Abstract
In this note we show that the entropy of BPS, rotating, electrically charged AdS7 × S4 black holes can be obtained by an extremization principle involving a particular combination of anomaly coefficients of the six-dimensional \( \mathcal{N}=\left(2,0\right) \) theory. This result extends our previous finding for BPS, rotating AdS5 × S5 black holes.
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References
F. Benini, K. Hristov and A. Zaffaroni, Black hole microstates in AdS 4 from supersymmetric localization, JHEP 05 (2016) 054 [arXiv:1511.04085] [INSPIRE].
F. Benini, K. Hristov and A. Zaffaroni, Exact microstate counting for dyonic black holes in AdS 4, Phys. Lett. B 771 (2017) 462 [arXiv:1608.07294] [INSPIRE].
F. Azzurli, N. Bobev, P.M. Crichigno, V.S. Min and A. Zaffaroni, A universal counting of black hole microstates in AdS 4, JHEP 02 (2018) 054 [arXiv:1707.04257] [INSPIRE].
S.M. Hosseini, K. Hristov and A. Passias, Holographic microstate counting for AdS 4 black holes in massive IIA supergravity, JHEP 10 (2017) 190 [arXiv:1707.06884] [INSPIRE].
F. Benini, H. Khachatryan and P. Milan, Black hole entropy in massive Type IIA, Class. Quant. Grav. 35 (2018) 035004 [arXiv:1707.06886] [INSPIRE].
N. Bobev, V.S. Min and K. Pilch, Mass-deformed ABJM and black holes in AdS 4, JHEP 03 (2018) 050 [arXiv:1801.03135] [INSPIRE].
J.B. Gutowski and H.S. Reall, Supersymmetric AdS 5 black holes, JHEP 02 (2004) 006 [hep-th/0401042] [INSPIRE].
J.B. Gutowski and H.S. Reall, General supersymmetric AdS 5 black holes, JHEP 04 (2004) 048 [hep-th/0401129] [INSPIRE].
Z.W. Chong, M. Cvetič, H. Lü and C.N. Pope, Five-dimensional gauged supergravity black holes with independent rotation parameters, Phys. Rev. D 72 (2005) 041901 [hep-th/0505112] [INSPIRE].
Z.W. Chong, M. Cvetič, H. Lü and C.N. Pope, General non-extremal rotating black holes in minimal five-dimensional gauged supergravity, Phys. Rev. Lett. 95 (2005) 161301 [hep-th/0506029] [INSPIRE].
H.K. Kunduri, J. Lucietti and H.S. Reall, Supersymmetric multi-charge AdS 5 black holes, JHEP 04 (2006) 036 [hep-th/0601156] [INSPIRE].
J. Kinney, J.M. Maldacena, S. Minwalla and S. Raju, An Index for 4 dimensional super conformal theories, Commun. Math. Phys. 275 (2007) 209 [hep-th/0510251] [INSPIRE].
L. Grant, P.A. Grassi, S. Kim and S. Minwalla, Comments on 1/16 BPS Quantum States and Classical Configurations, JHEP 05 (2008) 049 [arXiv:0803.4183] [INSPIRE].
C.-M. Chang and X. Yin, 1/16 BPS states in \( \mathcal{N}=4 \) super-Yang-Mills theory, Phys. Rev. D 88 (2013) 106005 [arXiv:1305.6314] [INSPIRE].
C. Romelsberger, Counting chiral primaries in N = 1, d = 4 superconformal field theories, Nucl. Phys. B 747 (2006) 329 [hep-th/0510060] [INSPIRE].
S.M. Hosseini, K. Hristov and A. Zaffaroni, An extremization principle for the entropy of rotating BPS black holes in AdS 5, JHEP 07 (2017) 106 [arXiv:1705.05383] [INSPIRE].
N. Bobev, M. Bullimore and H.-C. Kim, Supersymmetric Casimir Energy and the Anomaly Polynomial, JHEP 09 (2015) 142 [arXiv:1507.08553] [INSPIRE].
B. Assel, D. Cassani, L. Di Pietro, Z. Komargodski, J. Lorenzen and D. Martelli, The Casimir Energy in Curved Space and its Supersymmetric Counterpart, JHEP 07 (2015) 043 [arXiv:1503.05537] [INSPIRE].
B. Assel, D. Cassani and D. Martelli, Localization on Hopf surfaces, JHEP 08 (2014) 123 [arXiv:1405.5144] [INSPIRE].
J. Lorenzen and D. Martelli, Comments on the Casimir energy in supersymmetric field theories, JHEP 07 (2015) 001 [arXiv:1412.7463] [INSPIRE].
A. Arabi Ardehali, J.T. Liu and P. Szepietowski, High-Temperature Expansion of Supersymmetric Partition Functions, JHEP 07 (2015) 113 [arXiv:1502.07737] [INSPIRE].
A. Arabi Ardehali, High-temperature asymptotics of supersymmetric partition functions, JHEP 07 (2016) 025 [arXiv:1512.03376] [INSPIRE].
M. Cvetič, G.W. Gibbons, H. Lü and C.N. Pope, Rotating black holes in gauged supergravities: Thermodynamics, supersymmetric limits, topological solitons and time machines, hep-th/0504080 [INSPIRE].
Z.W. Chong, M. Cvetič, H. Lü and C.N. Pope, Non-extremal charged rotating black holes in seven-dimensional gauged supergravity, Phys. Lett. B 626 (2005) 215 [hep-th/0412094] [INSPIRE].
D.D.K. Chow, Equal charge black holes and seven dimensional gauged supergravity, Class. Quant. Grav. 25 (2008) 175010 [arXiv:0711.1975] [INSPIRE].
H.-C. Kim and S. Kim, M5-branes from gauge theories on the 5-sphere, JHEP 05 (2013) 144 [arXiv:1206.6339] [INSPIRE].
E. Witten, Topological Quantum Field Theory, Commun. Math. Phys. 117 (1988) 353 [INSPIRE].
E. Witten, Mirror manifolds and topological field theory, AMS/IP Stud. Adv. Math. 9 (1998) 121 [hep-th/9112056] [INSPIRE].
F. Benini and A. Zaffaroni, A topologically twisted index for three-dimensional supersymmetric theories, JHEP 07 (2015) 127 [arXiv:1504.03698] [INSPIRE].
N.A. Nekrasov and S.L. Shatashvili, Bethe/Gauge correspondence on curved spaces, JHEP 01 (2015) 100 [arXiv:1405.6046] [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].
J.L. Cardy, Operator Content of Two-Dimensional Conformally Invariant Theories, Nucl. Phys. B 270 (1986) 186 [INSPIRE].
M. Pernici, K. Pilch and P. van Nieuwenhuizen, Gauged Maximally Extended Supergravity in Seven-dimensions, Phys. Lett. B 143 (1984) 103 [INSPIRE].
H. Nastase, D. Vaman and P. van Nieuwenhuizen, Consistent nonlinear KK reduction of 11d supergravity on AdS 7 × S 4 and self-duality in odd dimensions, Phys. Lett. B 469 (1999) 96 [hep-th/9905075] [INSPIRE].
H. Nastase, D. Vaman and P. van Nieuwenhuizen, Consistency of the AdS 7 × S 4 reduction and the origin of self-duality in odd dimensions, Nucl. Phys. B 581 (2000) 179 [hep-th/9911238] [INSPIRE].
J.T. Liu and R. Minasian, Black holes and membranes in AdS 7, Phys. Lett. B 457 (1999) 39 [hep-th/9903269] [INSPIRE].
J. Kallen, J.A. Minahan, A. Nedelin and M. Zabzine, N 3 -behavior from 5D Yang-Mills theory, JHEP 10 (2012) 184 [arXiv:1207.3763] [INSPIRE].
H.-C. Kim and K. Lee, Supersymmetric M5 Brane Theories on R × CP 2, JHEP 07 (2013) 072 [arXiv:1210.0853] [INSPIRE].
G. Lockhart and C. Vafa, Superconformal Partition Functions and Non-perturbative Topological Strings, arXiv:1210.5909 [INSPIRE].
H.-C. Kim, J. Kim and S. Kim, Instantons on the 5-sphere and M5-branes, arXiv:1211.0144 [INSPIRE].
J.A. Minahan, A. Nedelin and M. Zabzine, 5D super Yang-Mills theory and the correspondence to AdS 7 /CFT 6, J. Phys. A 46 (2013) 355401 [arXiv:1304.1016] [INSPIRE].
H.-C. Kim, S. Kim, S.-S. Kim and K. Lee, The general M5-brane superconformal index, arXiv:1307.7660 [INSPIRE].
F. Brünner, D. Regalado and V.P. Spiridonov, Supersymmetric Casimir energy and SL(3,ℤ) transformations, JHEP 07 (2017) 041 [arXiv:1611.03831] [INSPIRE].
N. Halmagyi and S. Lal, On the on-shell: the action of AdS 4 black holes, JHEP 03 (2018) 146 [arXiv:1710.09580] [INSPIRE].
A. Cabo-Bizet, U. Kol, L.A. Pando Zayas, I. Papadimitriou and V. Rathee, Entropy functional and the holographic attractor mechanism, arXiv:1712.01849 [INSPIRE].
K. Hristov, I. Lodato and V. Reys, On the quantum entropy function in 4d gauged supergravity, arXiv:1803.05920 [INSPIRE].
I. Papadimitriou, Supercurrent anomalies in 4d SCFTs, JHEP 07 (2017) 038 [arXiv:1703.04299] [INSPIRE].
O.S. An, Anomaly-corrected supersymmetry algebra and supersymmetric holographic renormalization, JHEP 12 (2017) 107 [arXiv:1703.09607] [INSPIRE].
D. Klemm and W.A. Sabra, General (anti-)de Sitter black holes in five-dimensions, JHEP 02 (2001) 031 [hep-th/0011016] [INSPIRE].
S.L. Cacciatori and D. Klemm, Supersymmetric AdS 4 black holes and attractors, JHEP 01 (2010) 085 [arXiv:0911.4926] [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].
Y. Tachikawa, Five-dimensional supergravity dual of a-maximization, Nucl. Phys. B 733 (2006) 188 [hep-th/0507057] [INSPIRE].
S. Benvenuti, L.A. Pando Zayas and Y. Tachikawa, Triangle anomalies from Einstein manifolds, Adv. Theor. Math. Phys. 10 (2006) 395 [hep-th/0601054] [INSPIRE].
K. Hristov and A. Rota, 6d → 5d → 4d reduction of BPS attractors in flat gauged supergravities, Nucl. Phys. B 897 (2015) 213 [arXiv:1410.5386] [INSPIRE].
M. Naka, Various wrapped branes from gauged supergravities, hep-th/0206141 [INSPIRE].
N. Bobev and P.M. Crichigno, Universal RG Flows Across Dimensions and Holography, JHEP 12 (2017) 065 [arXiv:1708.05052] [INSPIRE].
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Hosseini, S.M., Hristov, K. & Zaffaroni, A. A note on the entropy of rotating BPS AdS7 × S4 black holes. J. High Energ. Phys. 2018, 121 (2018). https://doi.org/10.1007/JHEP05(2018)121
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DOI: https://doi.org/10.1007/JHEP05(2018)121