Abstract
We construct large families of supergravity solutions that are asymptotic to AdS2 and terminate with a cap that is singular in two dimensions but smooth in higher dimensions. These solutions break supersymmetry and conformal invariance. We list arguments suggesting that they correspond to finite-energy excitations in empty AdS2 that back-react on the geometry by inducing non-trivial bubbling topology. They are constructed from the novel technique associated with the Ernst formalism for AdSD × 𝒞 solitons in supergravity [1]. The technique is applied to D = 2 in M-theory with 𝒞 = S3 × T6. The directions of 𝒞 degenerate smoothly as a chain of bolts which ends the spacetime in the IR and generates non-supersymmetric bubbles supported by M2-brane flux. Some specific solutions have “flat” directions where the sizes of their bubbles are totally unconstrained and can be arbitrarily tuned while the asymptotics remains fixed. The solitons should correspond to regular non-supersymmetric states of a holographically dual CFT1.
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References
I. Bah and P. Heidmann, Non-BPS bubbling geometries in AdS3, JHEP 02 (2023) 133 [arXiv:2210.06483] [INSPIRE].
A. Strominger, AdS(2) quantum gravity and string theory, JHEP 01 (1999) 007 [hep-th/9809027] [INSPIRE].
M. Spradlin and A. Strominger, Vacuum states for AdS(2) black holes, JHEP 11 (1999) 021 [hep-th/9904143] [INSPIRE].
I. Bena, N. Bobev and N.P. Warner, Bubbles on Manifolds with a U(1) Isometry, JHEP 08 (2007) 004 [arXiv:0705.3641] [INSPIRE].
O. Lunin, Bubbling geometries for AdS2 × S2, JHEP 10 (2015) 167 [arXiv:1507.06670] [INSPIRE].
I. Bena, P. Heidmann and D. Turton, AdS2 holography: mind the cap, JHEP 12 (2018) 028 [arXiv:1806.02834] [INSPIRE].
P. Heidmann and S. Mondal, The full space of BPS multicenter states with pure D-brane charges, JHEP 06 (2019) 011 [arXiv:1810.10019] [INSPIRE].
A. Sen, Extremal black holes and elementary string states, Mod. Phys. Lett. A 10 (1995) 2081 [hep-th/9504147] [INSPIRE].
A. Strominger and C. Vafa, Microscopic origin of the Bekenstein-Hawking entropy, Phys. Lett. B 379 (1996) 99 [hep-th/9601029] [INSPIRE].
J.M. Maldacena, A. Strominger and E. Witten, Black hole entropy in M theory, JHEP 12 (1997) 002 [hep-th/9711053] [INSPIRE].
F. Benini, K. Hristov and A. Zaffaroni, Exact microstate counting for dyonic black holes in AdS4, Phys. Lett. B 771 (2017) 462 [arXiv:1608.07294] [INSPIRE].
F. Azzurli et al., A universal counting of black hole microstates in AdS4, JHEP 02 (2018) 054 [arXiv:1707.04257] [INSPIRE].
A. Sen, Quantum Entropy Function from AdS(2)/CFT(1) Correspondence, Int. J. Mod. Phys. A 24 (2009) 4225 [arXiv:0809.3304] [INSPIRE].
R.K. Gupta and A. Sen, Ads(3)/CFT(2) to Ads(2)/CFT(1), JHEP 04 (2009) 034 [arXiv:0806.0053] [INSPIRE].
A. Sen, State Operator Correspondence and Entanglement in AdS2/CFT1, Entropy 13 (2011) 1305 [arXiv:1101.4254] [INSPIRE].
J.M. Maldacena, J. Michelson and A. Strominger, Anti-de Sitter fragmentation, JHEP 02 (1999) 011 [hep-th/9812073] [INSPIRE].
A. Almheiri and J. Polchinski, Models of AdS2 backreaction and holography, JHEP 11 (2015) 014 [arXiv:1402.6334] [INSPIRE].
A. Kitaev, A simple model of quantum holography, talks at KITP, 7 April 2015 and 27 May 2015, http://online.kitp.ucsb.edu/online/entangled15/kitaev, http://online.kitp.ucsb.edu/online/entangled15/kitaev2.
J. Maldacena and D. Stanford, Remarks on the Sachdev-Ye-Kitaev model, Phys. Rev. D 94 (2016) 106002 [arXiv:1604.07818] [INSPIRE].
J.S. Cotler et al., Black Holes and Random Matrices, JHEP 05 (2017) 118 [Erratum ibid. 09 (2018) 002] [arXiv:1611.04650] [INSPIRE].
V. Balasubramanian, B. Craps, B. Czech and G. Sárosi, Echoes of chaos from string theory black holes, JHEP 03 (2017) 154 [arXiv:1612.04334] [INSPIRE].
A. Kitaev and S.J. Suh, The soft mode in the Sachdev-Ye-Kitaev model and its gravity dual, JHEP 05 (2018) 183 [arXiv:1711.08467] [INSPIRE].
R. Jackiw, Lower Dimensional Gravity, Nucl. Phys. B 252 (1985) 343 [INSPIRE].
C. Teitelboim, Gravitation and Hamiltonian Structure in Two Space-Time Dimensions, Phys. Lett. B 126 (1983) 41 [INSPIRE].
H. Lin, O. Lunin and J.M. Maldacena, Bubbling AdS space and 1/2 BPS geometries, JHEP 10 (2004) 025 [hep-th/0409174] [INSPIRE].
O. Lunin, J.M. Maldacena and L. Maoz, Gravity solutions for the D1-D5 system with angular momentum, hep-th/0212210 [INSPIRE].
I. Kanitscheider, K. Skenderis and M. Taylor, Fuzzballs with internal excitations, JHEP 06 (2007) 056 [arXiv:0704.0690] [INSPIRE].
S. Giusto, O. Lunin, S.D. Mathur and D. Turton, D1-D5-P microstates at the cap, JHEP 02 (2013) 050 [arXiv:1211.0306] [INSPIRE].
S. Giusto, E. Moscato and R. Russo, AdS3 holography for 1/4 and 1/8 BPS geometries, JHEP 11 (2015) 004 [arXiv:1507.00945] [INSPIRE].
I. Bena et al., Habemus Superstratum! A constructive proof of the existence of superstrata, JHEP 05 (2015) 110 [arXiv:1503.01463] [INSPIRE].
I. Bena, E. Martinec, D. Turton and N.P. Warner, Momentum Fractionation on Superstrata, JHEP 05 (2016) 064 [arXiv:1601.05805] [INSPIRE].
P. Heidmann and N.P. Warner, Superstratum Symbiosis, JHEP 09 (2019) 059 [arXiv:1903.07631] [INSPIRE].
P. Heidmann, D.R. Mayerson, R. Walker and N.P. Warner, Holomorphic Waves of Black Hole Microstructure, JHEP 02 (2020) 192 [arXiv:1910.10714] [INSPIRE].
M. Shigemori, Superstrata, Gen. Rel. Grav. 52 (2020) 51 [arXiv:2002.01592] [INSPIRE].
R.P. Geroch, A Method for generating solutions of Einstein’s equations, J. Math. Phys. 12 (1971) 918 [INSPIRE].
R.P. Geroch, A Method for generating new solutions of Einstein’s equation. 2, J. Math. Phys. 13 (1972) 394 [INSPIRE].
I. Bah and P. Heidmann, Topological stars, black holes and generalized charged Weyl solutions, JHEP 09 (2021) 147 [arXiv:2012.13407] [INSPIRE].
I. Bah and P. Heidmann, Smooth bubbling geometries without supersymmetry, JHEP 09 (2021) 128 [arXiv:2106.05118] [INSPIRE].
I. Bah and P. Heidmann, Bubble bag end: a bubbly resolution of curvature singularity, JHEP 10 (2021) 165 [arXiv:2107.13551] [INSPIRE].
P. Heidmann, Non-BPS floating branes and bubbling geometries, JHEP 02 (2022) 162 [arXiv:2112.03279] [INSPIRE].
H. Weyl, The theory of gravitation, Annalen Phys. 54 (1917) 117 [INSPIRE].
R. Emparan and H.S. Reall, Generalized Weyl solutions, Phys. Rev. D 65 (2002) 084025 [hep-th/0110258] [INSPIRE].
I. Bah and P. Heidmann, Topological Stars and Black Holes, Phys. Rev. Lett. 126 (2021) 151101 [arXiv:2011.08851] [INSPIRE].
H. Elvang and G.T. Horowitz, When black holes meet Kaluza-Klein bubbles, Phys. Rev. D 67 (2003) 044015 [hep-th/0210303] [INSPIRE].
I. Bah, P. Heidmann and P. Weck, Schwarzschild-like topological solitons, JHEP 08 (2022) 269 [arXiv:2203.12625] [INSPIRE].
E. Cremmer, B. Julia, H. Lu and C.N. Pope, Dualization of dualities. 1., Nucl. Phys. B 523 (1998) 73 [hep-th/9710119] [INSPIRE].
J. Bellorin, P. Meessen and T. Ortin, All the supersymmetric solutions of N=1,d=5 ungauged supergravity, JHEP 01 (2007) 020 [hep-th/0610196] [INSPIRE].
A. Castro, D. Grumiller, F. Larsen and R. McNees, Holographic Description of AdS(2) Black Holes, JHEP 11 (2008) 052 [arXiv:0809.4264] [INSPIRE].
M. Cvetič and I. Papadimitriou, AdS2 holographic dictionary, JHEP 12 (2016) 008 [Erratum ibid. 01 (2017) 120] [arXiv:1608.07018] [INSPIRE].
C. Chamon, R. Jackiw, S.-Y. Pi and L. Santos, Conformal quantum mechanics as the CFT1 dual to AdS2, Phys. Lett. B 701 (2011) 503 [arXiv:1106.0726] [INSPIRE].
R. Jackiw and S.-Y. Pi, Conformal Blocks for the 4-Point Function in Conformal Quantum Mechanics, Phys. Rev. D 86 (2012) 045017 [Erratum ibid. 86 (2012) 089905] [arXiv:1205.0443] [INSPIRE].
G.W. Gibbons and S.W. Hawking, Action Integrals and Partition Functions in Quantum Gravity, Phys. Rev. D 15 (1977) 2752 [INSPIRE].
J.W. York Jr., Role of conformal three geometry in the dynamics of gravitation, Phys. Rev. Lett. 28 (1972) 1082 [INSPIRE].
M.S. Costa and M.J. Perry, Interacting black holes, Nucl. Phys. B 591 (2000) 469 [hep-th/0008106] [INSPIRE].
I. Kanitscheider, K. Skenderis and M. Taylor, Holographic anatomy of fuzzballs, JHEP 04 (2007) 023 [hep-th/0611171] [INSPIRE].
M. Taylor, Matching of correlators in AdS(3) / CFT(2), JHEP 06 (2008) 010 [arXiv:0709.1838] [INSPIRE].
S. Giusto, S. Rawash and D. Turton, Ads3 holography at dimension two, JHEP 07 (2019) 171 [arXiv:1904.12880] [INSPIRE].
S. Rawash and D. Turton, Supercharged AdS3 Holography, JHEP 07 (2021) 178 [arXiv:2105.13046] [INSPIRE].
E. Witten, Instability of the Kaluza-Klein Vacuum, Nucl. Phys. B 195 (1982) 481 [INSPIRE].
I. Bah, A. Dey and P. Heidmann, Stability of topological solitons, and black string to bubble transition, JHEP 04 (2022) 168 [arXiv:2112.11474] [INSPIRE].
B.D. Chowdhury and S.D. Mathur, Radiation from the non-extremal fuzzball, Class. Quant. Grav. 25 (2008) 135005 [arXiv:0711.4817] [INSPIRE].
I. Bena, P. Heidmann, R. Monten and N.P. Warner, Thermal Decay without Information Loss in Horizonless Microstate Geometries, SciPost Phys. 7 (2019) 063 [arXiv:1905.05194] [INSPIRE].
I. Bena, F. Eperon, P. Heidmann and N.P. Warner, The Great Escape: Tunneling out of Microstate Geometries, JHEP 04 (2021) 112 [arXiv:2005.11323] [INSPIRE].
V.A. Belinsky and V.E. Sakharov, Stationary Gravitational Solitons with Axial Symmetry, Sov. Phys. JETP 50 (1979) 1 [INSPIRE].
B.K. Harrison, Bäcklund Transformation for the Ernst Equation of General Relativity, Phys. Rev. Lett. 41 (1978) 1197.
G.A. Alekseev, Monodromy transform approach to solution of some field equations in general relativity and string theory, in the proceedings of the Nonlinearity, Integrability and All That: Twenty Years after NEEDS 79, (1999) [https://doi.org/10.1142/9789812817587_0002] [gr-qc/9911045] [INSPIRE].
G.A. Alekseev, Gravitational solitons and monodromy transform approach to solution of integrable reductions of Einstein equations, Physica D 152 (2001) 97 [gr-qc/0001012] [INSPIRE].
H. Stephani et al., Exact solutions of Einstein’s field equations, Cambridge Univ. Press, Cambridge (2003) [https://doi.org/10.1017/CBO9780511535185] [INSPIRE].
J.P. Gauntlett et al., All supersymmetric solutions of minimal supergravity in five- dimensions, Class. Quant. Grav. 20 (2003) 4587 [hep-th/0209114] [INSPIRE].
I. Bena and N.P. Warner, Bubbling supertubes and foaming black holes, Phys. Rev. D 74 (2006) 066001 [hep-th/0505166] [INSPIRE].
I. Bena and N.P. Warner, Black holes, black rings and their microstates, Lect. Notes Phys. 755 (2008) 1 [hep-th/0701216] [INSPIRE].
P. Heidmann, Four-center bubbled BPS solutions with a Gibbons-Hawking base, JHEP 10 (2017) 009 [arXiv:1703.10095] [INSPIRE].
I. Bena, P. Heidmann and P.F. Ramirez, A systematic construction of microstate geometries with low angular momentum, JHEP 10 (2017) 217 [arXiv:1709.02812] [INSPIRE].
Acknowledgments
We are grateful to Iosif Bena, Ibou Bah, and Nick Warner for interesting and stimulating discussions. The work of PH is supported by NSF grant PHY-2112699. The work of AH is supported in part by the ERC Grant 787320 - QBH Structure.
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Heidmann, P., Houppe, A. Solitonic excitations in AdS2. J. High Energ. Phys. 2023, 186 (2023). https://doi.org/10.1007/JHEP07(2023)186
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DOI: https://doi.org/10.1007/JHEP07(2023)186