Abstract
We derive the explicit action of the U-duality group of the STU model on both BPS and non-BPS extremal multi-center solutions. As the class of known non-BPS extremal solutions is not closed under U-duality, we generate in this way new solutions. These should represent the most general class of extremal non-BPS multi-center under-rotating solutions of the STU model.
Similar content being viewed by others
References
F. Denef, Supergravity flows and D-brane stability, JHEP 08 (2000) 050 [hep-th/0005049] [SPIRES].
J. de Boer, S. El-Showk, I. Messamah and D. Van den Bleeken, Quantizing N = 2 multicenter solutions, JHEP 05 (2009) 002 [arXiv:0807.4556] [SPIRES].
I. Bena and N.P. Warner, One ring to rule them all… And in the darkness bind them?, Adv. Theor. Math. Phys. 9 (2005) 667 [hep-th/0408106] [SPIRES].
P. Berglund, e.g. Gimon and T.S. Levi, Supergravity microstates for BPS black holes and black rings, JHEP 06 (2006) 007 [hep-th/0505167] [SPIRES].
I. Bena, N. Bobev, S. Giusto, C. Ruef and N.P. Warner, An infinite-dimensional family of black-hole microstate geometries, arXiv:1006.3497 [SPIRES].
S.D. Mathur, The fuzzball proposal for black holes: an elementary review, Fortsch. Phys. 53 (2005) 793 [hep-th/0502050] [SPIRES].
I. Bena and N.P. Warner, Black holes, black rings and their microstates, Lect. Notes Phys. 755 (2008) 1 [hep-th/0701216] [SPIRES].
K. Skenderis and M. Taylor, The fuzzball proposal for black holes, Phys. Rept. 467 (2008) 117 [arXiv:0804.0552] [SPIRES].
B.D. Chowdhury and A. Virmani, Modave lectures on fuzzballs and emission from the D1-D5 system, arXiv:1001.1444 [SPIRES].
A. Ceresole and G. Dall’Agata, Flow equations for non-BPS extremal black holes, JHEP 03 (2007) 110 [hep-th/0702088] [SPIRES].
G. Lopes Cardoso, A. Ceresole, G. Dall’Agata et al., First-order flow equations for extremal black holes in very special geometry, JHEP 0710 (2007) 063 [arXiv:0706.3373] [SPIRES].
J.P. Gauntlett, J.B. Gutowski, C.M. Hull, S. Pakis and H.S. Reall, All supersymmetric solutions of minimal supergravity in five dimensions, Class. Quant. Grav. 20 (2003) 4587 [hep-th/0209114] [SPIRES].
J.B. Gutowski and H.S. Reall, General supersymmetric AdS 5 black holes, JHEP 04 (2004) 048 [hep-th/0401129] [SPIRES].
K. Goldstein and S. Katmadas, Almost BPS black holes, JHEP 05 (2009) 058 [arXiv:0812.4183] [SPIRES].
E. Bergshoeff, W. Chemissany, A. Ploegh, M. Trigiante and T. Van Riet, Generating geodesic flows and supergravity solutions, Nucl. Phys. B 812 (2009) 343 [arXiv:0806.2310] [SPIRES].
W. Chemissany, J. Rosseel, M. Trigiante and T. Van Riet, The full integration of black hole solutions to symmetric supergravity theories, Nucl. Phys. B 830 (2010) 391 [arXiv:0903.2777] [SPIRES].
G. Bossard, H. Nicolai and K.S. Stelle, Universal BPS structure of stationary supergravity solutions, JHEP 07 (2009) 003 [arXiv:0902.4438] [SPIRES].
G. Bossard and H. Nicolai, Multi-black holes from nilpotent Lie algebra orbits, Gen. Rel. Grav. 42 (2010) 509 [arXiv:0906.1987] [SPIRES].
G. Bossard, Y. Michel and B. Pioline, Extremal black holes, nilpotent orbits and the true fake superpotential, JHEP 01 (2010) 038 [arXiv:0908.1742] [SPIRES].
S.-S. Kim, J.L. Hörnlund, J. Palmkvist and A. Virmani, Extremal solutions of the S 3 model and nilpotent orbits of G2(2), JHEP 08 (2010) 072 [arXiv:1004.5242] [SPIRES].
I. Bena, S. Giusto, C. Ruef and N.P. Warner, Supergravity solutions from floating branes, JHEP 03 (2010) 047 [arXiv:0910.1860] [SPIRES].
D. Lüst, F. Marchesano, L. Martucci and D. Tsimpis, Generalized non-supersymmetric flux vacua, JHEP 11 (2008) 021 [arXiv:0807.4540] [SPIRES].
D. Cassani, S. Ferrara, A. Marrani, J.F. Morales and H. Samtleben, A special road to AdS vacua, JHEP 02 (2010) 027 [arXiv:0911.2708] [SPIRES].
I. Bena, G. Dall’Agata, S. Giusto, C. Ruef and N.P. Warner, Non-BPS black rings and black holes in Taub-NUT, JHEP 06 (2009) 015 [arXiv:0902.4526] [SPIRES].
I. Bena, S. Giusto, C. Ruef and N.P. Warner, Multi-center non-BPS black holes — the solution, JHEP 11 (2009) 032 [arXiv:0908.2121] [SPIRES].
S. Ferrara and A. Marrani, Matrix norms, BPS bounds and marginal stability in N = 8 supergravity, JHEP 12 (2010) 038 [arXiv:1009.3251] [SPIRES].
S. Ferrara, A. Marrani and E. Orazi, Split attractor flowin N = 2 minimally coupled supergravity, arXiv:1010.2280 [SPIRES].
S. Ferrara, A. Marrani, E. Orazi, R. Stora and A. Yeranyan, Two-center black holes duality-invariants for STU model and its lower-rank descendants, arXiv:1011.5864 [SPIRES].
I. Bena, N. Bobev and N.P. Warner, Spectral flow and the spectrum of multi-center solutions, Phys. Rev. D 77 (2008) 125025 [arXiv:0803.1203] [SPIRES].
P. Galli, K. Goldstein, S. Katmadas and J. Perz, First-order flows and stabilisation equations for non-BPS extremal black holes, arXiv:1012.4020 [SPIRES].
I. Bena and N.P. Warner, Bubbling supertubes and foaming black holes, Phys. Rev. D 74 (2006) 066001 [hep-th/0505166] [SPIRES].
K. Behrndt, R. Kallosh, J. Rahmfeld, M. Shmakova and W.K. Wong, STU black holes and string triality, Phys. Rev. D 54 (1996) 6293 [hep-th/9608059] [SPIRES].
R. Kallosh, N. Sivanandam and M. Soroush, Exact attractive non-BPS STU black holes, Phys. Rev. D 74 (2006) 065008 [hep-th/0606263] [SPIRES].
e.g. Gimon, F. Larsen and J. Simon, Black holes in supergravity: the non-BPS branch, JHEP 01 (2008) 040 [arXiv:0710.4967] [SPIRES].
S. Bellucci, S. Ferrara, A. Marrani and A. Yeranyan, STU black holes unveiled, arXiv:0807.3503 [SPIRES].
E. Bergshoeff, C.M. Hull and T. Ortín, Duality in the type-II superstring effective action, Nucl. Phys. B 451 (1995) 547 [hep-th/9504081] [SPIRES].
S.F. Hassan, T-duality, space-time spinors and RR fields in curved backgrounds, Nucl. Phys. B 568 (2000) 145 [hep-th/9907152] [SPIRES].
V. Balasubramanian, J. de Boer, E. Keski-Vakkuri and S.F. Ross, Supersymmetric conical defects: towards a string theoretic description of black hole formation, Phys. Rev. D 64 (2001) 064011 [hep-th/0011217] [SPIRES].
J.M. Maldacena and L. Maoz, De-singularization by rotation, JHEP 12 (2002) 055 [hep-th/0012025] [SPIRES].
O. Lunin, Adding momentum to D1-D5 system, JHEP 04 (2004) 054 [hep-th/0404006] [SPIRES].
S. Giusto, S.D. Mathur and A. Saxena, Dual geometries for a set of 3-charge microstates, Nucl. Phys. B 701 (2004) 357 [hep-th/0405017] [SPIRES].
J. Ford, S. Giusto and A. Saxena, A class of BPS time-dependent 3-charge microstates from spectral flow, Nucl. Phys. B 790 (2008) 258 [hep-th/0612227] [SPIRES].
J.H. Al-Alawi and S.F. Ross, Spectral flow of the non-supersymmetric microstates of the D1-D5-K K system, JHEP 10 (2009) 082 [arXiv:0908.0417] [SPIRES].
S. Ferrara and S. Sabharwal, Dimensional reduction of type II superstrings, Class. Quant. Grav. 6 (1989) L77 [SPIRES].
M. Bodner, A.C. Cadavid and S. Ferrara, (2, 2) vacuum configurations for type IIA superstrings: N = 2 supergravity Lagrangians and algebraic geometry, Class. Quant. Grav. 8 (1991) 789 [SPIRES].
B. de Wit, F. Vanderseypen and A. Van Proeyen, Symmetry structure of special geometries, Nucl. Phys. B 400 (1993) 463 [hep-th/9210068] [SPIRES].
C. Toldo, Black holes and duality, Master thesis, Padua university, Padua Italy (2010).
D. Rasheed, The rotating dyonic black holes of Kaluza-Klein theory, Nucl. Phys. B 454 (1995) 379 [hep-th/9505038] [SPIRES].
F. Larsen, Kaluza-Klein black holes in string theory, hep-th/0002166 [SPIRES].
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1012.4803
Rights and permissions
About this article
Cite this article
Dall’Agata, G., Giusto, S. & Ruef, C. U-duality and non-BPS solutions. J. High Energ. Phys. 2011, 74 (2011). https://doi.org/10.1007/JHEP02(2011)074
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP02(2011)074