Abstract
An often fruitful route to study quantum gravity is the determination and study of quantum mechanical models — that is, models with finite degrees of freedom — that capture the dynamics of a black hole’s microstates. An example of such a model is the superconformal quantum mechanics of Yang-Mills instantons, which has a proposed gravitational dual description as M-theory on a background of the form X7 × S4. This model arises in the strongly-coupled limit of the BFSS matrix model with additional fundamental hypermultiplets, offering a route towards useful numerical simulation. We construct a six-parameter black hole solution in this theory, which is generically non-supersymmetric and non-extremal, and is shown to arise in an “ultra-spinning” limit of the recently-found six-parameter AdS7 solution. We compute its thermodynamic properties, and show that in the supersymmetric limit the entropy and on-shell action match precisely the expected results as computed from the superconformal index of the quantum mechanics, to leading order in the supergravity regime. The low-lying spectrum thus provides access to the dynamics of near-extremal black holes, whose spectra are expected to receive strong quantum corrections.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
A. Strominger and C. Vafa, Microscopic origin of the Bekenstein-Hawking entropy, Phys. Lett. B 379 (1996) 99 [hep-th/9601029] [INSPIRE].
F. Benini, K. Hristov and A. Zaffaroni, Black hole microstates in AdS4 from supersymmetric localization, JHEP 05 (2016) 054 [arXiv:1511.04085] [INSPIRE].
A. Cabo-Bizet, D. Cassani, D. Martelli and S. Murthy, Microscopic origin of the Bekenstein-Hawking entropy of supersymmetric AdS5 black holes, JHEP 10 (2019) 062 [arXiv:1810.11442] [INSPIRE].
S. Choi, J. Kim, S. Kim and J. Nahmgoong, Large AdS black holes from QFT, arXiv:1810.12067 [INSPIRE].
F. Benini and E. Milan, Black Holes in 4D \( \mathcal{N} \) = 4 Super-Yang-Mills Field Theory, Phys. Rev. X 10 (2020) 021037 [arXiv:1812.09613] [INSPIRE].
S. Choi, C. Hwang, S. Kim and J. Nahmgoong, Entropy Functions of BPS Black Holes in AdS4 and AdS6, J. Korean Phys. Soc. 76 (2020) 101 [arXiv:1811.02158] [INSPIRE].
K. Hristov, S. Katmadas and C. Toldo, Rotating attractors and BPS black holes in AdS4, JHEP 01 (2019) 199 [arXiv:1811.00292] [INSPIRE].
S. Choi and C. Hwang, Universal 3d Cardy Block and Black Hole Entropy, JHEP 03 (2020) 068 [arXiv:1911.01448] [INSPIRE].
F. Benini and A. Zaffaroni, Supersymmetric partition functions on Riemann surfaces, Proc. Symp. Pure Math. 96 (2017) 13 [arXiv:1605.06120] [INSPIRE].
C. Closset and H. Kim, Comments on twisted indices in 3d supersymmetric gauge theories, JHEP 08 (2016) 059 [arXiv:1605.06531] [INSPIRE].
S.M. Hosseini, K. Hristov and A. Passias, Holographic microstate counting for AdS4 black holes in massive IIA supergravity, JHEP 10 (2017) 190 [arXiv:1707.06884] [INSPIRE].
F. Benini, H. Khachatryan and E. Milan, Black hole entropy in massive Type IIA, Class. Quant. Grav. 35 (2018) 035004 [arXiv:1707.06886] [INSPIRE].
S.M. Hosseini, A. Nedelin and A. Zaffaroni, The Cardy limit of the topologically twisted index and black strings in AdS5, JHEP 04 (2017) 014 [arXiv:1611.09374] [INSPIRE].
D. Gang, N. Kim and L.A. Pando Zayas, Precision Microstate Counting for the Entropy of Wrapped M5-branes, JHEP 03 (2020) 164 [arXiv:1905.01559] [INSPIRE].
N. Bobev and P.M. Crichigno, Universal spinning black holes and theories of class \( \mathcal{R} \), JHEP 12 (2019) 054 [arXiv:1909.05873] [INSPIRE].
S.M. Hosseini, K. Hristov and A. Zaffaroni, An extremization principle for the entropy of rotating BPS black holes in AdS5, JHEP 07 (2017) 106 [arXiv:1705.05383] [INSPIRE].
S.M. Hosseini, K. Hristov and A. Zaffaroni, A note on the entropy of rotating BPS AdS7 × S4 black holes, JHEP 05 (2018) 121 [arXiv:1803.07568] [INSPIRE].
J. Nian and L.A. Pando Zayas, Microscopic entropy of rotating electrically charged AdS4 black holes from field theory localization, JHEP 03 (2020) 081 [arXiv:1909.07943] [INSPIRE].
S. Choi and S. Kim, Large AdS6 black holes from CFT5, arXiv:1904.01164 [INSPIRE].
G. Kántor, C. Papageorgakis and P. Richmond, AdS7 black-hole entropy and 5D \( \mathcal{N} \) = 2 Yang-Mills, JHEP 01 (2020) 017 [arXiv:1907.02923] [INSPIRE].
J. Nahmgoong, 6d superconformal Cardy formulas, JHEP 02 (2021) 092 [arXiv:1907.12582] [INSPIRE].
A. Zaffaroni, AdS black holes, holography and localization, Living Rev. Rel. 23 (2020) 2 [arXiv:1902.07176] [INSPIRE].
F. Benini, S. Soltani and Z. Zhang, A quantum mechanics for magnetic horizons, JHEP 05 (2023) 070 [arXiv:2212.00672] [INSPIRE].
S. Sachdev, Bekenstein-Hawking Entropy and Strange Metals, Phys. Rev. X 5 (2015) 041025 [arXiv:1506.05111] [INSPIRE].
D. Anninos, T. Anous and R.T. D’Agnolo, Marginal deformations & rotating horizons, JHEP 12 (2017) 095 [arXiv:1707.03380] [INSPIRE].
P. Nayak et al., On the Dynamics of Near-Extremal Black Holes, JHEP 09 (2018) 048 [arXiv:1802.09547] [INSPIRE].
S. Hadar, Near-extremal black holes at late times, backreacted, JHEP 01 (2019) 214 [arXiv:1811.01022] [INSPIRE].
F. Larsen and Y. Zeng, Black hole spectroscopy and AdS2 holography, JHEP 04 (2019) 164 [arXiv:1811.01288] [INSPIRE].
S. Sachdev, Universal low temperature theory of charged black holes with AdS2 horizons, J. Math. Phys. 60 (2019) 052303 [arXiv:1902.04078] [INSPIRE].
A. Castro and V. Godet, Breaking away from the near horizon of extreme Kerr, SciPost Phys. 8 (2020) 089 [arXiv:1906.09083] [INSPIRE].
F. Larsen and S. Paranjape, Thermodynamics of near BPS black holes in AdS4 and AdS7, JHEP 10 (2021) 198 [arXiv:2010.04359] [INSPIRE].
A.M. Charles and F. Larsen, A one-loop test of the near-AdS2/near-CFT1 correspondence, JHEP 07 (2020) 186 [arXiv:1908.03575] [INSPIRE].
J. Hong, F. Larsen and J.T. Liu, The scales of black holes with nAdS2 geometry, JHEP 10 (2019) 260 [arXiv:1907.08862] [INSPIRE].
U. Moitra, S.K. Sake, S.P. Trivedi and V. Vishal, Jackiw-Teitelboim Gravity and Rotating Black Holes, JHEP 11 (2019) 047 [arXiv:1905.10378] [INSPIRE].
A. Castro, F. Larsen and I. Papadimitriou, 5D rotating black holes and the nAdS2/nCFT1 correspondence, JHEP 10 (2018) 042 [arXiv:1807.06988] [INSPIRE].
U. Moitra, S.P. Trivedi and V. Vishal, Extremal and near-extremal black holes and near-CFT1, JHEP 07 (2019) 055 [arXiv:1808.08239] [INSPIRE].
G. Turiaci and H. Verlinde, Towards a 2d QFT Analog of the SYK Model, JHEP 10 (2017) 167 [arXiv:1701.00528] [INSPIRE].
A. Almheiri and B. Kang, Conformal Symmetry Breaking and Thermodynamics of Near-Extremal Black Holes, JHEP 10 (2016) 052 [arXiv:1606.04108] [INSPIRE].
G. Sárosi, AdS2 holography and the SYK model, PoS Modave2017 (2018) 001 [arXiv:1711.08482] [INSPIRE].
L.V. Iliesiu and G.J. Turiaci, The statistical mechanics of near-extremal black holes, JHEP 05 (2021) 145 [arXiv:2003.02860] [INSPIRE].
M. Heydeman, L.V. Iliesiu, G.J. Turiaci and W. Zhao, The statistical mechanics of near-BPS black holes, J. Phys. A 55 (2022) 014004 [arXiv:2011.01953] [INSPIRE].
J. Boruch, M.T. Heydeman, L.V. Iliesiu and G.J. Turiaci, BPS and near-BPS black holes in AdS5 and their spectrum in \( \mathcal{N} \) = 4 SYM, arXiv:2203.01331 [INSPIRE].
Y. Nishida and D.T. Son, Nonrelativistic conformal field theories, Phys. Rev. D 76 (2007) 086004 [arXiv:0706.3746] [INSPIRE].
W.D. Goldberger, AdS/CFT duality for non-relativistic field theory, JHEP 03 (2009) 069 [arXiv:0806.2867] [INSPIRE].
J. Maldacena, D. Martelli and Y. Tachikawa, Comments on string theory backgrounds with non-relativistic conformal symmetry, JHEP 10 (2008) 072 [arXiv:0807.1100] [INSPIRE].
D.T. Son, Toward an AdS/cold atoms correspondence: A Geometric realization of the Schrodinger symmetry, Phys. Rev. D 78 (2008) 046003 [arXiv:0804.3972] [INSPIRE].
K. Balasubramanian and J. McGreevy, Gravity duals for non-relativistic CFTs, Phys. Rev. Lett. 101 (2008) 061601 [arXiv:0804.4053] [INSPIRE].
J.L.F. Barbon and C.A. Fuertes, On the spectrum of nonrelativistic AdS/CFT, JHEP 09 (2008) 030 [arXiv:0806.3244] [INSPIRE].
A. Adams, K. Balasubramanian and J. McGreevy, Hot Spacetimes for Cold Atoms, JHEP 11 (2008) 059 [arXiv:0807.1111] [INSPIRE].
C.P. Herzog, M. Rangamani and S.F. Ross, Heating up Galilean holography, JHEP 11 (2008) 080 [arXiv:0807.1099] [INSPIRE].
N. Dorey and R. Mouland, Conformal quantum mechanics, holomorphic factorisation, and ultra-spinning black holes, JHEP 02 (2024) 086 [arXiv:2302.14850] [INSPIRE].
D.T. Son and M. Wingate, General coordinate invariance and conformal invariance in nonrelativistic physics: Unitary Fermi gas, Annals Phys. 321 (2006) 197 [cond-mat/0509786] [INSPIRE].
S.M. Kravec and S. Pal, Nonrelativistic Conformal Field Theories in the Large Charge Sector, JHEP 02 (2019) 008 [arXiv:1809.08188] [INSPIRE].
S.M. Kravec and S. Pal, The Spinful Large Charge Sector of Non-Relativistic CFTs: From Phonons to Vortex Crystals, JHEP 05 (2019) 194 [arXiv:1904.05462] [INSPIRE].
D. Orlando, V. Pellizzani and S. Reffert, Near-Schrödinger dynamics at large charge, Phys. Rev. D 103 (2021) 105018 [arXiv:2010.07942] [INSPIRE].
V. Pellizzani, Operator spectrum of nonrelativistic CFTs at large charge, Phys. Rev. D 105 (2022) 125018 [arXiv:2107.12127] [INSPIRE].
S. Hellerman et al., Nonrelativistic CFTs at large charge: Casimir energy and logarithmic enhancements, JHEP 05 (2022) 135 [arXiv:2111.12094] [INSPIRE].
J.M. Maldacena, The Large N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [hep-th/9711200] [INSPIRE].
N. Seiberg, Why is the matrix model correct?, Phys. Rev. Lett. 79 (1997) 3577 [hep-th/9710009] [INSPIRE].
S. Hellerman and J. Polchinski, Compactification in the lightlike limit, Phys. Rev. D 59 (1999) 125002 [hep-th/9711037] [INSPIRE].
A.L. Fitzpatrick et al., Lightcone effective Hamiltonians and RG flows, JHEP 08 (2018) 120 [arXiv:1803.10793] [INSPIRE].
O. Aharony et al., Matrix description of interacting theories in six-dimensions, Adv. Theor. Math. Phys. 1 (1998) 148 [hep-th/9707079] [INSPIRE].
O. Aharony, M. Berkooz and N. Seiberg, Light cone description of (2, 0) superconformal theories in six-dimensions, Adv. Theor. Math. Phys. 2 (1998) 119 [hep-th/9712117] [INSPIRE].
N. Dorey, R. Mouland and B. Zhao, Black hole entropy from quantum mechanics, JHEP 06 (2023) 166 [arXiv:2207.12477] [INSPIRE].
M. Berkooz and M.R. Douglas, Five-branes in M(atrix) theory, Phys. Lett. B 395 (1997) 196 [hep-th/9610236] [INSPIRE].
T. Banks, W. Fischler, S.H. Shenker and L. Susskind, M theory as a matrix model: A Conjecture, Phys. Rev. D 55 (1997) 5112 [hep-th/9610043] [INSPIRE].
H. Gharibyan, M. Hanada, M. Honda and J. Liu, Toward simulating superstring/M-theory on a quantum computer, JHEP 07 (2021) 140 [arXiv:2011.06573] [INSPIRE].
E. Rinaldi et al., Matrix-Model Simulations Using Quantum Computing, Deep Learning, and Lattice Monte Carlo, PRX Quantum 3 (2022) 010324 [arXiv:2108.02942] [INSPIRE].
C.W. Bauer et al., Quantum Simulation for High-Energy Physics, PRX Quantum 4 (2023) 027001 [arXiv:2204.03381] [INSPIRE].
J. Maldacena, A simple quantum system that describes a black hole, arXiv:2303.11534 [INSPIRE].
N. Bobev, M. David, J. Hong and R. Mouland, AdS7 black holes from rotating M5-branes, JHEP 09 (2023) 143 [Erratum ibid. 09 (2023) 198] [arXiv:2307.06364] [INSPIRE].
A. Gnecchi et al., Rotating black holes in 4d gauged supergravity, JHEP 01 (2014) 127 [arXiv:1311.1795] [INSPIRE].
D. Klemm, Four-dimensional black holes with unusual horizons, Phys. Rev. D 89 (2014) 084007 [arXiv:1401.3107] [INSPIRE].
R.A. Hennigar, D. Kubizňák and R.B. Mann, Entropy Inequality Violations from Ultraspinning Black Holes, Phys. Rev. Lett. 115 (2015) 031101 [arXiv:1411.4309] [INSPIRE].
R.A. Hennigar, D. Kubizňák, R.B. Mann and N. Musoke, Ultraspinning limits and super-entropic black holes, JHEP 06 (2015) 096 [arXiv:1504.07529] [INSPIRE].
D. Wu and S.-Q. Wu, Ultra-spinning Chow’s black holes in six-dimensional gauged supergravity and their properties, JHEP 11 (2021) 031 [arXiv:2106.14218] [INSPIRE].
R. Emparan and R.C. Myers, Instability of ultra-spinning black holes, JHEP 09 (2003) 025 [hep-th/0308056] [INSPIRE].
M.M. Caldarelli, R. Emparan and M.J. Rodriguez, Black Rings in (Anti)-deSitter space, JHEP 11 (2008) 011 [arXiv:0806.1954] [INSPIRE].
M.M. Caldarelli et al., Vorticity in holographic fluids, PoS CORFU2011 (2011) 076 [arXiv:1206.4351] [INSPIRE].
M. Appels et al., Are “Superentropic” black holes superentropic?, JHEP 02 (2020) 195 [arXiv:1911.12817] [INSPIRE].
H.-C. Kim, S. Kim, S.-S. Kim and K. Lee, The general M5-brane superconformal index, arXiv:1307.7660 [INSPIRE].
H. Nastase, D. Vaman and P. van Nieuwenhuizen, Consistent nonlinear K K reduction of 11-d supergravity on AdS7 × S4 and selfduality in odd dimensions, Phys. Lett. B 469 (1999) 96 [hep-th/9905075] [INSPIRE].
H. Nastase, D. Vaman and P. van Nieuwenhuizen, Consistency of the AdS7 × S4 reduction and the origin of selfduality in odd dimensions, Nucl. Phys. B 581 (2000) 179 [hep-th/9911238] [INSPIRE].
J.T. Liu and R. Minasian, Black holes and membranes in AdS7, Phys. Lett. B 457 (1999) 39 [hep-th/9903269] [INSPIRE].
K. Pilch, P. van Nieuwenhuizen and P.K. Townsend, Compactification of d = 11 supergravity on S4 (or 11 = 7 + 4, too), Nucl. Phys. B 242 (1984) 377 [INSPIRE].
G.W. Gibbons and S.W. Hawking, Action Integrals and Partition Functions in Quantum Gravity, Phys. Rev. D 15 (1977) 2752 [INSPIRE].
V.E. Hubeny, M. Rangamani and S.F. Ross, Causal structures and holography, JHEP 07 (2005) 037 [hep-th/0504034] [INSPIRE].
D. Marolf, Chern-Simons terms and the three notions of charge, in the proceedings of the International Conference on Quantization, Gauge Theory, and Strings: Conference Dedicated to the Memory of Professor Efim Fradkin, Moscow, Russia(2000), pg. 312 [hep-th/0006117] [INSPIRE].
A. Ashtekar and A. Magnon, Asymptotically anti-de Sitter space-times, Class. Quant. Grav. 1 (1984) L39 [INSPIRE].
A. Ashtekar and S. Das, Asymptotically Anti-de Sitter space-times: Conserved quantities, Class. Quant. Grav. 17 (2000) L17 [hep-th/9911230] [INSPIRE].
W. Chen, H. Lu and C.N. Pope, Mass of rotating black holes in gauged supergravities, Phys. Rev. D 73 (2006) 104036 [hep-th/0510081] [INSPIRE].
M. Cvetic, G.W. Gibbons, H. Lu and C.N. Pope, Rotating black holes in gauged supergravities: Thermodynamics, supersymmetric limits, topological solitons and time machines, hep-th/0504080 [INSPIRE].
D. Cassani and L. Papini, The BPS limit of rotating AdS black hole thermodynamics, JHEP 09 (2019) 079 [arXiv:1906.10148] [INSPIRE].
A.J. Singleton, The geometry and representation theory of superconformal quantum mechanics, Ph.D. thesis, Cambridge University, Cambridge, U.K. (2016) [INSPIRE].
N. Dorey and A. Singleton, An Index for Superconformal Quantum Mechanics, arXiv:1812.11816 [INSPIRE].
A.E. Barns-Graham, Much ado about nothing: The superconformal index and Hilbert series of three dimensional \( \mathcal{N} \) = 4 vacua, Ph.D. thesis, Cambridge University, Cambridge, U.K. (2018).
A.E. Barns-Graham and N. Dorey, A Superconformal Index for HyperKähler Cones, arXiv:1812.04565 [INSPIRE].
M. Dine and A. Rajaraman, Multigraviton scattering in the matrix model, Phys. Lett. B 425 (1998) 77 [hep-th/9710174] [INSPIRE].
E. Bergshoeff, J. Gomis and Z. Yan, Nonrelativistic String Theory and T-Duality, JHEP 11 (2018) 133 [arXiv:1806.06071] [INSPIRE].
J. Lahnsteiner, DLCQ, Non-Lorentzian Supergravity, and T-Duality, PoS CORFU2021 (2022) 202 [INSPIRE].
G. Oling and Z. Yan, Aspects of Nonrelativistic Strings, Front. in Phys. 10 (2022) 832271 [arXiv:2202.12698] [INSPIRE].
C.D.A. Blair, D. Gallegos and N. Zinnato, A non-relativistic limit of M-theory and 11-dimensional membrane Newton-Cartan geometry, JHEP 10 (2021) 015 [arXiv:2104.07579] [INSPIRE].
N. Lambert and R. Mouland, Non-Lorentzian RG flows and Supersymmetry, JHEP 06 (2019) 130 [arXiv:1904.05071] [INSPIRE].
R. Mouland, Supersymmetric soliton σ-models from non-Lorentzian field theories, JHEP 04 (2020) 129 [arXiv:1911.11504] [INSPIRE].
H.-C. Kim et al., On instantons as Kaluza-Klein modes of M5-branes, JHEP 12 (2011) 031 [arXiv:1110.2175] [INSPIRE].
D. Cassani and Z. Komargodski, EFT and the SUSY Index on the 2nd Sheet, SciPost Phys. 11 (2021) 004 [arXiv:2104.01464] [INSPIRE].
K. Lee and J. Nahmgoong, Cardy Limits of 6d Superconformal Theories, JHEP 05 (2021) 118 [arXiv:2006.10294] [INSPIRE].
J. Markeviciute and J.E. Santos, Evidence for the existence of a novel class of supersymmetric black holes with AdS5 × S5 asymptotics, Class. Quant. Grav. 36 (2019) 02LT01 [arXiv:1806.01849] [INSPIRE].
A. Bilal, DLCQ of M theory as the lightlike limit, Phys. Lett. B 435 (1998) 312 [hep-th/9805070] [INSPIRE].
Acknowledgments
I am grateful to Eric Bergshoeff, Micha Berkooz, Davide Cassani, Alejandra Castro, Robie Hennigar, Matt Heydeman, Seyed Morteza Hosseini, Seok Kim, Johannes Lahnsteiner, Gerben Oling, Domenico Orlando, Vito Pellizzani, Aaron Poole, Susanne Reffert and Ziqi Yan for helpful discussions. Special thanks go to Nick Dorey and Boan Zhao for the enjoyable collaboration [51, 64] that lead to this project. Yet more special thanks go in particular to Nikolay Bobev, Marina David, and Junho Hong, for inspiring discussions on black holes in supergravity as we completed our work [71]. Finally, thank you to Jackson Fliss and Bernardo Zan, for the inspiration behind figure 1.
I am supported by David Tong’s Simons Investigator Award. This work has also been partially supported by the STFC consolidated grant ST/T000694/1.
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: 2311.13636
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
Mouland, R. How to build a black hole out of instantons. J. High Energ. Phys. 2024, 2 (2024). https://doi.org/10.1007/JHEP03(2024)002
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP03(2024)002