Advertisement

Orientiholes

Article

Abstract

By T-dualizing space-filling D-branes in 4d IIB orientifold compactifications along the three non-internal spatial directions, we obtain black hole bound states living in a universe with a gauged spatial reflection symmetry. We call these objects orientiholes. The gravitational entropy of various IIA orientihole configurations provides an “experimental” estimate of the number of vacua in various sectors of the IIB landscape. Furthermore, basic physical properties of orientiholes map to (sometimes subtle) microscopic features, thus providing a useful alternative viewpoint on a number of issues arising in D-brane model building. More generally, we give orientihole generalizations of recently derived wall crossing formulae, and conjecture a relation to the topological string analogous to the OSV conjecture, but with a linear rather than a quadratic identification of partition functions.

Keywords

Black Holes in String Theory Superstring Vacua 

References

  1. [1]
    S. Kachru, R. Kallosh, A.D. Linde and S.P. Trivedi, de Sitter vacua in string theory, Phys. Rev. D 68 (2003) 046005 [hep-th/0301240] [SPIRES].MathSciNetADSGoogle Scholar
  2. [2]
    M.R. Douglas and S. Kachru, Flux compactification, Rev. Mod. Phys. 79 (2007) 733 [hep-th/0610102] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  3. [3]
    C. Beasley, J.J. Heckman and C. Vafa, GUTs and Exceptional Branes in F-theory - I, JHEP 01 (2009) 058 [arXiv:0802.3391] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  4. [4]
    C. Beasley, J.J. Heckman and C. Vafa, GUTs and Exceptional Branes in F-theory - II: Experimental Predictions, JHEP 01 (2009) 059 [arXiv:0806.0102] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  5. [5]
    J.J. Heckman and C. Vafa, From F-theory GUTs to the LHC, arXiv:0809.3452 [SPIRES].
  6. [6]
    R. Blumenhagen, V. Braun, T.W. Grimm and T. Weigand, GUTs in Type IIB Orientifold Compactifications, Nucl. Phys. B 815 (2009) 1 [arXiv:0811.2936] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  7. [7]
    R. Blumenhagen, B. Körs, D. Lüst and S. Stieberger, Four-dimensional String Compactifications with D-branes, Orientifolds and Fluxes, Phys. Rept. 445 (2007) 1 [hep-th/0610327] [SPIRES].CrossRefADSGoogle Scholar
  8. [8]
    D. Baumann, A. Dymarsky, I.R. Klebanov and L. McAllister, Towards an Explicit Model of D-brane Ination, JCAP 01 (2008) 024 [arXiv:0706.0360] [SPIRES].MathSciNetADSGoogle Scholar
  9. [9]
    H.-Y. Chen, L.-Y. Hung and G. Shiu, Ination on an Open Racetrack, JHEP 03 (2009) 083 [arXiv:0901.0267] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  10. [10]
    A. Collinucci, F. Denef and M. Esole, D-brane Deconstructions in IIB Orientifolds, JHEP 02 (2009) 005 [arXiv:0805.1573] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  11. [11]
    F. Denef, Les Houches Lectures on Constructing String Vacua, arXiv:0803.1194 [SPIRES].
  12. [12]
    M.R. Douglas, The statistics of string/M theory vacua, JHEP 05 (2003) 046 [hep-th/0303194] [SPIRES].CrossRefADSGoogle Scholar
  13. [13]
    R. Bousso and J. Polchinski, Quantization of four-form fluxes and dynamical neutralization of the cosmological constant, JHEP 06 (2000) 006 [hep-th/0004134] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  14. [14]
    S. Ashok and M.R. Douglas, Counting flux vacua, JHEP 01 (2004) 060 [hep-th/0307049] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  15. [15]
    F. Denef and M.R. Douglas, Distributions of flux vacua, JHEP 05 (2004) 072 [hep-th/0404116] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  16. [16]
    F. Denef and M.R. Douglas, Distributions of nonsupersymmetric flux vacua, JHEP 03 (2005) 061 [hep-th/0411183] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  17. [17]
    B.S. Acharya, F. Denef and R. Valandro, Statistics of M-theory vacua, JHEP 06 (2005) 056 [hep-th/0502060] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  18. [18]
    M.R. Douglas, B. Shiffman and S. Zelditch, Critical points and supersymmetric vacua. III: String/M models, Commun. Math. Phys. 265 (2006) 617 [math-ph/0506015] [SPIRES].MATHCrossRefMathSciNetADSGoogle Scholar
  19. [19]
    F. Denef, Les Houches Lectures on Constructing String Vacua, arXiv:0803.1194 [SPIRES].
  20. [20]
    R. Blumenhagen, F. Gmeiner, G. Honecker, D. Lüst and T. Weigand, The statistics of supersymmetric D-brane models, Nucl. Phys. B 713 (2005) 83 [hep-th/0411173] [SPIRES].CrossRefADSGoogle Scholar
  21. [21]
    F. Gmeiner, R. Blumenhagen, G. Honecker, D. Lüst and T. Weigand, One in a billion: MSSM-like D-brane statistics, JHEP 01 (2006) 004 [hep-th/0510170] [SPIRES].CrossRefADSGoogle Scholar
  22. [22]
    F. Gmeiner and M. Stein, Statistics of SU(5) D-brane models on a type-II orientifold, Phys. Rev. D 73 (2006) 126008 [hep-th/0603019] [SPIRES].MathSciNetADSGoogle Scholar
  23. [23]
    M.R. Douglas and W. Taylor, The landscape of intersecting brane models, JHEP 01 (2007) 031 [hep-th/0606109] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  24. [24]
    F. Denef, Supergravity flows and D-brane stability, JHEP 08 (2000) 050 [hep-th/0005049] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  25. [25]
    K. Behrndt, D. Lüst and W.A. Sabra, Stationary solutions of N = 2 supergravity, Nucl. Phys. B 510 (1998) 264 [hep-th/9705169] [SPIRES].CrossRefADSGoogle Scholar
  26. [26]
    G. Lopes Cardoso, B. de Wit, J. Kappeli and T. Mohaupt, Stationary BPS solutions in N = 2 supergravity with R 2 interactions, JHEP 12 (2000) 019 [hep-th/0009234] [SPIRES].CrossRefADSGoogle Scholar
  27. [27]
    F. Denef, Quantum quivers and Hall/hole halos, JHEP 10 (2002) 023 [hep-th/0206072] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  28. [28]
    F. Denef and G.W. Moore, Split states, entropy enigmas, holes and halos, hep-th/0702146 [SPIRES].
  29. [29]
    H. Ooguri, A. Strominger and C. Vafa, Black hole attractors and the topological string, Phys. Rev. D 70 (2004) 106007 [hep-th/0405146] [SPIRES].MathSciNetADSGoogle Scholar
  30. [30]
    B. Bates and F. Denef, Exact solutions for supersymmetric stationary black hole composites, hep-th/0304094 [SPIRES].
  31. [31]
    B.S. Acharya, M. Aganagic, K. Hori and C. Vafa, Orientifolds, mirror symmetry and superpotentials, hep-th/0202208 [SPIRES].
  32. [32]
    I. Brunner and K. Hori, Orientifolds and mirror symmetry, JHEP 11 (2004) 005 [hep-th/0303135] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  33. [33]
    J. Polchinski, S. Chaudhuri and C.V. Johnson, Notes on D-branes, hep-th/9602052 [SPIRES].
  34. [34]
    A. Dabholkar and J. Park, Strings on Orientifolds, Nucl. Phys. B 477 (1996) 701 [hep-th/9604178] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  35. [35]
    T.W. Grimm and J. Louis, The effective action of N = 1 Calabi-Yau orientifolds, Nucl. Phys. B 699 (2004) 387 [hep-th/0403067] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  36. [36]
    A. Strominger, Special geometry, Commun. Math. Phys. 133 (1990) 163 [SPIRES].MATHCrossRefMathSciNetADSGoogle Scholar
  37. [37]
    S. Ferrara, R. Kallosh and A. Strominger, N = 2 extremal black holes, Phys. Rev. D 52 (1995) 5412 [hep-th/9508072] [SPIRES].MathSciNetADSGoogle Scholar
  38. [38]
    S. Ferrara, G.W. Gibbons and R. Kallosh, Black holes and critical points in moduli space, Nucl. Phys. B 500 (1997) 75 [hep-th/9702103] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  39. [39]
    G.W. Moore, Arithmetic and attractors, hep-th/9807087 [SPIRES].
  40. [40]
    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] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  41. [41]
    M. Shmakova, Calabi-Yau Black Holes, Phys. Rev. D 56 (1997) 540 [hep-th/9612076] [SPIRES].MathSciNetADSGoogle Scholar
  42. [42]
    F. Denef, On the correspondence between D-branes and stationary supergravity solutions of type-II Calabi-Yau compactifications, hep-th/0010222 [SPIRES].
  43. [43]
    N. Seiberg and E. Witten, Gauge dynamics and compactification to three dimensions, hep-th/9607163 [SPIRES].
  44. [44]
    A. Sen, Strong coupling dynamics of branes from M-theory, JHEP 10 (1997) 002 [hep-th/9708002] [SPIRES].CrossRefADSGoogle Scholar
  45. [45]
    E. Witten, An SU(2) anomaly, Phys. Lett. B117 (1982) 324 [SPIRES].MathSciNetADSGoogle Scholar
  46. [46]
    A.M. Uranga, D-brane probes, RR tadpole cancellation and k-theory charge, Nucl. Phys. B 598 (2001) 225 [hep-th/0011048] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  47. [47]
    J. Distler, D. Freed and G. W. Moore, Orientifold Precis arXiv:0906.0795.
  48. [48]
  49. [49]
    K. Hori and D. Gao, to appear.Google Scholar
  50. [50]
  51. [51]
    S. Cecotti, P. Fendley, K.A. Intriligator and C. Vafa, A New supersymmetric index, Nucl. Phys. B 386 (1992) 405 [hep-th/9204102] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  52. [52]
    E. Kiritsis, Introduction to non-perturbative string theory, hep-th/9708130 [SPIRES].
  53. [53]
    M. Kontsevich and Y. Soibelman, Stability structures, motivic Donaldson-Thomas invariants and cluster transformations, arXiv:0811.2435.
  54. [54]
    D. Gaiotto, G.W. Moore and A. Neitzke, Four-dimensional wall-crossing via three-dimensional field theory, arXiv:0807.4723 [SPIRES].
  55. [55]
    I. Brunner, K. Hori, K. Hosomichi and J. Walcher, Orientifolds of Gepner models, JHEP 02 (2007) 001 [hep-th/0401137] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  56. [56]
    G. Lopes Cardoso, B. de Wit and T. Mohaupt, Corrections to macroscopic supersymmetric black-hole entropy, Phys. Lett. B 451 (1999) 309 [hep-th/9812082] [SPIRES].ADSGoogle Scholar
  57. [57]
    G. Lopes Cardoso, B. de Wit and T. Mohaupt, Deviations from the area law for supersymmetric black holes, Fortsch. Phys. 48 (2000) 49 [hep-th/9904005] [SPIRES].CrossRefADSGoogle Scholar
  58. [58]
    G. Lopes Cardoso, B. de Wit and T. Mohaupt, Area law corrections from state counting and supergravity, Class. Quant. Grav. 17 (2000) 1007 [hep-th/9910179] [SPIRES].MATHCrossRefADSGoogle Scholar
  59. [59]
    A.P. Braun, A. Hebecker and H. Triendl, D7-Brane Motion from M-theory Cycles and Obstructions in the Weak Coupling Limit, Nucl. Phys. B 800 (2008) 298 [arXiv:0801.2163] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  60. [60]
    I. Brunner and M. Herbst, Orientifolds and D-branes in N = 2 gauged linear σ-models, arXiv:0812.2880 [SPIRES].
  61. [61]
    P. Candelas, X.C. De La Ossa, P.S. Green and L. Parkes, A pair of Calabi-Yau manifolds as an exactly soluble superconformal theory, Nucl. Phys. B 359 (1991) 21 [SPIRES].CrossRefADSGoogle Scholar
  62. [62]
    I. Brunner, M.R. Douglas, A.E. Lawrence and C. Romelsberger, D-branes on the quintic, JHEP 08 (2000) 015 [hep-th/9906200] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  63. [63]
    A. Strominger, Massless black holes and conifolds in string theory, Nucl. Phys. B 451 (1995) 96 [hep-th/9504090] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  64. [64]
    A. Collinucci and T. Wyder, The elliptic genus from split flows and Donaldson-Thomas invariants, arXiv:0810.4301 [SPIRES].
  65. [65]
    F. Denef, D. Gaiotto, A. Strominger, D. Van den Bleeken and X. Yin, Black hole deconstruction, hep-th/0703252 [SPIRES].
  66. [66]
    S.D. Mathur, The fuzzball proposal for black holes: An elementary review, Fortsch. Phys. 53 (2005) 793 [hep-th/0502050] [SPIRES].MATHCrossRefMathSciNetADSGoogle Scholar
  67. [67]
    I. Bena, C.-W. Wang and N.P. Warner, Plumbing the Abyss: Black Ring Microstates, JHEP 07 (2008) 019 [arXiv:0706.3786] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  68. [68]
    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] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  69. [69]
    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].CrossRefGoogle Scholar
  70. [70]
    D. Gaiotto, A. Strominger and X. Yin, From AdS 3/CFT 2 to black holes /topological strings, JHEP 09 (2007) 050 [hep-th/0602046] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  71. [71]
    J. de Boer, M.C.N. Cheng, R. Dijkgraaf, J. Manschot and E. Verlinde, A farey tail for attractor black holes, JHEP 11 (2006) 024 [hep-th/0608059] [SPIRES].CrossRefGoogle Scholar
  72. [72]
    D. Gaiotto, A. Strominger and X. Yin, The M5-brane elliptic genus: Modularity and BPS states, JHEP 08 (2007) 070 [hep-th/0607010] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  73. [73]
    A. Sen, Walls of Marginal Stability and Dyon Spectrum in N = 4 Supersymmetric String Theories, JHEP 05 (2007) 039 [hep-th/0702141] [SPIRES].CrossRefADSGoogle Scholar
  74. [74]
    M.C.N. Cheng and E. Verlinde, Dying Dyons Don't Count, JHEP 09 (2007) 070 [arXiv:0706.2363] [SPIRES].MathSciNetADSGoogle Scholar
  75. [75]
    A. Sen, N = 8 Dyon Partition Function and Walls of Marginal Stability, JHEP 07 (2008) 118 [arXiv:0803.1014] [SPIRES].CrossRefADSGoogle Scholar
  76. [76]
    A. Sen, Wall Crossing Formula for N = 4 Dyons: A Macroscopic Derivation, JHEP 07 (2008) 078 [arXiv:0803.3857] [SPIRES].CrossRefADSGoogle Scholar
  77. [77]
    M.C.N. Cheng and E.P. Verlinde, Wall Crossing, Discrete Attractor Flow and Borcherds Algebra, arXiv:0806.2337 [SPIRES].
  78. [78]
    M.C.N. Cheng and A. Dabholkar, Borcherds-Kac-Moody Symmetry of N = 4 Dyons, arXiv:0809.4258 [SPIRES].
  79. [79]
    M.C.N. Cheng and L. Hollands, A Geometric Derivation of the Dyon Wall-Crossing Group, JHEP 04 (2009) 067 [arXiv:0901.1758] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  80. [80]
    R. Dijkgraaf, E.P. Verlinde and H.L. Verlinde, Counting Dyons in N = 4 String Theory, Nucl. Phys. B 484 (1997) 543 [hep-th/9607026] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  81. [81]
    M. Aganagic, A. Neitzke and C. Vafa, BPS microstates and the open topological string wave function, hep-th/0504054 [SPIRES].

Copyright information

© SISSA, Trieste, Italy 2010

Authors and Affiliations

  1. 1.Jefferson Physical LaboratoryHarvard UniversityCambridgeU.S.A.
  2. 2.Instituut voor Theoretische FysicaKU LeuvenLeuvenBelgium

Personalised recommendations