The full space of BPS multicenter states with pure D-brane charges

  • Pierre Heidmann
  • Swapnamay MondalEmail author
Open Access
Regular Article - Theoretical Physics


We investigate the space of BPS states in type IIA string theory on a T6 wrapped by one D6 brane and three D2 branes wrapping three disjoint 2-tori. This system of branes has 12 ground states. We show that these 12 states are all recovered as Coulomb branch BPS multicenter bound states, in which each center preserves 16 supercharges. Moreover, we show that these multicenter solutions can only exist with zero angular momentum, supporting the conjecture that all black hole microstates have zero angular momentum. For large charges, they might describe “near-horizon limit” of fuzzballs.


Black Holes in String Theory D-branes 


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.


  1. [1]
    A. Strominger and C. Vafa, Microscopic origin of the Bekenstein-Hawking entropy, Phys. Lett. B 379 (1996) 99 [hep-th/9601029] [INSPIRE].
  2. [2]
    J.R. David, G. Mandal and S.R. Wadia, Microscopic formulation of black holes in string theory, Phys. Rept. 369 (2002) 549 [hep-th/0203048] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    A. Sen, Black hole entropy function, attractors and precision counting of microstates, Gen. Rel. Grav. 40 (2008) 2249 [arXiv:0708.1270] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    R. Dijkgraaf, G.W. Moore, E.P. Verlinde and H.L. Verlinde, Elliptic genera of symmetric products and second quantized strings, Commun. Math. Phys. 185 (1997) 197 [hep-th/9608096] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    J.M. Maldacena, G.W. Moore and A. Strominger, Counting BPS black holes in toroidal Type II string theory, hep-th/9903163 [INSPIRE].
  6. [6]
    D. Shih, A. Strominger and X. Yin, Counting dyons in N = 8 string theory, JHEP 06 (2006) 037 [hep-th/0506151] [INSPIRE].
  7. [7]
    J.R. David, D.P. Jatkar and A. Sen, Dyon spectrum in generic N = 4 supersymmetric Z(N ) orbifolds, JHEP 01 (2007) 016 [hep-th/0609109] [INSPIRE].
  8. [8]
    F. Denef, Quantum quivers and Hall/hole halos, JHEP 10 (2002) 023 [hep-th/0206072] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  9. [9]
    N. Gaddam, Elliptic genera from multi-centers, JHEP 05 (2016) 076 [arXiv:1603.01724] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    A. Chowdhury, R.S. Garavuso, S. Mondal and A. Sen, BPS state counting in N = 8 supersymmetric string theory for pure D-brane configurations, JHEP 10 (2014) 186 [arXiv:1405.0412] [INSPIRE].
  11. [11]
    A. Chowdhury, R.S. Garavuso, S. Mondal and A. Sen, Do all BPS black hole microstates carry zero angular momentum?, JHEP 04 (2016) 082 [arXiv:1511.06978] [INSPIRE].MathSciNetGoogle Scholar
  12. [12]
    F. Denef, Supergravity flows and D-brane stability, JHEP 08 (2000) 050 [hep-th/0005049] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  13. [13]
    F. Denef, B.R. Greene and M. Raugas, Split attractor flows and the spectrum of BPS D-branes on the quintic, JHEP 05 (2001) 012 [hep-th/0101135] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  14. [14]
    F. Denef, (Dis)assembling special Lagrangians, hep-th/0107152 [INSPIRE].
  15. [15]
    B. Bates and F. Denef, Exact solutions for supersymmetric stationary black hole composites, JHEP 11 (2011) 127 [hep-th/0304094] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  16. [16]
    F. Denef and G.W. Moore, Split states, entropy enigmas, holes and halos, JHEP 11 (2011) 129 [hep-th/0702146] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  17. [17]
    I. Bena and N.P. Warner, Resolving the structure of black holes: philosophizing with a hammer, arXiv:1311.4538 [INSPIRE].
  18. [18]
    A. Sen, Black hole entropy function and the attractor mechanism in higher derivative gravity, JHEP 09 (2005) 038 [hep-th/0506177] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  19. [19]
    A. Sen, Quantum entropy function from AdS 2 /CF T 1 correspondence, Int. J. Mod. Phys. A 24 (2009) 4225 [arXiv:0809.3304] [INSPIRE].
  20. [20]
    I. Bena, P. Heidmann and D. Turton, AdS 2 holography: mind the cap, JHEP 12 (2018) 028 [arXiv:1806.02834] [INSPIRE].
  21. [21]
    J. Avila, P.F. Ramirez and A. Ruiperez, One thousand and one bubbles, JHEP 01 (2018) 041 [arXiv:1709.03985] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  22. [22]
    V. Balasubramanian, E.G. Gimon and T.S. Levi, Four dimensional black hole microstates: from D-branes to spacetime foam, JHEP 01 (2008) 056 [hep-th/0606118] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  23. [23]
    I. Bena, S. Giusto, R. Russo, M. Shigemori and N.P. Warner, Habemus superstratum! A constructive proof of the existence of superstrata, JHEP 05 (2015) 110 [arXiv:1503.01463] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  24. [24]
    D. Mateos and P.K. Townsend, Supertubes, Phys. Rev. Lett. 87 (2001) 011602 [hep-th/0103030] [INSPIRE].
  25. [25]
    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] [INSPIRE].
  26. [26]
    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] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  27. [27]
    O. Vasilakis and N.P. Warner, Mind the gap: supersymmetry breaking in scaling, microstate geometries, JHEP 10 (2011) 006 [arXiv:1104.2641] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  28. [28]
    P. Heidmann, Four-center bubbled BPS solutions with a Gibbons-Hawking base, JHEP 10 (2017) 009 [arXiv:1703.10095] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  29. [29]
    I. Bena et al., Moulting black holes, JHEP 03 (2012) 094 [arXiv:1108.0411] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  30. [30]
    P. Heidmann, Walls of marginal stability for collinear multicenter solutions in the scaling limit, to appear.Google Scholar
  31. [31]
    C. Bachas and E. Kiritsis, F 4 terms in N = 4 string vacua, Nucl. Phys. Proc. Suppl. 55B (1997) 194 [hep-th/9611205] [INSPIRE].
  32. [32]
    A. Gregori et al., R 2 corrections and nonperturbative dualities of N = 4 string ground states, Nucl. Phys. B 510 (1998) 423 [hep-th/9708062] [INSPIRE].
  33. [33]
    M. Bianchi, J.F. Morales, L. Pieri and N. Zinnato, More on microstate geometries of 4d black holes, JHEP 05 (2017) 147 [arXiv:1701.05520] [INSPIRE].
  34. [34]
    J. Manschot, B. Pioline and A. Sen, Wall crossing from boltzmann black hole halos, JHEP 07 (2011) 059 [arXiv:1011.1258] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  35. [35]
    A. Sen, Arithmetic of quantum entropy function, JHEP 08 (2009) 068 [arXiv:0903.1477] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  36. [36]
    A. Dabholkar, J. Gomes, S. Murthy and A. Sen, Supersymmetric index from black hole entropy, JHEP 04 (2011) 034 [arXiv:1009.3226] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  37. [37]
    M.R. Douglas and G.W. Moore, D-branes, quivers and ALE instantons, hep-th/9603167 [INSPIRE].
  38. [38]
    I. Bena et al., Scaling BPS solutions and pure-Higgs states, JHEP 11 (2012) 171 [arXiv:1205.5023] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  39. [39]
    A. Dabholkar, S. Murthy and D. Zagier, Quantum black holes, wall crossing and mock modular forms, arXiv:1208.4074 [INSPIRE].
  40. [40]
    J.P. Gauntlett et al., All supersymmetric solutions of minimal supergravity in five-dimensions, Class. Quant. Grav. 20 (2003) 4587 [hep-th/0209114] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  41. [41]
    I. Bena, S.F. Ross and N.P. Warner, On the oscillation of species, JHEP 09 (2014) 113 [arXiv:1312.3635] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  42. [42]
    I. Bena et al., An infinite-dimensional family of black-hole microstate geometries, JHEP 03 (2011) 022 [Erratum ibid. 04 (2011) 059] [arXiv:1006.3497] [INSPIRE].
  43. [43]
    I. Bena et al., Smooth horizonless geometries deep inside the black-hole regime, Phys. Rev. Lett. 117 (2016) 201601 [arXiv:1607.03908] [INSPIRE].CrossRefGoogle Scholar
  44. [44]
    G. Dall’Agata, S. Giusto and C. Ruef, U-duality and non-BPS solutions, JHEP 02 (2011) 074 [arXiv:1012.4803] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Institut de Physique ThéoriqueUniversité Paris Saclay, CEA, CNRSGif sur YvetteFrance
  2. 2.International Centre for Theoretical Sciences, Tata Institute of Fundamental ResearchBangaloreIndia

Personalised recommendations