Abstract
We study non-perturbative instabilities of AdS spacetime in General Relativity with a cosmological constant in arbitrary dimensions. In this simple setup we explicitly construct a class of gravitational instantons generalizing Witten’s bubble of nothing. We calculate the corresponding Euclidean action and show that its change is finite. The expansion of these bubbles is described by a lower-dimensional de Sitter geometry within a non- compact foliation of the background spacetime. Moreover we discuss the existence of covariantly constant spinors as a possible topological obstruction for such decays to occur. This mechanism is further connected to the stability of supersymmetric vacua in string theory.
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References
S.R. Coleman and F. De Luccia, Gravitational effects on and of vacuum decay, Phys. Rev. D 21 (1980) 3305 [INSPIRE].
J. Brown and C. Teitelboim, Neutralization of the cosmological constant by membrane creation, Nucl. Phys. B 297 (1988) 787 [INSPIRE].
E. Witten, Instability of the Kaluza-Klein vacuum, Nucl. Phys. B 195 (1982) 481 [INSPIRE].
E. Witten, Constraints on supersymmetry breaking, Nucl. Phys. B 202 (1982) 253 [INSPIRE].
E. Witten, Anti-de Sitter space, thermal phase transition, and confinement in gauge theories, Adv. Theor. Math. Phys. 2 (1998) 505 [hep-th/9803131] [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].
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].
R. Argurio, M. Bertolini, S. Franco and S. Kachru, Gauge/gravity duality and meta-stable dynamical supersymmetry breaking, JHEP 01 (2007) 083 [hep-th/0610212] [INSPIRE].
N. Arkani-Hamed, L. Motl, A. Nicolis and C. Vafa, The string landscape, black holes and gravity as the weakest force, JHEP 06 (2007) 060 [hep-th/0601001] [INSPIRE].
T.D. Brennan, F. Carta and C. Vafa, The string landscape, the swampland, and the missing corner, PoS(TASI2017)015 (2017) [arXiv:1711.00864] [INSPIRE].
E. Palti, The swampland: introduction and review, Fortsch. Phys. 67 (2019) 1900037 [arXiv:1903.06239] [INSPIRE].
H. Ooguri and C. Vafa, Non-supersymmetric AdS and the swampland, Adv. Theor. Math. Phys. 21 (2017) 1787 [arXiv:1610.01533] [INSPIRE].
B. Freivogel and M. Kleban, Vacua morghulis, arXiv:1610.04564 [INSPIRE].
G.T. Horowitz and R.C. Myers, The AdS/CFT correspondence and a new positive energy conjecture for general relativity, Phys. Rev. D 59 (1998) 026005 [hep-th/9808079] [INSPIRE].
V. Balasubramanian and S.F. Ross, The dual of nothing, Phys. Rev. D 66 (2002) 086002 [hep-th/0205290] [INSPIRE].
G. Obied, H. Ooguri, L. Spodyneiko and C. Vafa, De Sitter space and the swampland, arXiv:1806.08362 [INSPIRE].
K. Dasgupta, M. Emelin, E. McDonough and R. Tatar, Quantum corrections and the de Sitter swampland conjecture, JHEP 01 (2019) 145 [arXiv:1808.07498] [INSPIRE].
K. Dasgupta, M. Emelin, M.M. Faruk and R. Tatar, How a four-dimensional de Sitter solution remains outside the swampland, arXiv:1911.02604 [INSPIRE].
J. Blåbäck, U. Danielsson and G. Dibitetto, Accelerated universes from type IIA compactifications, JCAP 03 (2014) 003 [arXiv:1310.8300] [INSPIRE].
J.J. Heckman, C. Lawrie, L. Lin, J. Sakstein and G. Zoccarato, Pixelated dark energy, Fortsch. Phys. 67 (2019) 1900071 [arXiv:1901.10489] [INSPIRE].
C. Córdova, G. De Luca and A. Tomasiello, AdS8 solutions in type II supergravity, JHEP 07 (2019) 127 [arXiv:1811.06987] [INSPIRE].
C. Córdova, G.B. De Luca and A. Tomasiello, Classical de Sitter solutions of 10-dimensional supergravity, Phys. Rev. Lett. 122 (2019) 091601 [arXiv:1812.04147] [INSPIRE].
C. Córdova, G.B. De Luca and A. Tomasiello, New de Sitter solutions in ten dimensions and orientifold singularities, arXiv:1911.04498 [INSPIRE].
O. Aharony, M. Fabinger, G.T. Horowitz and E. Silverstein, Clean time dependent string backgrounds from bubble baths, JHEP 07 (2002) 007 [hep-th/0204158] [INSPIRE].
D. Harlow, Metastability in anti de Sitter space, arXiv:1003.5909 [INSPIRE].
J.L.F. Barbón and E. Rabinovici, Holography of AdS vacuum bubbles, JHEP 04 (2010) 123 [arXiv:1003.4966] [INSPIRE].
D. Birmingham and M. Rinaldi, Bubbles in anti-de Sitter space, Phys. Lett. B 544 (2002) 316 [hep-th/0205246] [INSPIRE].
R.-G. Cai, Constant curvature black hole and dual field theory, Phys. Lett. B 544 (2002) 176 [hep-th/0206223] [INSPIRE].
G.T. Horowitz, J. Orgera and J. Polchinski, Nonperturbative instability of AdS5 × S5 /Zk , Phys. Rev. D 77 (2008) 024004 [arXiv:0709.4262] [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, H.S. Ramadhan and B. Shlaer, Decay of flux vacua to nothing, JCAP 10 (2010) 029 [arXiv:1009.0753] [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].
U.H. Danielsson, G. Dibitetto and S.C. Vargas, A swamp of non-SUSY vacua, JHEP 11 (2017) 152 [arXiv:1708.03293] [INSPIRE].
F. Apruzzi, G. Bruno De Luca, A. Gnecchi, G. Lo Monaco and A. Tomasiello, On AdS7 stability, JHEP 07 (2020) 033 [arXiv:1912.13491] [INSPIRE].
S. Weinberg, The cosmological constant problem, Rev. Mod. Phys. 61 (1989) 1 [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].
J.K. Ghosh, E. Kiritsis, F. Nitti and L.T. Witkowski, De Sitter and anti-de Sitter branes in self-tuning models, JHEP 11 (2018) 128 [arXiv:1807.09794] [INSPIRE].
S. Banerjee, U. Danielsson, G. Dibitetto, S. Giri and M. Schillo, Emergent de Sitter cosmology from decaying anti-de Sitter space, Phys. Rev. Lett. 121 (2018) 261301 [arXiv:1807.01570] [INSPIRE].
S. Banerjee, U. Danielsson, G. Dibitetto, S. Giri and M. Schillo, De Sitter cosmology on an expanding bubble, JHEP 10 (2019) 164 [arXiv:1907.04268] [INSPIRE].
A. Amariti, C. Charmousis, D. Forcella, E. Kiritsis and F. Nitti, Brane cosmology and the self-tuning of the cosmological constant, JCAP 10 (2019) 007 [arXiv:1904.02727] [INSPIRE].
I.-S. Yang, Stretched extra dimensions and bubbles of nothing in a toy model landscape, Phys. Rev. D 81 (2010) 125020 [arXiv:0910.1397] [INSPIRE].
L. Randall, The boundaries of KKLT, arXiv:1912.06693 [INSPIRE].
R. Schon and S.-T. Yau, On the proof of the positive mass conjecture in general relativity, Commun. Math. Phys. 65 (1979) 45 [INSPIRE].
R. Schon and S.-T. Yau, Proof of the positive mass theorem. 2, Commun. Math. Phys. 79 (1981) 231 [INSPIRE].
E. Witten, A simple proof of the positive energy theorem, Commun. Math. Phys. 80 (1981) 381 [INSPIRE].
S.R. Coleman, The fate of the false vacuum. 1. Semiclassical theory, Phys. Rev. D 15 (1977) 2929 [Erratum ibid. 16 (1977) 1248] [INSPIRE].
M. Godazgar and H.S. Reall, Algebraically special axisymmetric solutions of the higher-dimensional vacuum Einstein equation, Class. Quant. Grav. 26 (2009) 165009 [arXiv:0904.4368] [INSPIRE].
R. Emparan and H.S. Reall, Black holes in higher dimensions, Living Rev. Rel. 11 (2008) 6 [arXiv:0801.3471] [INSPIRE].
P. Draper and S. Farkas, Gravitational instabilities and censorship of large scalar field excursions, JHEP 05 (2019) 158 [arXiv:1901.00515] [INSPIRE].
P. Draper and S. Farkas, Transplanckian censorship and the local swampland distance conjecture, JHEP 01 (2020) 133 [arXiv:1910.04804] [INSPIRE].
A. Ceresole and G. Dall’Agata, Flow equations for non-BPS extremal black holes, JHEP 03 (2007) 110 [hep-th/0702088] [INSPIRE].
L. Andrianopoli, R. D’Auria, E. Orazi and M. Trigiante, First order description of D = 4 static black holes and the Hamilton-Jacobi equation, Nucl. Phys. B 833 (2010) 1 [arXiv:0905.3938] [INSPIRE].
G. Lopes Cardoso, A. Ceresole, G. Dall’Agata, J.M. Oberreuter and J. Perz, First-order flow equations for extremal black holes in very special geometry, JHEP 10 (2007) 063 [arXiv:0706.3373] [INSPIRE].
G. Dall’Agata and A. Gnecchi, Flow equations and attractors for black holes in N = 2 U(1) gauged supergravity, JHEP 03 (2011) 037 [arXiv:1012.3756] [INSPIRE].
M. Trigiante, T. Van Riet and B. Vercnocke, Fake supersymmetry versus Hamilton-Jacobi, JHEP 05 (2012) 078 [arXiv:1203.3194] [INSPIRE].
D. Klemm, N. Petri and M. Rabbiosi, Symplectically invariant flow equations for N = 2, D = 4 gauged supergravity with hypermultiplets, JHEP 04 (2016) 008 [arXiv:1602.01334] [INSPIRE].
F. Apruzzi, G. Dibitetto and L. Tizzano, A new 6d fixed point from holography, JHEP 11 (2016) 126 [arXiv:1603.06576] [INSPIRE].
D. Klemm, N. Petri and M. Rabbiosi, Black string first order flow in N = 2, d = 5 Abelian gauged supergravity, JHEP 01 (2017) 106 [arXiv:1610.07367] [INSPIRE].
D. Klemm and M. Rabbiosi, First order flow equations for nonextremal black holes in AdS (super)gravity, JHEP 10 (2017) 149 [arXiv:1706.05862] [INSPIRE].
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Dibitetto, G., Petri, N. & Schillo, M. Nothing really matters. J. High Energ. Phys. 2020, 40 (2020). https://doi.org/10.1007/JHEP08(2020)040
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DOI: https://doi.org/10.1007/JHEP08(2020)040