arXiv:2005.06494] [INSPIRE].
P. Bomans, D. Cassani, G. Dibitetto and N. Petri, Bubble instability of mIIA on AdS4 × S6, SciPost Phys. 12 (2022) 099 [arXiv:2110.08276] [INSPIRE].
J.J. Blanco-Pillado, H.S. Ramadhan and B. Shlaer, Bubbles from Nothing, JCAP 01 (2012) 045 [arXiv:1104.5229] [INSPIRE].
J.B. Hartle and S.W. Hawking, Wave Function of the Universe, Phys. Rev. D 28 (1983) 2960 [INSPIRE].
A.D. Linde, Quantum Creation of the Inflationary Universe, Lett. Nuovo Cim. 39 (1984) 401 [INSPIRE].
A. Vilenkin, Quantum Creation of Universes, Phys. Rev. D 30 (1984) 509 [INSPIRE].
S.W. Hawking and N. Turok, Open inflation without false vacua, Phys. Lett. B 425 (1998) 25 [hep-th/9802030] [INSPIRE].
N. Turok and S.W. Hawking, Open inflation, the four form and the cosmological constant, Phys. Lett. B 432 (1998) 271 [hep-th/9803156] [INSPIRE].
J. Garriga, Smooth ‘creation’ of an open universe in five-dimensions, hep-th/9804106 [INSPIRE].
J. Garriga, Open inflation and the singular boundary, Phys. Rev. D 61 (2000) 047301 [hep-th/9803210] [INSPIRE].
R. Bousso and A. Chamblin, Open inflation from nonsingular instantons: Wrapping the universe with a membrane, Phys. Rev. D 59 (1999) 063504 [hep-th/9805167] [INSPIRE].
S. Cespedes, S. de Alwis, F. Muia and F. Quevedo, Quantum Transitions, Detailed Balance, Black Holes and Nothingness, arXiv:2307.13614 [INSPIRE].
I.R. Klebanov and M.J. Strassler, Supergravity and a confining gauge theory: Duality cascades and chi SB resolution of naked singularities, JHEP 08 (2000) 052 [hep-th/0007191] [INSPIRE].
F. Brummer, A. Hebecker and E. Trincherini, The throat as a Randall-Sundrum model with Goldberger-Wise stabilization, Nucl. Phys. B 738 (2006) 283 [hep-th/0510113] [INSPIRE].
L. Randall and R. Sundrum, A large mass hierarchy from a small extra dimension, Phys. Rev. Lett. 83 (1999) 3370 [hep-ph/9905221] [INSPIRE].
J. McNamara and C. Vafa, Cobordism Classes and the Swampland, arXiv:1909.10355 [INSPIRE].
M. Montero and C. Vafa, Cobordism Conjecture, Anomalies, and the String Lamppost Principle, JHEP 01 (2021) 063 [arXiv:2008.11729] [INSPIRE].
M. Dierigl, J.J. Heckman, M. Montero and E. Torres, IIB string theory explored: Reflection 7-branes, Phys. Rev. D 107 (2023) 086015 [arXiv:2212.05077] [INSPIRE].
A. Debray, M. Dierigl, J.J. Heckman and M. Montero, The Chronicles of IIBordia: Dualities, Bordisms, and the Swampland, arXiv:2302.00007 [INSPIRE].
G. Buratti, J. Calderón-Infante, M. Delgado and A.M. Uranga, Dynamical Cobordism and Swampland Distance Conjectures, JHEP 10 (2021) 037 [arXiv:2107.09098] [INSPIRE].
G. Buratti, M. Delgado and A.M. Uranga, Dynamical tadpoles, stringy cobordism, and the SM from spontaneous compactification, JHEP 06 (2021) 170 [arXiv:2104.02091] [INSPIRE].
R. Angius et al., At the end of the world: Local Dynamical Cobordism, JHEP 06 (2022) 142 [arXiv:2203.11240] [INSPIRE].
R. Angius, M. Delgado and A.M. Uranga, Dynamical Cobordism and the beginning of time: supercritical strings and tachyon condensation, JHEP 08 (2022) 285 [arXiv:2207.13108] [INSPIRE].
D. Andriot, N. Carqueville and N. Cribiori, Looking for structure in the cobordism conjecture, SciPost Phys. 13 (2022) 071 [arXiv:2204.00021] [INSPIRE].
R. Blumenhagen, N. Cribiori, C. Kneissl and A. Makridou, Dimensional Reduction of Cobordism and K-theory, JHEP 03 (2023) 181 [arXiv:2208.01656] [INSPIRE].
R. Blumenhagen, N. Cribiori, C. Kneissl and A. Makridou, Dynamical cobordism of a domain wall and its companion defect 7-brane, JHEP 08 (2022) 204 [arXiv:2205.09782] [INSPIRE].
R. Blumenhagen, C. Kneissl and C. Wang, Dynamical Cobordism Conjecture: solutions for end-of-the-world branes, JHEP 05 (2023) 123 [arXiv:2303.03423] [INSPIRE].
M. Dine, P.J. Fox and E. Gorbatov, Catastrophic decays of compactified space-times, JHEP 09 (2004) 037 [hep-th/0405190] [INSPIRE].
F. Denef and M.R. Douglas, Distributions of flux vacua, JHEP 05 (2004) 072 [hep-th/0404116] [INSPIRE].
S. Kachru, R. Kallosh, A.D. Linde and S.P. Trivedi, De Sitter vacua in string theory, Phys. Rev. D 68 (2003) 046005 [hep-th/0301240] [INSPIRE].
V. Balasubramanian, P. Berglund, J.P. Conlon and F. Quevedo, Systematics of moduli stabilisation in Calabi-Yau flux compactifications, JHEP 03 (2005) 007 [hep-th/0502058] [INSPIRE].
J.P. Conlon, F. Quevedo and K. Suruliz, Large-volume flux compactifications: Moduli spectrum and D3/D7 soft supersymmetry breaking, JHEP 08 (2005) 007 [hep-th/0505076] [INSPIRE].
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] [INSPIRE].
B. Freivogel and M. Lippert, Evidence for a bound on the lifetime of de Sitter space, JHEP 12 (2008) 096 [arXiv:0807.1104] [INSPIRE].
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 [arXiv:1308.1222] [INSPIRE].
S.R. Coleman, V. Glaser and A. Martin, Action Minima Among Solutions to a Class of Euclidean Scalar Field Equations, Commun. Math. Phys. 58 (1978) 211 [INSPIRE].
D. Garfinkle, General Relativistic Strings, Phys. Rev. D 32 (1985) 1323 [INSPIRE].
A. Vilenkin, Cosmic Strings and Domain Walls, Phys. Rept. 121 (1985) 263 [INSPIRE].
T. Takayanagi, Holographic Dual of BCFT, Phys. Rev. Lett. 107 (2011) 101602 [arXiv:1105.5165] [INSPIRE].
M. Fujita, T. Takayanagi and E. Tonni, Aspects of AdS/BCFT, JHEP 11 (2011) 043 [arXiv:1108.5152] [INSPIRE].
E. Witten, A Simple Proof of the Positive Energy Theorem, Commun. Math. Phys. 80 (1981) 381 [INSPIRE].
X.-Z. Dai, A positive mass theorem for spaces with asymptotic SUSY compactification, Commun. Math. Phys. 244 (2004) 335 [math/0308249] [INSPIRE].
X.-Z. Dai, A note on positive energy theorem for spaces with asymptotic SUSY compactification, J. Math. Phys. 46 (2005) 042505 [math-ph/0406006] [INSPIRE].
S. Giri, L. Martucci and A. Tomasiello, On the stability of string theory vacua, JHEP 04 (2022) 054 [arXiv:2112.10795] [INSPIRE].
J. Garriga, D. Schwartz-Perlov, A. Vilenkin and S. Winitzki, Probabilities in the inflationary multiverse, JCAP 01 (2006) 017 [hep-th/0509184] [INSPIRE].
A. De Simone, A.H. Guth, M.P. Salem and A. Vilenkin, Predicting the cosmological constant with the scale-factor cutoff measure, Phys. Rev. D 78 (2008) 063520 [arXiv:0805.2173] [INSPIRE].
J. Garriga and A. Vilenkin, Watchers of the multiverse, JCAP 05 (2013) 037 [arXiv:1210.7540] [INSPIRE].
B. Friedrich et al., A local Wheeler-DeWitt measure for the string landscape, Nucl. Phys. B 992 (2023) 116230 [arXiv:2205.09772] [INSPIRE].
J. Feldbrugge, J.-L. Lehners and N. Turok, No smooth beginning for spacetime, Phys. Rev. Lett. 119 (2017) 171301 [arXiv:1705.00192] [INSPIRE].
J. Feldbrugge, J.-L. Lehners and N. Turok, No rescue for the no boundary proposal: Pointers to the future of quantum cosmology, Phys. Rev. D 97 (2018) 023509 [arXiv:1708.05104] [INSPIRE].
J. Feldbrugge, J.-L. Lehners and N. Turok, Inconsistencies of the New No-Boundary Proposal, Universe 4 (2018) 100 [arXiv:1805.01609] [INSPIRE].
A. Vilenkin and M. Yamada, Tunneling wave function of the universe, Phys. Rev. D 98 (2018) 066003 [arXiv:1808.02032] [INSPIRE].
A. Vilenkin and M. Yamada, Tunneling wave function of the universe II: the backreaction problem, Phys. Rev. D 99 (2019) 066010 [arXiv:1812.08084] [INSPIRE].
S.B. Giddings, S. Kachru and J. Polchinski, Hierarchies from fluxes in string compactifications, Phys. Rev. D 66 (2002) 106006 [hep-th/0105097] [INSPIRE].
A. Strominger, S.-T. Yau and E. Zaslow, Mirror symmetry is T duality, Nucl. Phys. B 479 (1996) 243 [hep-th/9606040] [INSPIRE].
M. Cvetic, S. Griffies and S.-J. Rey, Static domain walls in N = 1 supergravity, Nucl. Phys. B 381 (1992) 301 [hep-th/9201007] [INSPIRE].
M. Cvetic and H.H. Soleng, Supergravity domain walls, Phys. Rept. 282 (1997) 159 [hep-th/9604090] [INSPIRE].
A. Ceresole et al., Domain walls, near-BPS bubbles, and probabilities in the landscape, Phys. Rev. D 74 (2006) 086010 [hep-th/0605266] [INSPIRE].
J. Bagger and D.V. Belyaev, Supersymmetric branes with (almost) arbitrary tensions, Phys. Rev. D 67 (2003) 025004 [hep-th/0206024] [INSPIRE].
F.F. Gautason, M. Schillo, T. Van Riet and M. Williams, Remarks on scale separation in flux vacua, JHEP 03 (2016) 061 [arXiv:1512.00457] [INSPIRE].
F.F. Gautason, V. Van Hemelryck and T. Van Riet, The Tension between 10D Supergravity and dS Uplifts, Fortsch. Phys. 67 (2019) 1800091 [arXiv:1810.08518] [INSPIRE].
D. Lüst, E. Palti and C. Vafa, AdS and the Swampland, Phys. Lett. B 797 (2019) 134867 [arXiv:1906.05225] [INSPIRE].
A. Westphal, Lifetime of Stringy de Sitter Vacua, JHEP 01 (2008) 012 [arXiv:0705.1557] [INSPIRE].
I. Bena, E. Dudas, M. Graña and S. Lüst, Uplifting Runaways, Fortsch. Phys. 67 (2019) 1800100 [arXiv:1809.06861] [INSPIRE].
R. Blumenhagen, D. Kläwer and L. Schlechter, Swampland Variations on a Theme by KKLT, JHEP 05 (2019) 152 [arXiv:1902.07724] [INSPIRE].
S. Lüst and L. Randall, Effective Theory of Warped Compactifications and the Implications for KKLT, Fortsch. Phys. 70 (2022) 2200103 [arXiv:2206.04708] [INSPIRE].
F. Carta, J. Moritz and A. Westphal, Gaugino condensation and small uplifts in KKLT, JHEP 08 (2019) 141 [arXiv:1902.01412] [INSPIRE].
X. Gao, A. Hebecker and D. Junghans, Control issues of KKLT, Fortsch. Phys. 68 (2020) 2000089 [arXiv:2009.03914] [INSPIRE].
D. Junghans, LVS de Sitter vacua are probably in the swampland, Nucl. Phys. B 990 (2023) 116179 [arXiv:2201.03572] [INSPIRE].
X. Gao, A. Hebecker, S. Schreyer and G. Venken, The LVS parametric tadpole constraint, JHEP 07 (2022) 056 [arXiv:2202.04087] [INSPIRE].
A. Hebecker, S. Schreyer and G. Venken, Curvature corrections to KPV: do we need deep throats?, JHEP 10 (2022) 166 [arXiv:2208.02826] [INSPIRE].
S. Schreyer and G. Venken, α’ corrections to KPV: an uplifting story, JHEP 07 (2023) 235 [arXiv:2212.07437] [INSPIRE].
J. Feldbrugge, J.-L. Lehners and N. Turok, Lorentzian Quantum Cosmology, Phys. Rev. D 95 (2017) 103508 [arXiv:1703.02076] [INSPIRE].
L. Martucci and P. Smyth, Supersymmetric D-branes and calibrations on general N = 1 backgrounds, JHEP 11 (2005) 048 [hep-th/0507099] [INSPIRE].
A. Tomasiello, Geometry of String Theory Compactifications, Cambridge University Press (2022) [https://doi.org/10.1017/9781108635745] [INSPIRE].
K. Eckerle, A unified system for Coleman–De Luccia transitions, Annals Phys. 424 (2021) 168362 [arXiv:2003.04365] [INSPIRE].
Acknowledgments
We are very grateful for useful discussions with Giuseppe Dibitetto, Luca Martucci, Jacob McNamara, Miguel Montero, Simon Schreyer, Irene Valenzuela, Gerben Venken and Timo Weigand. This work was supported by Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy EXC 2181/1 - 390900948 (the Heidelberg STRUCTURES Excellence Cluster).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2310.06021
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Friedrich, B., Hebecker, A. & Walcher, J. Cobordism and bubbles of anything in the string landscape. J. High Energ. Phys. 2024, 127 (2024). https://doi.org/10.1007/JHEP02(2024)127
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP02(2024)127