Abstract
We construct new classes of supersymmetric AdS2 × Σ solutions of 4d gauged supergravity in presence of charged hypermultiplet scalars, with Σ the complex weighted projective space known as a spindle. These solutions can be viewed as near-horizon geome- tries of asymptotically Anti de-Sitter (AdS4) black holes with magnetic fluxes that admit embedding in 11d on Sasaki-Einstein (SE7) manifolds, which renders them of holographic interest. We show that in each case the Bekenstein-Hawking entropy follows from the procedure of gluing two gravitational blocks, ultimately determined by SE7 data. This allows us to establish the general form of the gravitational blocks in gauged 4d \( \mathcal{N} \) = 2 supergravity with charged scalars and massive vectors. Holographically, our results provide a large N answer for the spindle index with anti-twist and additional mesonic or baryonic fluxes of a number of \( \mathcal{N} \) = 2 Chern-Simons-matter theories.
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References
J.M. Maldacena, The large N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [hep-th/9711200] [INSPIRE].
P. Ferrero et al., D3-Branes Wrapped on a Spindle, Phys. Rev. Lett. 126 (2021) 111601 [arXiv:2011.10579] [INSPIRE].
P. Ferrero et al., 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].
A. Boido, J.M.P. Ipiña and J. Sparks, Twisted D3-brane and M5-brane compactifications from multi-charge spindles, JHEP 07 (2021) 222 [arXiv:2104.13287] [INSPIRE].
P. Ferrero, J.P. Gauntlett, D. Martelli and J. Sparks, M5-branes wrapped on a spindle, JHEP 11 (2021) 002 [arXiv:2105.13344] [INSPIRE].
D. Cassani, J.P. Gauntlett, D. Martelli and J. Sparks, Thermodynamics of accelerating and supersymmetric AdS4 black holes, Phys. Rev. D 104 (2021) 086005 [arXiv:2106.05571] [INSPIRE].
P. Ferrero, M. Inglese, D. Martelli and J. Sparks, Multicharge accelerating black holes and spinning spindles, Phys. Rev. D 105 (2022) 126001 [arXiv:2109.14625] [INSPIRE].
C. Couzens, K. Stemerdink and D. van de Heisteeg, M2-branes on discs and multi-charged spindles, JHEP 04 (2022) 107 [arXiv:2110.00571] [INSPIRE].
F. Faedo and D. Martelli, D4-branes wrapped on a spindle, JHEP 02 (2022) 101 [arXiv:2111.13660] [INSPIRE].
P. Ferrero, J.P. Gauntlett and J. Sparks, Supersymmetric spindles, JHEP 01 (2022) 102 [arXiv:2112.01543] [INSPIRE].
S. Giri, Black holes with spindles at the horizon, JHEP 06 (2022) 145 [arXiv:2112.04431] [INSPIRE].
C. Couzens, A tale of (M)2 twists, JHEP 03 (2022) 078 [arXiv:2112.04462] [INSPIRE].
K.C.M. Cheung, J.H.T. Fry, J.P. Gauntlett and J. Sparks, M5-branes wrapped on four-dimensional orbifolds, JHEP 08 (2022) 082 [arXiv:2204.02990] [INSPIRE].
M. Suh, M5-branes and D4-branes wrapped on a direct product of spindle and Riemann surface, arXiv:2207.00034 [INSPIRE].
I. Arav, J.P. Gauntlett, M.M. Roberts and C. Rosen, Leigh-Strassler compactified on a spindle, JHEP 10 (2022) 067 [arXiv:2207.06427] [INSPIRE].
C. Couzens and K. Stemerdink, Universal spindles: D2’s on Σ and M5’s on Σ × ℍ3, arXiv:2207.06449 [INSPIRE].
C. Couzens, N.T. Macpherson and A. Passias, A plethora of Type IIA embeddings for d = 5 minimal supergravity, JHEP 01 (2023) 047 [arXiv:2209.15540] [INSPIRE].
C. Couzens et al., D4-branes wrapped on four-dimensional orbifolds through consistent truncation, JHEP 02 (2023) 025 [arXiv:2210.15695] [INSPIRE].
F. Faedo, A. Fontanarossa and D. Martelli, Branes wrapped on orbifolds and their gravitational blocks, Lett. Math. Phys. 113 (2023) 51 [arXiv:2210.16128] [INSPIRE].
M. Suh, Spindle black holes from mass-deformed ABJM, arXiv:2211.11782 [INSPIRE].
M. Suh, Baryonic spindles from conifolds, arXiv:2304.03308 [INSPIRE].
A. Amariti, N. Petri and A. Segati, T1,1 truncation on the spindle, JHEP 07 (2023) 087 [arXiv:2304.03663] [INSPIRE].
H. Kim, N. Kim, Y. Lee and A. Poole, Thermodynamics of accelerating AdS4 black holes from the covariant phase space, arXiv:2306.16187 [INSPIRE].
I. Bah, F. Bonetti, R. Minasian and E. Nardoni, Holographic Duals of Argyres-Douglas Theories, Phys. Rev. Lett. 127 (2021) 211601 [arXiv:2105.11567] [INSPIRE].
I. Bah, F. Bonetti, R. Minasian and E. Nardoni, M5-brane sources, holography, and Argyres-Douglas theories, JHEP 11 (2021) 140 [arXiv:2106.01322] [INSPIRE].
C. Couzens, N.T. Macpherson and A. Passias, \( \mathcal{N} \) = (2, 2) AdS3 from D3-branes wrapped on Riemann surfaces, JHEP 02 (2022) 189 [arXiv:2107.13562] [INSPIRE].
M. Suh, D3-branes and M5-branes wrapped on a topological disc, JHEP 03 (2022) 043 [arXiv:2108.01105] [INSPIRE].
M. Suh, D4-branes wrapped on a topological disk, JHEP 06 (2023) 008 [arXiv:2108.08326] [INSPIRE].
M. Suh, M2-branes wrapped on a topological disk, JHEP 09 (2022) 048 [arXiv:2109.13278] [INSPIRE].
P. Karndumri and P. Nuchino, Five-branes wrapped on topological disks from 7D N = 2 gauged supergravity, Phys. Rev. D 105 (2022) 066010 [arXiv:2201.05037] [INSPIRE].
C. Couzens, H. Kim, N. Kim and Y. Lee, Holographic duals of M5-branes on an irregularly punctured sphere, JHEP 07 (2022) 102 [arXiv:2204.13537] [INSPIRE].
I. Bah, F. Bonetti, E. Nardoni and T. Waddleton, Aspects of irregular punctures via holography, JHEP 11 (2022) 131 [arXiv:2207.10094] [INSPIRE].
M. Gutperle and N. Klein, A note on co-dimension 2 defects in N = 4, d = 7 gauged supergravity, Nucl. Phys. B 984 (2022) 115969 [arXiv:2203.13839] [INSPIRE].
M. Gutperle, N. Klein and D. Rathore, Holographic 6d co-dimension 2 defect solutions in M-theory, arXiv:2304.12899 [INSPIRE].
D. Cassani, P. Koerber and O. Varela, All homogeneous N = 2 M-theory truncations with supersymmetric AdS4 vacua, JHEP 11 (2012) 173 [arXiv:1208.1262] [INSPIRE].
N. Halmagyi, M. Petrini and A. Zaffaroni, BPS black holes in AdS4 from M-theory, JHEP 08 (2013) 124 [arXiv:1305.0730] [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. Kim and N. Kim, Uplifting dyonic AdS4 black holes on seven-dimensional Sasaki-Einstein manifolds, JHEP 03 (2021) 108 [arXiv:2012.09757] [INSPIRE].
R. Monten and C. Toldo, Black holes with halos, Class. Quant. Grav. 35 (2018) 035001 [arXiv:1612.02399] [INSPIRE].
R. Monten and C. Toldo, On the search for multicenter AdS black holes from M-theory, JHEP 02 (2022) 009 [arXiv:2111.06879] [INSPIRE].
S.M. Hosseini, K. Hristov and A. Zaffaroni, Gluing gravitational blocks for AdS black holes, JHEP 12 (2019) 168 [arXiv:1909.10550] [INSPIRE].
J.M. Maldacena and C. Nunez, Supergravity description of field theories on curved manifolds and a no go theorem, Int. J. Mod. Phys. A 16 (2001) 822 [hep-th/0007018] [INSPIRE].
J.B. Gutowski and H.S. Reall, General supersymmetric AdS(5) black holes, JHEP 04 (2004) 048 [hep-th/0401129] [INSPIRE].
S.L. Cacciatori and D. Klemm, Supersymmetric AdS(4) black holes and attractors, JHEP 01 (2010) 085 [arXiv:0911.4926] [INSPIRE].
K. Hristov, S. Katmadas and C. Toldo, Rotating attractors and BPS black holes in AdS4, JHEP 01 (2019) 199 [arXiv:1811.00292] [INSPIRE].
K. Hristov, S. Katmadas and C. Toldo, Matter-coupled supersymmetric Kerr-Newman-AdS4 black holes, Phys. Rev. D 100 (2019) 066016 [arXiv:1907.05192] [INSPIRE].
S.M. Hosseini, K. Hristov and A. Zaffaroni, Microstates of rotating AdS5 strings, JHEP 11 (2019) 090 [arXiv:1909.08000] [INSPIRE].
P. Benetti Genolini, J.M. Perez Ipiña and J. Sparks, Localization of the action in AdS/CFT, JHEP 10 (2019) 252 [arXiv:1906.11249] [INSPIRE].
K. Hristov, 4d \( \mathcal{N} \) = 2 supergravity observables from Nekrasov-like partition functions, JHEP 02 (2022) 079 [arXiv:2111.06903] [INSPIRE].
K. Hristov, Maximally symmetric nuts in 4d N = 2 higher derivative supergravity, JHEP 02 (2023) 110 [arXiv:2212.10590] [INSPIRE].
P. Benetti Genolini, J.P. Gauntlett and J. Sparks, Equivariant Localization in Supergravity, Phys. Rev. Lett. 131 (2023) 121602 [arXiv:2306.03868] [INSPIRE].
D. Martelli and A. Zaffaroni, Equivariant localization and holography, arXiv:2306.03891 [INSPIRE].
A. Boido, J.P. Gauntlett, D. Martelli and J. Sparks, Entropy Functions For Accelerating Black Holes, Phys. Rev. Lett. 130 (2023) 091603 [arXiv:2210.16069] [INSPIRE].
A. Boido, J.P. Gauntlett, D. Martelli and J. Sparks, Gravitational Blocks, Spindles and GK Geometry, Commun. Math. Phys. 403 (2023) 917 [arXiv:2211.02662] [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].
S.M. Hosseini and K. Hristov, 4d F(4) gauged supergravity and black holes of class , JHEP 02 (2021) 177 [arXiv:2011.01943] [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].
F. Benini, C. Closset and S. Cremonesi, Chiral flavors and M2-branes at toric CY4 singularities, JHEP 02 (2010) 036 [arXiv:0911.4127] [INSPIRE].
S. Cremonesi, Type IIB construction of flavoured ABJ(M) and fractional M2 branes, JHEP 01 (2011) 076 [arXiv:1007.4562] [INSPIRE].
M. Inglese, D. Martelli and A. Pittelli, The Spindle Index from Localization, arXiv:2303.14199 [INSPIRE].
F. Benini and A. Zaffaroni, A topologically twisted index for three-dimensional supersymmetric theories, JHEP 07 (2015) 127 [arXiv:1504.03698] [INSPIRE].
F. Benini, K. Hristov and A. Zaffaroni, Black hole microstates in AdS4 from supersymmetric localization, JHEP 05 (2016) 054 [arXiv:1511.04085] [INSPIRE].
S.M. Hosseini and A. Zaffaroni, Geometry of ℐ-extremization and black holes microstates, JHEP 07 (2019) 174 [arXiv:1904.04269] [INSPIRE].
F. Azzurli et al., A universal counting of black hole microstates in AdS4, JHEP 02 (2018) 054 [arXiv:1707.04257] [INSPIRE].
C. Couzens, J.P. Gauntlett, D. Martelli and J. Sparks, A geometric dual of c-extremization, JHEP 01 (2019) 212 [arXiv:1810.11026] [INSPIRE].
J.P. Gauntlett, D. Martelli and J. Sparks, Toric geometry and the dual of ℐ-extremization, JHEP 06 (2019) 140 [arXiv:1904.04282] [INSPIRE].
H. Kim and N. Kim, Black holes with baryonic charge and ℐ-extremization, JHEP 11 (2019) 050 [arXiv:1904.05344] [INSPIRE].
D. Martelli and J. Sparks, Moduli spaces of Chern-Simons quiver gauge theories and AdS4/CFT3, Phys. Rev. D 78 (2008) 126005 [arXiv:0808.0912] [INSPIRE].
C.P. Herzog, I.R. Klebanov, S.S. Pufu and T. Tesileanu, Multi-Matrix Models and Tri-Sasaki Einstein Spaces, Phys. Rev. D 83 (2011) 046001 [arXiv:1011.5487] [INSPIRE].
S. Cheon, H. Kim and N. Kim, Calculating the partition function of N = 2 Gauge theories on S3 and AdS/CFT correspondence, JHEP 05 (2011) 134 [arXiv:1102.5565] [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.R. Gulotta, C.P. Herzog and S.S. Pufu, Operator Counting and Eigenvalue Distributions for 3D Supersymmetric Gauge Theories, JHEP 11 (2011) 149 [arXiv:1106.5484] [INSPIRE].
D.R. Gulotta, C.P. Herzog and S.S. Pufu, From Necklace Quivers to the F-theorem, Operator Counting, and T(U(N)), JHEP 12 (2011) 077 [arXiv:1105.2817] [INSPIRE].
D.L. Jafferis, The Exact Superconformal R-Symmetry Extremizes Z, JHEP 05 (2012) 159 [arXiv:1012.3210] [INSPIRE].
N. Bobev, V.S. Min and K. Pilch, Mass-deformed ABJM and black holes in AdS4, JHEP 03 (2018) 050 [arXiv:1801.03135] [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].
A. Guarino, D.L. Jafferis and O. Varela, String Theory Origin of Dyonic N = 8 Supergravity and Its Chern-Simons Duals, Phys. Rev. Lett. 115 (2015) 091601 [arXiv:1504.08009] [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, Gravitational blocks: Symplectic covariance unveiled, Phys. Lett. B 843 (2023) 138044 [arXiv:2303.07365] [INSPIRE].
N. Kim and J.-D. Park, Comments on AdS(2) solutions of D = 11 supergravity, JHEP 09 (2006) 041 [hep-th/0607093] [INSPIRE].
J.P. Gauntlett and N. Kim, Geometries with Killing Spinors and Supersymmetric AdS Solutions, Commun. Math. Phys. 284 (2008) 897 [arXiv:0710.2590] [INSPIRE].
H. Erbin and N. Halmagyi, Abelian hypermultiplet gaugings and BPS vacua in \( \mathcal{N} \) = 2 supergravity, JHEP 05 (2015) 122 [arXiv:1409.6310] [INSPIRE].
S.M. Hosseini and A. Zaffaroni, Large N matrix models for 3d \( \mathcal{N} \) = 2 theories: twisted index, free energy and black holes, JHEP 08 (2016) 064 [arXiv:1604.03122] [INSPIRE].
S.M. Hosseini and N. Mekareeya, Large N topologically twisted index: necklace quivers, dualities, and Sasaki-Einstein spaces, JHEP 08 (2016) 089 [arXiv:1604.03397] [INSPIRE].
E. Cremmer, B. Julia and J. Scherk, Supergravity Theory in Eleven-Dimensions, Phys. Lett. B 76 (1978) 409 [INSPIRE].
N. Halmagyi, M. Petrini and A. Zaffaroni, Non-Relativistic Solutions of N = 2 Gauged Supergravity, JHEP 08 (2011) 041 [arXiv:1102.5740] [INSPIRE].
L. Andrianopoli et al., N = 2 supergravity and N = 2 superYang-Mills theory on general scalar manifolds: Symplectic covariance, gaugings and the momentum map, J. Geom. Phys. 23 (1997) 111 [hep-th/9605032] [INSPIRE].
A. Ceresole, G. Dall’Agata, R. Kallosh and A. Van Proeyen, Hypermultiplets, domain walls and supersymmetric attractors, Phys. Rev. D 64 (2001) 104006 [hep-th/0104056] [INSPIRE].
Acknowledgments
We would like to thank Seyed Morteza Hosseini, Hyojoong Kim and Chiara Toldo for useful discussions. The study of KH is financed by the European Union- NextGenerationEU, through the National Recovery and Resilience Plan of the Republic of Bulgaria, project No BG-RRP-2.004-0008-C01. MS was supported by the Kavli Institute for Theoretical Sciences (KITS) and the University of Chinese Academy of Sciences (UCAS).
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Hristov, K., Suh, M. Spindle black holes in AdS4 × SE7. J. High Energ. Phys. 2023, 141 (2023). https://doi.org/10.1007/JHEP10(2023)141
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DOI: https://doi.org/10.1007/JHEP10(2023)141