Journal of High Energy Physics

, 2011:116 | Cite as

Double, double supertube bubble

  • Iosif Bena
  • Jan de Boer
  • Masaki Shigemori
  • Nicholas P. Warner
Open Access


We argue that there exists a new class of completely smooth \( \frac{1}{8} \)-BPS, three-charge bound state configurations that depend upon arbitrary functions of two variables. These configurations are locally \( \frac{1}{2} \)-BPS objects in that if they form an infinite flat sheet then they preserve 16 supersymmetries but even with arbitrary two-dimensional shape modes they still preserve 4 supersymmetries. They have three electric charges and can be thought of the result of two successive supertube transitions that involve adding two independent dipole moments and giving rise to the arbitrary two-dimensional shape modes. We further argue that in the D1-D5-P duality frame this construction will give rise to smooth, horizonless solutions, or microstate geometries. We expect these solutions to be extremely important in the semi-classical and holographic descriptions of black-hole entropy.


Black Holes in String Theory Extended Supersymmetry D-branes 


  1. [1]
    D. Mateos and P.K. Townsend, Supertubes, Phys. Rev. Lett. 87 (2001) 011602 [hep-th/0103030] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  2. [2]
    D. Mateos, S. Ng and P.K. Townsend, Supercurves, Phys. Lett. B 538 (2002) 366 [hep-th/0204062] [SPIRES].MathSciNetADSGoogle Scholar
  3. [3]
    O. Lunin and S.D. Mathur, Metric of the multiply wound rotating string, Nucl. Phys. B 610 (2001) 49 [hep-th/0105136] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  4. [4]
    A. Dabholkar, J.P. Gauntlett, J.A. Harvey and D. Waldram, Strings as Solitons and Black Holes as Strings, Nucl. Phys. B 474 (1996) 85 [hep-th/9511053] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  5. [5]
    R. Emparan, D. Mateos and P.K. Townsend, Supergravity supertubes, JHEP 07 (2001) 011 [hep-th/0106012] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  6. [6]
    O. Lunin and S.D. Mathur, AdS/CFT duality and the black hole information paradox, Nucl. Phys. B 623 (2002) 342 [hep-th/0109154] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  7. [7]
    O. Lunin, J.M. Maldacena and L. Maoz, Gravity solutions for the D1 − D5 system with angular momentum, hep-th/0212210 [SPIRES].
  8. [8]
    I. Kanitscheider, K. Skenderis and M. Taylor, Fuzzballs with internal excitations, JHEP 06 (2007) 056 [arXiv:0704.0690] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  9. [9]
    B.C. Palmer and D. Marolf, Counting supertubes, JHEP 06 (2004) 028 [hep-th/0403025] [SPIRES].CrossRefGoogle Scholar
  10. [10]
    D. Bak, Y. Hyakutake, S. Kim and N. Ohta, A geometric look on the microstates of supertubes, Nucl. Phys. B 712 (2005) 115 [hep-th/0407253] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  11. [11]
    V.S. Rychkov, D1 − D5 black hole microstate counting from supergravity, JHEP 01 (2006) 063 [hep-th/0512053] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  12. [12]
    S.D. Mathur, The fuzzball proposal for black holes: An elementary review, Fortsch. Phys. 53 (2005) 793 [hep-th/0502050] [SPIRES].MathSciNetADSMATHCrossRefGoogle Scholar
  13. [13]
    I. Bena and N.P. Warner, Black holes, black rings and their microstates, Lect. Notes Phys. 755 (2008) 1 [hep-th/0701216] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  14. [14]
    K. Skenderis and M. Taylor, The fuzzball proposal for black holes, Phys. Rept. 467 (2008) 117 [arXiv:0804.0552] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  15. [15]
    V. Balasubramanian, J. de Boer, S. El-Showk and I. Messamah, Black Holes as Effective Geometries, Class. Quant. Grav. 25 (2008) 214004 [arXiv:0811.0263] [SPIRES].ADSCrossRefGoogle Scholar
  16. [16]
    B.D. Chowdhury and A. Virmani, Modave Lectures on Fuzzballs and Emission from the D1 − D5 System, arXiv:1001.1444 [SPIRES].
  17. [17]
    J. de Boer, S. El-Showk, I. Messamah and D. Van den Bleeken, A bound on the entropy of supergravity?, JHEP 02 (2010) 062 [arXiv:0906.0011] [SPIRES].CrossRefGoogle Scholar
  18. [18]
    I. Bena, N. Bobev, S. Giusto, C. Ruef and N.P. Warner, An Infinite-Dimensional Family of Black-Hole Microstate Geometries, JHEP 03 (2011) 022 [arXiv:1006.3497] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  19. [19]
    J. de Boer and M. Shigemori, Exotic branes and non-geometric backgrounds, Phys. Rev. Lett. 104 (2010) 251603 [arXiv:1004.2521] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  20. [20]
    I. Bena and P. Kraus, Three Charge Supertubes and Black Hole Hair, Phys. Rev. D 70 (2004) 046003 [hep-th/0402144] [SPIRES].MathSciNetADSGoogle Scholar
  21. [21]
    I. Bena, Splitting hairs of the three charge black hole, Phys. Rev. D 70 (2004) 105018 [hep-th/0404073] [SPIRES].MathSciNetADSGoogle Scholar
  22. [22]
    L.F. Alday, J. de Boer and I. Messamah, What is the dual of a dipole?, Nucl. Phys. B 746 (2006) 29 [hep-th/0511246] [SPIRES].ADSCrossRefGoogle Scholar
  23. [23]
    I. Kanitscheider, K. Skenderis and M. Taylor, Holographic anatomy of fuzzballs, JHEP 04 (2007) 023 [hep-th/0611171] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  24. [24]
    J. Polchinski and M.J. Strassler, The string dual of a confining four-dimensional gauge theory, hep-th/0003136 [SPIRES].
  25. [25]
    S.D. Mathur, A. Saxena and Y.K. Srivastava, Constructing ’hair’ for the three charge hole, Nucl. Phys. B 680 (2004) 415 [hep-th/0311092] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  26. [26]
    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].MathSciNetADSCrossRefGoogle Scholar
  27. [27]
    J.B. Gutowski, D. Martelli and H.S. Reall, All supersymmetric solutions of minimal supergravity in six dimensions, Class. Quant. Grav. 20 (2003) 5049 [hep-th/0306235] [SPIRES].MathSciNetADSMATHCrossRefGoogle Scholar
  28. [28]
    I. Bena and R. Roiban, Supergravity pp-wave solutions with 28 and 24 supercharges, Phys. Rev. D 67 (2003) 125014 [hep-th/0206195] [SPIRES].MathSciNetADSGoogle Scholar
  29. [29]
    M. Graña, D3-brane action in a supergravity background: The fermionic story, Phys. Rev. D 66 (2002) 045014 [hep-th/0202118] [SPIRES].ADSGoogle Scholar
  30. [30]
    S.F. Hassan, T-duality, space-time spinors and RR fields in curved backgrounds, Nucl. Phys. B 568 (2000) 145 [hep-th/9907152] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  31. [31]
    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].MathSciNetMATHGoogle Scholar
  32. [32]
    H. Elvang, R. Emparan, D. Mateos and H.S. Reall, Supersymmetric black rings and three-charge supertubes, Phys. Rev. D 71 (2005) 024033 [hep-th/0408120] [SPIRES].MathSciNetADSGoogle Scholar
  33. [33]
    J.P. Gauntlett and J.B. Gutowski, General concentric black rings, Phys. Rev. D 71 (2005) 045002 [hep-th/0408122] [SPIRES].MathSciNetADSGoogle Scholar
  34. [34]
    I. Bena and P. Kraus, Microscopic description of black rings in AdS/CFT, JHEP 12 (2004) 070 [hep-th/0408186] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  35. [35]
    A. Dabholkar, N. Iizuka, A. Iqubal, A. Sen and M. Shigemori, Spinning strings as small black rings, JHEP 04 (2007) 017 [hep-th/0611166] [SPIRES].MathSciNetADSCrossRefGoogle Scholar

Copyright information

© SISSA, Trieste, Italy 2011

Authors and Affiliations

  • Iosif Bena
    • 1
  • Jan de Boer
    • 2
  • Masaki Shigemori
    • 3
  • Nicholas P. Warner
    • 4
  1. 1.Institut de Physique ThéoriqueGif sur YvetteFrance
  2. 2.Institute for Theoretical PhysicsUniversity of AmsterdamAmsterdamThe Netherlands
  3. 3.Kobayashi-Maskawa Institute for the Origin of Particles and the UniverseNagoya UniversityNagoyaJapan
  4. 4.Department of Physics and AstronomyUniversity of Southern CaliforniaLos AngelesU.S.A.

Personalised recommendations