Journal of High Energy Physics

, 2010:56

Stabilizing all Kähler moduli in type IIB orientifolds

  • Konstantin Bobkov
  • Volker Braun
  • Piyush Kumar
  • Stuart Raby
Open Access


We describe a simple and robust mechanism that stabilizes all Kähler moduli in Type IIB orientifold compactifications. This is shown to be possible with just one non-perturbative contribution to the superpotential coming from either a D3-instanton or D7-branes wrapped on an ample divisor. This moduli-stabilization mechanism is similar to and motivated by the one used in the fluxless G2 compactifications of M theory. After explaining the general idea, explicit examples of Calabi-Yau orientifolds with one and three Kähler moduli are worked out. We find that the stabilized volumes of all two-and four-cycles as well as the volume of the Calabi-Yau manifold are controlled by a single parameter, namely, the volume of the ample divisor. This feature would dramatically constrain any realistic models of particle physics embedded into such compactifications. Broad consequences for phenomenology are discussed, in particular the dynamical solution to the strong CP-problem within the framework.


dS vacua in string theory Compactification and String Models Superstrings and Heterotic Strings Superstring Vacua 


  1. [1]
    K. Bobkov, V. Braun, P. Kumar, S. Raby, Part two, to appear.Google Scholar
  2. [2]
    B.S. Acharya, A moduli fixing mechanism in M-theory, hep-th/0212294 [SPIRES].
  3. [3]
    B.S. Acharya, F. Benini and R. Valandro, Fixing moduli in exact type IIA flux vacua, JHEP 02 (2007) 018 [hep-th/0607223] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  4. [4]
    B.S. Acharya and K. Bobkov, Kähler Independence of the G2-MSSM, JHEP 09 (2010) 001 [arXiv:0810.3285] [SPIRES].CrossRefADSGoogle Scholar
  5. [5]
    B.S. Acharya, K. Bobkov, G. Kane, P. Kumar and D. Vaman, An M-theory solution to the hierarchy problem, Phys. Rev. Lett. 97 (2006) 191601 [hep-th/0606262] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  6. [6]
    B.S. Acharya, K. Bobkov, G.L. Kane, P. Kumar and J. Shao, Explaining the electroweak scale and stabilizing moduli in M-theory, Phys. Rev. D 76 (2007) 126010 [hep-th/0701034] [SPIRES].ADSMathSciNetGoogle Scholar
  7. [7]
    B.S. Acharya, K. Bobkov and P. Kumar, An M-theory Solution to the Strong CP Problem and Constraints on the A xiverse, JHEP 11 (2010) 105 [arXiv:1004.5138] [SPIRES].CrossRefADSGoogle Scholar
  8. [8]
    A. Achucarro, B. de Carlos, J.A. Casas and L. Doplicher, de Sitter vacua from uplifting D-terms in effective supergravities from realistic strings, JHEP 06 (2006) 014 [hep-th/0601190] [SPIRES].CrossRefADSGoogle Scholar
  9. [9]
    S.P. de Alwis, Classical and Quantum SUSY Breaking Effects in IIB Local Models, JHEP 03 (2010) 078 [arXiv:0912.2950] [SPIRES].CrossRefGoogle Scholar
  10. [10]
    A. Arvanitaki, S. Dimopoulos, S. Dubovsky, N. Kaloper and J. March-Russell, String Axiverse, Phys. Rev. D 81 (2010) 123530 [arXiv:0905.4720] [SPIRES].ADSGoogle Scholar
  11. [11]
    V. Balasubramanian, P. Berglund, J.P. Conlon and F. Quevedo, Systematics of Moduli Stabilisation in Calabi-Yau Flux Compactifications, JHEP 03 (2005) 007 [hep-th/0502058] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  12. [12]
    A. Beauville, New trends in algebraic geometry (Warwick, 1996), London Math. Soc. Lecture Note Ser. 264, Cambridge University Press, Cambridge, U.K. (1999), pg. 13–17.CrossRefGoogle Scholar
  13. [13]
    M. Becker, G. Curio and A. Krause, de Sitter vacua from heterotic M-theory, Nucl. Phys. B 693 (2004) 223 [hep-th/0403027] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  14. [14]
    I. Bena, M. Graña and N. Halmagyi, On the Existence of Meta-stable Vacua in Klebanov-Strassler, JHEP 09 (2010) 087 [arXiv:0912.3519] [SPIRES].CrossRefADSGoogle Scholar
  15. [15]
    F. Benini et al., Holographic Gauge Mediation, JHEP 12 (2009) 031 [arXiv:0903.0619] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  16. [16]
    M. Berg, M. Haack and B. Körs, On volume stabilization by quantum corrections, Phys. Rev. Lett. 96 (2006) 021601 [hep-th/0508171] [SPIRES].CrossRefADSGoogle Scholar
  17. [17]
    E. Bergshoeff, R. Kallosh, A.-K. Kashani-Poor, D. Sorokin and A. Tomasiello, An index for the Dirac operator on D3 branes with background fluxes, JHEP 10 (2005) 102 [hep-th/0507069] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  18. [18]
    R. Blumenhagen, Basics of F-theory from the Type IIB Perspective, Fortsch. Phys. 58 (2010) 820 [arXiv:1002.2836] [SPIRES].CrossRefMathSciNetGoogle Scholar
  19. [19]
    R. Blumenhagen, A. Collinucci and B. Jurke, On Instanton Effects in F-theory, JHEP 08 (2010) 079 [arXiv:1002.1894] [SPIRES].CrossRefADSGoogle Scholar
  20. [20]
    R. Blumenhagen, S. Moster and E. Plauschinn, Moduli Stabilisation versus Chirality for MSSM like Type IIB Orientifolds, JHEP 01 (2008) 058 [arXiv:0711.3389] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  21. [21]
    L. Borisov, Z. Hua, On Calabi-Yau threefolds with large nonabelian fundamental groups, Proc. Amer. Math. Soc. 136 (2008) 1549 [math.AG/0609728].CrossRefMATHMathSciNetGoogle Scholar
  22. [22]
    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].CrossRefADSMathSciNetGoogle Scholar
  23. [23]
    V. Braun, On Free Quotients of Complete Intersection Calabi-Yau Manifolds, arXiv:1003.3235 [SPIRES].
  24. [24]
    V. Braun, P. Candelas and R. Davies, A Three-Generation Calabi-Yau Manifold with Small Hodge Numbers, Fortsch. Phys. 58 (2010) 467 [arXiv:0910.5464] [SPIRES].CrossRefMATHMathSciNetGoogle Scholar
  25. [25]
    R. Brustein and S.P. de Alwis, Moduli potentials in string compactifications with fluxes: Mapping the discretuum, Phys. Rev. D 69 (2004) 126006 [hep-th/0402088] [SPIRES].ADSGoogle Scholar
  26. [26]
    M. Buican, D. Malyshev and H. Verlinde, On the Geometry of Metastable Supersymmetry Breaking, JHEP 06 (2008) 108 [arXiv:0710.5519] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  27. [27]
    P.G. Camara, A. Font and L.E. Ibáñez, Fluxes, moduli fixing and MSSM-like vacua in a simple IIA orientifold, JHEP 09 (2005) 013 [hep-th/0506066] [SPIRES].CrossRefADSGoogle Scholar
  28. [28]
    P. Candelas and R. Davies, New Calabi-Yau Manifolds with Small Hodge Numbers, Fortsch. Phys. 58 (2010) 383 [arXiv:0809.4681] [SPIRES].CrossRefMATHMathSciNetGoogle Scholar
  29. [29]
    B. de Carlos, S. Gurrieri, A. Lukas and A. Micu, Moduli stabilisation in heterotic string compactifications, JHEP 03 (2006) 005 [hep-th/0507173] [SPIRES].CrossRefGoogle Scholar
  30. [30]
    B. de Carlos, A. Lukas and S. Morris, Non-perturbative vacua for M-theory on G 2 manifolds, JHEP 12 (2004) 018 [hep-th/0409255] [SPIRES].CrossRefGoogle Scholar
  31. [31]
    K. Choi, A. Falkowski, H.P. Nilles and M. Olechowski, Soft supersymmetry breaking in KKLT flux compactification, Nucl. Phys. B 718 (2005) 113 [hep-th/0503216] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  32. [32]
    K. Choi, A. Falkowski, H.P. Nilles, M. Olechowski and S. Pokorski, Stability of flux compactifications and the pattern of supersymmetry breaking, JHEP 11 (2004) 076 [hep-th/0411066] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  33. [33]
    K. Choi and K.S. Jeong, String theoretic QCD axion with stabilized saxion and the pattern of supersymmetry breaking, JHEP 01 (2007) 103 [hep-th/0611279] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  34. [34]
    K. Choi, K.S. Jeong, S. Nakamura, K.-I. Okumura and M. Yamaguchi, Sparticle masses in deflected mirage mediation, JHEP 04 (2009) 107 [arXiv:0901.0052] [SPIRES].CrossRefADSGoogle Scholar
  35. [35]
    M. Cicoli, J.P. Conlon and F. Quevedo, General Analysis of LARGE Volume Scenarios with String Loop Moduli Stabilisation, JHEP 10 (2008) 105 [arXiv:0805.1029] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  36. [36]
    J.P. Conlon, F. Quevedo and K. Suruliz, Large-volume flux compactifications: Moduli spectrum and D 3/D 7 soft supersymmetry breaking, JHEP 08 (2005) 007 [hep-th/0505076] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  37. [37]
    G. Curio, A. Klemm, D. Lüst and S. Theisen, On the vacuum structure of type-II string compactifications on Calabi-Yau spaces with H-fluxes, Nucl. Phys. B 609 (2001) 3 [hep-th/0012213] [SPIRES].CrossRefADSGoogle Scholar
  38. [38]
    G. Curio, A. Krause and D. Lüst, Moduli stabilization in the heterotic / IIB discretuum, Fortsch. Phys. 54 (2006) 225 [hep-th/0502168] [SPIRES].CrossRefMATHADSGoogle Scholar
  39. [39]
    K. Dasgupta, G. Rajesh and S. Sethi, M theory, orientifolds and G-flux, JHEP 08 (1999) 023 [hep-th/9908088] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  40. [40]
    F. Denef, M.R. Douglas and B. Florea, Building a better racetrack, JHEP 06 (2004) 034 [hep-th/0404257] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  41. [41]
    F. Denef, M.R. Douglas, B. Florea, A. Grassi and S. Kachru, Fixing all moduli in a simple F-theory compactification, Adv. Theor. Math. Phys. 9 (2005) 861 [hep-th/0503124] [SPIRES].MATHMathSciNetGoogle Scholar
  42. [42]
    O. DeWolfe, A. Giryavets, S. Kachru and W. Taylor, Type IIA moduli stabilization, JHEP 07 (2005) 066 [hep-th/0505160] [SPIRES].ADSMathSciNetGoogle Scholar
  43. [43]
    O. DeWolfe, S. Kachru and M. Mulligan, A Gravity Dual of Metastable Dynamical Supersymmetry Breaking, Phys. Rev. D 77 (2008) 065011 [arXiv:0801.1520] [SPIRES].ADSMathSciNetGoogle Scholar
  44. [44]
    D.-E. Diaconescu, B. Florea, S. Kachru and P. Svrček, Gauge-mediated supersymmetry breaking in string compactifications, JHEP 02 (2006) 020 [hep-th/0512170] [SPIRES].CrossRefADSGoogle Scholar
  45. [45]
    P. Fox, A. Pierce and S.D. Thomas, Probing a QCD string axion with precision cosmological measurements, hep-th/0409059 [SPIRES].
  46. [46]
    D.S. Freed and E. Witten, Anomalies in string theory with D-branes, hep-th/9907189 [SPIRES].
  47. [47]
    D. Gallego and M. Serone, An Effective Description of the Landscape - I, JHEP 01 (2009) 056 [arXiv:0812.0369] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  48. [48]
    D. Gallego and M. Serone, An Effective Description of the Landscape - II, JHEP 06 (2009) 057 [arXiv:0904.2537] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  49. [49]
    G. von Gersdorff and A. Hebecker, Kähler corrections for the volume modulus of flux compactifications, Phys. Lett. B 624 (2005) 270 [hep-th/0507131] [SPIRES].ADSGoogle Scholar
  50. [50]
    S.B. Giddings, S. Kachru and J. Polchinski, Hierarchies from fluxes in string compactifications, Phys. Rev. D 66 (2002) 106006 [hep-th/0105097] [SPIRES].ADSMathSciNetGoogle Scholar
  51. [51]
    A. Giryavets, S. Kachru and P.K. Tripathy, On the taxonomy of flux vacua, JHEP 08 (2004) 002 [hep-th/0404243] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  52. [52]
    A. Giryavets, S. Kachru, P.K. Tripathy and S.P. Trivedi, Flux compactifications on Calabi-Yau threefolds, JHEP 04 (2004) 003 [hep-th/0312104] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  53. [53]
    L. Görlich, S. Kachru, P.K. Tripathy and S.P. Trivedi, Gaugino condensation and nonperturbative superpotentials in flux compactifications, JHEP 12 (2004) 074 [hep-th/0407130] [SPIRES].Google Scholar
  54. [54]
    G.M. Grauel, G. P fister, H. Schönemann, Singular 3.0, Centre for Computer Algebra, University of Kaiserslauten, Kaiserslauten, Germany (2005),
  55. [55]
    S. Gukov, S. Kachru, X. Liu and L. McAllister, Heterotic moduli stabilization with fractional Chern-Simons invariants, Phys. Rev. D 69 (2004) 086008 [hep-th/0310159] [SPIRES].ADSMathSciNetGoogle Scholar
  56. [56]
    S. Gukov, C. Vafa and E. Witten, CFT’s from Calabi-Yau four-folds, Nucl. Phys. B 584 (2000) 69 [hep-th/9906070] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  57. [57]
    Z. Hua, Classification of free actions on complete intersections of four quadrics [arXiv:0707.4339].
  58. [58]
    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].ADSMathSciNetGoogle Scholar
  59. [59]
    S. Kachru, L. McAllister and R. Sundrum, Sequestering in string theory, JHEP 10 (2007) 013 [hep-th/0703105] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  60. [60]
    S. Kachru, M.B. Schulz and S. Trivedi, Moduli stabilization from fluxes in a simple IIB orientifold, JHEP 10 (2003) 007 [hep-th/0201028] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  61. [61]
    I.R. Klebanov and M.J. Strassler, Supergravity and a confining gauge theory: Duality cascades and χSB-resolution of naked singularities, JHEP 08 (2000) 052 [hep-th/0007191] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  62. [62]
    O. Lebedev, H.P. Nilles and M. Ratz, de Sitter vacua from matter superpotentials, Phys. Lett. B 636 (2006) 126 [hep-th/0603047] [SPIRES].ADSMathSciNetGoogle Scholar
  63. [63]
    M.M. Lopes, R. Pardini, Numerical Campedelli surfaces with fundamental group of order 9, J. Eur. Math. Soc. 10 (2008) 457.CrossRefMATHMathSciNetGoogle Scholar
  64. [64]
    D. Lüst, S. Reffert, E. Scheidegger, W. Schulgin and S. Stieberger, Moduli stabilization in type IIB orientifolds. II, Nucl. Phys. B 766 (2007) 178 [hep-th/0609013] [SPIRES].CrossRefADSGoogle Scholar
  65. [65]
    D. Lüst, S. Reffert, W. Schulgin and S. Stieberger, Moduli stabilization in type IIB orientifolds. I: Orbifold limits, Nucl. Phys. B 766 (2007) 68 [hep-th/0506090] [SPIRES].CrossRefADSGoogle Scholar
  66. [66]
    P. McGuirk, G. Shiu and Y. Sumitomo, Holographic gauge mediation via strongly coupled messengers, Phys. Rev. D 81 (2010) 026005 [arXiv:0911.0019] [SPIRES].ADSGoogle Scholar
  67. [67]
    A. Micu, Moduli Stabilisation in Heterotic Models with Standard Embedding, JHEP 01 (2010) 011 [arXiv:0911.2311] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  68. [68]
    J. Park, D3 instantons in Calabi-Yau orientifolds with(out) fluxes, Eur. Phys. J. C 67 (2010) 263 [hep-th/0507091] [SPIRES].ADSGoogle Scholar
  69. [69]
    D. Robbins and S. Sethi, A barren landscape, Phys. Rev. D 71 (2005) 046008 [hep-th/0405011] [SPIRES].ADSGoogle Scholar
  70. [70]
    E. Silverstein, Simple de Sitter Solutions, Phys. Rev. D 77 (2008) 106006 [arXiv:0712.1196] [SPIRES].ADSMathSciNetGoogle Scholar
  71. [71]
    T.R. Taylor and C. Vafa, RR flux on Calabi-Yau and partial supersymmetry breaking, Phys. Lett. B 474 (2000) 130 [hep-th/9912152] [SPIRES].ADSMathSciNetGoogle Scholar
  72. [72]
    G. Villadoro and F. Zwirner, N = 1 effective potential from dual type-IIA D6/O6 orientifolds with general fluxes, JHEP 06 (2005) 047 [hep-th/0503169] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  73. [73]
    E. Witten, Non-Perturbative Superpotentials In String Theory, Nucl. Phys. B 474 (1996) 343 [hep-th/9604030] [SPIRES].CrossRefADSMathSciNetGoogle Scholar

Copyright information

© The Author(s) 2010

Open Access This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

Authors and Affiliations

  • Konstantin Bobkov
    • 1
  • Volker Braun
    • 2
  • Piyush Kumar
    • 3
  • Stuart Raby
    • 1
  1. 1.Department of PhysicsThe Ohio State UniversityColumbusU.S.A.
  2. 2.Dublin Institute for Advanced StudiesDublinIreland
  3. 3.Department of PhysicsUniversity of California, Theoretical Physics Group, Lawrence Berkeley National LaboratoryBerkeleyU.S.A.

Personalised recommendations