Abstract
We initiate a systematic study of supersymmetric backgrounds in 4d š© = 2 Euclidean supergravity in the presence of infinite towers of higher derivative corrections. Adopting a Gibbons-Hawking view towards the evaluation of the action in terms of nuts and bolts, we consider the two maximally symmetric vacua ā4 and ā4 (Euclidean AdS4) and their unique supersymmetric deformations with (anti-) self-dual Maxwell tensors corresponding to a single nut at the center. These are the Omega background of Nekrasov-Okounkov, Ī©ā4, and its generalization with a cosmological constant of Martelli-Passias-Sparks, denoted Ī©ā4 (also known as the gravity dual of the U(1) Ć U(1) squashed sphere). We write down the BPS configurations in the superconformal formalism in the presence of vector multiplets and derive the corresponding off- and on-shell actions. Our results provide a rigorous proof for important parts of the conjecture in [1] and its holographic corollary in [2], which we discuss in detail along with extensions such as the addition of hypermultiplets and the presence of conical defects.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
K. Hristov, 4d š© = 2 supergravity observables from Nekrasov-like partition functions, JHEP 02 (2022) 079 [arXiv:2111.06903] [INSPIRE].
K. Hristov, ABJM at finite N via 4d supergravity, JHEP 10 (2022) 190 [arXiv:2204.02992] [INSPIRE].
G.W. Gibbons and S.W. Hawking, Action Integrals and Partition Functions in Quantum Gravity, Phys. Rev. D 15 (1977) 2752 [INSPIRE].
G.W. Gibbons and S.W. Hawking, Classification of Gravitational Instanton Symmetries, Commun. Math. Phys. 66 (1979) 291 [INSPIRE].
A. Chamblin, R. Emparan, C.V. Johnson and R.C. Myers, Large N phases, gravitational instantons and the nuts and bolts of AdS holography, Phys. Rev. D 59 (1999) 064010 [hep-th/9808177] [INSPIRE].
D. Martelli, A. Passias and J. Sparks, The supersymmetric NUTs and bolts of holography, Nucl. Phys. B 876 (2013) 810 [arXiv:1212.4618] [INSPIRE].
D. Farquet, J. Lorenzen, D. Martelli and J. Sparks, Gravity duals of supersymmetric gauge theories on three-manifolds, JHEP 08 (2016) 080 [arXiv:1404.0268] [INSPIRE].
P. Benetti Genolini, D. Cassani, D. Martelli and J. Sparks, Holographic renormalization and supersymmetry, JHEP 02 (2017) 132 [arXiv:1612.06761] [INSPIRE].
C. Toldo and B. Willett, Partition functions on 3d circle bundles and their gravity duals, JHEP 05 (2018) 116 [arXiv:1712.08861] [INSPIRE].
P. Benetti Genolini, J.M. Perez IpiƱa and J. Sparks, Localization of the action in AdS/CFT, JHEP 10 (2019) 252 [arXiv:1906.11249] [INSPIRE].
A.A. Belavin, A.M. Polyakov and A.B. Zamolodchikov, Infinite Conformal Symmetry in Two-Dimensional Quantum Field Theory, Nucl. Phys. B 241 (1984) 333 [INSPIRE].
N.A. Nekrasov, Seiberg-Witten prepotential from instanton counting, Adv. Theor. Math. Phys. 7 (2003) 831 [hep-th/0206161] [INSPIRE].
N.A. Nekrasov, Localizing gauge theories, in 14th International Congress on Mathematical Physics, (2003).
C. Beem, T. Dimofte and S. Pasquetti, Holomorphic Blocks in Three Dimensions, JHEP 12 (2014) 177 [arXiv:1211.1986] [INSPIRE].
G. Festuccia, J. Qiu, J. Winding and M. Zabzine, Twisting with a Flip (the Art of Pestunization), Commun. Math. Phys. 377 (2020) 341 [arXiv:1812.06473] [INSPIRE].
V. Pestun, Localization of gauge theory on a four-sphere and supersymmetric Wilson loops, Commun. Math. Phys. 313 (2012) 71 [arXiv:0712.2824] [INSPIRE].
V. Pestun et al., Localization techniques in quantum field theories, J. Phys. A 50 (2017) 440301 [arXiv:1608.02952] [INSPIRE].
S.M. Hosseini, K. Hristov and A. Zaffaroni, Gluing gravitational blocks for AdS black holes, JHEP 12 (2019) 168 [arXiv:1909.10550] [INSPIRE].
N. Nekrasov and A. Okounkov, Seiberg-Witten theory and random partitions, Prog. Math. 244 (2006) 525 [hep-th/0306238] [INSPIRE].
J.F. Plebanski and M. Demianski, Rotating, charged, and uniformly accelerating mass in general relativity, Annals Phys. 98 (1976) 98 [INSPIRE].
N. Alonso-Alberca, P. Meessen and T. Ortin, Supersymmetry of topological Kerr-Newman-Taub-NUT-AdS space-times, Class. Quant. Grav. 17 (2000) 2783 [hep-th/0003071] [INSPIRE].
D. Martelli, A. Passias and J. Sparks, The gravity dual of supersymmetric gauge theories on a squashed three-sphere, Nucl. Phys. B 864 (2012) 840 [arXiv:1110.6400] [INSPIRE].
C. Klare and A. Zaffaroni, Extended Supersymmetry on Curved Spaces, JHEP 10 (2013) 218 [arXiv:1308.1102] [INSPIRE].
E. Lauria and A. Van Proeyen, š© = 2 Supergravity in D = 4, 5, 6 Dimensions, arXiv e-prints (2020) arXiv:2004.11433 [arXiv:2004.11433].
B. de Wit and V. Reys, Euclidean supergravity, JHEP 12 (2017) 011 [arXiv:1706.04973] [INSPIRE].
E. Bergshoeff, M. de Roo and B. de Wit, Extended Conformal Supergravity, Nucl. Phys. B 182 (1981) 173 [INSPIRE].
D. Butter, B. de Wit, S.M. Kuzenko and I. Lodato, New higher-derivative invariants in N=2 supergravity and the Gauss-Bonnet term, JHEP 12 (2013) 062 [arXiv:1307.6546] [INSPIRE].
K. Hristov, H. Looyestijn and S. Vandoren, Maximally supersymmetric solutions of D=4 N=2 gauged supergravity, JHEP 11 (2009) 115 [arXiv:0909.1743] [INSPIRE].
N. Hama and K. Hosomichi, Seiberg-Witten Theories on Ellipsoids, JHEP 09 (2012) 033 [arXiv:1206.6359] [INSPIRE].
N. Bobev, F.F. Gautason and K. Hristov, Holographic dual of the Ī© -background, Phys. Rev. D 100 (2019) 021901 [arXiv:1903.05095] [INSPIRE].
K. Skenderis, Lecture notes on holographic renormalization, Class. Quant. Grav. 19 (2002) 5849 [hep-th/0209067] [INSPIRE].
N. Bobev, A.M. Charles, K. Hristov and V. Reys, The Unreasonable Effectiveness of Higher-Derivative Supergravity in AdS4 Holography, Phys. Rev. Lett. 125 (2020) 131601 [arXiv:2006.09390] [INSPIRE].
N. Bobev, A.M. Charles, K. Hristov and V. Reys, Higher-derivative supergravity, AdS4 holography, and black holes, JHEP 08 (2021) 173 [arXiv:2106.04581] [INSPIRE].
P.B. Genolini and P. Richmond, Supersymmetry of higher-derivative supergravity in AdS4 holography, Phys. Rev. D 104 (2021) L061902 [arXiv:2107.04590] [INSPIRE].
D.L. Jafferis, The Exact Superconformal R-Symmetry Extremizes Z, JHEP 05 (2012) 159 [arXiv:1012.3210] [INSPIRE].
D.L. Jafferis, I.R. Klebanov, S.S. Pufu and B.R. Safdi, Towards the F-Theorem: N=2 Field Theories on the Three-Sphere, JHEP 06 (2011) 102 [arXiv:1103.1181] [INSPIRE].
D.Z. Freedman and S.S. Pufu, The holography of F -maximization, JHEP 03 (2014) 135 [arXiv:1302.7310] [INSPIRE].
D.J. Binder, D.Z. Freedman, S.S. Pufu and B. Zan, The holographic contributions to the sphere free energy, JHEP 01 (2022) 171 [arXiv:2107.12382] [INSPIRE].
B. Zan, D.Z. Freedman and S.S. Pufu, The š© = 2 prepotential and the sphere free energy, JHEP 06 (2022) 045 [arXiv:2112.06931] [INSPIRE].
B. de Wit and M. van Zalk, Electric and magnetic charges in N=2 conformal supergravity theories, JHEP 10 (2011) 050 [arXiv:1107.3305] [INSPIRE].
K. Hristov, S. Katmadas and I. Lodato, Higher derivative corrections to BPS black hole attractors in 4d gauged supergravity, JHEP 05 (2016) 173 [arXiv:1603.00039] [INSPIRE].
B. de Wit, B. Kleijn and S. Vandoren, Superconformal hypermultiplets, Nucl. Phys. B 568 (2000) 475 [hep-th/9909228] [INSPIRE].
B. de Wit, M. Rocek and S. Vandoren, Gauging isometries on hyperKahler cones and quaternion Kahler manifolds, Phys. Lett. B 511 (2001) 302 [hep-th/0104215] [INSPIRE].
N. Bobev, A.M. Charles and V.S. Min, Euclidean black saddles and AdS4 black holes, JHEP 10 (2020) 073 [arXiv:2006.01148] [INSPIRE].
D. Butter, B. de Wit and I. Lodato, Non-renormalization theorems and N=2 supersymmetric backgrounds, JHEP 03 (2014) 131 [arXiv:1401.6591] [INSPIRE].
N. Banerjee, S. Bansal and I. Lodato, The Resolution of an Entropy Puzzle for 4D non-BPS Black Holes, JHEP 05 (2016) 142 [arXiv:1602.05326] [INSPIRE].
J.W. York, Jr., Black hole thermodynamics and the Euclidean Einstein action, Phys. Rev. D 33 (1986) 2092 [INSPIRE].
H.W. Braden, J.D. Brown, B.F. Whiting and J.W. York, Jr., Charged black hole in a grand canonical ensemble, Phys. Rev. D 42 (1990) 3376 [INSPIRE].
A. Sen, Black hole entropy function and the attractor mechanism in higher derivative gravity, JHEP 09 (2005) 038 [hep-th/0506177] [INSPIRE].
K. Hristov and V. Reys, Factorization of log-corrections in AdS4/CFT3 from supergravity localization, JHEP 12 (2021) 031 [arXiv:2107.12398] [INSPIRE].
G. Lopes Cardoso, B. de Wit and T. Mohaupt, Corrections to macroscopic supersymmetric black hole entropy, Phys. Lett. B 451 (1999) 309 [hep-th/9812082] [INSPIRE].
G. Lopes Cardoso, B. de Wit and T. Mohaupt, Macroscopic entropy formulae and nonholomorphic corrections for supersymmetric black holes, Nucl. Phys. B 567 (2000) 87 [hep-th/9906094] [INSPIRE].
G. Lopes Cardoso, B. de Wit, J. Kappeli and T. Mohaupt, Stationary BPS solutions in N=2 supergravity with R2 interactions, JHEP 12 (2000) 019 [hep-th/0009234] [INSPIRE].
K. Hristov, The dark (BPS) side of thermodynamics in Minkowski4, JHEP 09 (2022) 204 [arXiv:2207.12437] [INSPIRE].
O. Aharony, O. Bergman, D.L. Jafferis and J. Maldacena, N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals, JHEP 10 (2008) 091 [arXiv:0806.1218] [INSPIRE].
H. Fuji, S. Hirano and S. Moriyama, Summing Up All Genus Free Energy of ABJM Matrix Model, JHEP 08 (2011) 001 [arXiv:1106.4631] [INSPIRE].
M. Marino and P. Putrov, ABJM theory as a Fermi gas, J. Stat. Mech. 1203 (2012) P03001 [arXiv:1110.4066] [INSPIRE].
T. Nosaka, Instanton effects in ABJM theory with general R-charge assignments, JHEP 03 (2016) 059 [arXiv:1512.02862] [INSPIRE].
Y. Hatsuda, ABJM on ellipsoid and topological strings, JHEP 07 (2016) 026 [arXiv:1601.02728] [INSPIRE].
S.M. Chester, R.R. Kalloor and A. Sharon, Squashing, Mass, and Holography for 3d Sphere Free Energy, JHEP 04 (2021) 244 [arXiv:2102.05643] [INSPIRE].
N. Bobev, J. Hong and V. Reys, Large N Partition Functions, Holography, and Black Holes, Phys. Rev. Lett. 129 (2022) 041602 [arXiv:2203.14981] [INSPIRE].
N. Bobev, S. Choi, J. Hong and V. Reys, Large N superconformal indices for 3d holographic SCFTs, JHEP 02 (2023) 027 [arXiv:2210.15326] [INSPIRE].
S.M. Hosseini and A. Zaffaroni, The large N limit of topologically twisted indices: a direct approach, JHEP 12 (2022) 025 [arXiv:2209.09274] [INSPIRE].
F. Benini, K. Hristov and A. Zaffaroni, Black hole microstates in AdS4 from supersymmetric localization, JHEP 05 (2016) 054 [arXiv:1511.04085] [INSPIRE].
F. Faedo and D. Martelli, D4-branes wrapped on a spindle, JHEP 02 (2022) 101 [arXiv:2111.13660] [INSPIRE].
A. Boido, J.P. Gauntlett, D. Martelli and J. Sparks, Gravitational Blocks, Spindles and GK Geometry, Imperial/TP/2022/JG/04 (2022), arXiv:2211.02662 [INSPIRE].
D. Robles-Llana, F. Saueressig and S. Vandoren, String loop corrected hypermultiplet moduli spaces, JHEP 03 (2006) 081 [hep-th/0602164] [INSPIRE].
I. Antoniadis, R. Minasian, S. Theisen and P. Vanhove, String loop corrections to the universal hypermultiplet, Class. Quant. Grav. 20 (2003) 5079 [hep-th/0307268] [INSPIRE].
L. Anguelova, M. Rocek and S. Vandoren, Quantum corrections to the universal hypermultiplet and superspace, Phys. Rev. D 70 (2004) 066001 [hep-th/0402132] [INSPIRE].
K. Hristov, H. Looyestijn and S. Vandoren, BPS black holes in N=2 D=4 gauged supergravities, JHEP 08 (2010) 103 [arXiv:1005.3650] [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].
S.M. Hosseini, K. Hristov, Y. Tachikawa and A. Zaffaroni, Anomalies, Black strings and the charged Cardy formula, JHEP 09 (2020) 167 [arXiv:2006.08629] [INSPIRE].
P. Ferrero, J.P. Gauntlett, J.M. PƩrez IpiƱa, D. Martelli and J. Sparks, D3-Branes Wrapped on a Spindle, Phys. Rev. Lett. 126 (2021) 111601 [arXiv:2011.10579] [INSPIRE].
P. Ferrero, J.P. Gauntlett, J.M.P. IpiƱa, D. Martelli and J. Sparks, Accelerating black holes and spinning spindles, Phys. Rev. D 104 (2021) 046007 [arXiv:2012.08530] [INSPIRE].
S.M. Hosseini, K. Hristov and A. Zaffaroni, Rotating multi-charge spindles and their microstates, JHEP 07 (2021) 182 [arXiv:2104.11249] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisherās Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2212.10590
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
Hristov, K. Maximally symmetric nuts in 4d š© = 2 higher derivative supergravity. J. High Energ. Phys. 2023, 110 (2023). https://doi.org/10.1007/JHEP02(2023)110
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP02(2023)110