Understanding KKLT from a 10d perspective

  • Yuta HamadaEmail author
  • Arthur Hebecker
  • Gary Shiu
  • Pablo Soler
Open Access
Regular Article - Theoretical Physics


Some of the most well-celebrated constructions of metastable de Sitter vacua from string theory, such as the KKLT proposal, involve the interplay of gaugino condensation on a D7-brane stack and an uplift by a positive tension object. These constructions have recently been challenged using arguments that rely on the trace-reversed and integrated 10d Einstein equation. We give a critical assessment of such concerns. We first relate an integrated 10d Einstein equation to the extremization condition for a 10d-derived 4d effective potential. Then we argue how to obtain the latter from a 10d action which incorporates gaugino condensation in a (recently proposed) manifestly finite, perfect-square form. This effective potential is consistent with 4d supergravity and does not present obstacles for an uplifted minimum. Moreover, within standard approximations, we understand the uplift explicitly in one of the popular versions of the integrated 10d equation. Our conclusion is that de Sitter constructions of the KKLT type cannot be dismissed simply based on the integrated 10d equations considered so far.


D-branes Flux compactifications Supergravity Models Superstring Vacua 


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]
    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] [INSPIRE].
  2. [2]
    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] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  3. [3]
    G. Obied, H. Ooguri, L. Spodyneiko and C. Vafa, de Sitter Space and the Swampland, arXiv:1806.08362 [INSPIRE].
  4. [4]
    H. Ooguri, E. Palti, G. Shiu and C. Vafa, Distance and de Sitter Conjectures on the Swampland, Phys. Lett. B 788 (2019) 180 [arXiv:1810.05506] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  5. [5]
    S.K. Garg and C. Krishnan, Bounds on Slow Roll and the de Sitter Swampland, arXiv:1807.05193 [INSPIRE].
  6. [6]
    Y. Hamada, A. Hebecker, G. Shiu and P. Soler, On brane gaugino condensates in 10d, JHEP 04 (2019) 008 [arXiv:1812.06097] [INSPIRE].ADSCrossRefGoogle Scholar
  7. [7]
    R. Kallosh, Gaugino Condensation and Geometry of the Perfect Square, Phys. Rev. D 99 (2019) 066003 [arXiv:1901.02023] [INSPIRE].ADSGoogle Scholar
  8. [8]
    J. Moritz, A. Retolaza and A. Westphal, Toward de Sitter space from ten dimensions, Phys. Rev. D 97 (2018) 046010 [arXiv:1707.08678] [INSPIRE].ADSMathSciNetGoogle Scholar
  9. [9]
    F.F. Gautason, V. Van Hemelryck and T. Van Riet, The Tension between 10D Supergravity and dS Uplifts, Fortsch. Phys. 67 (2019) 1800091 [arXiv:1810.08518] [INSPIRE].CrossRefGoogle Scholar
  10. [10]
    I. Bena, M. Graña and N. Halmagyi, On the Existence of Meta-stable Vacua in Klebanov-Strassler, JHEP 09 (2010) 087 [arXiv:0912.3519] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  11. [11]
    J. McOrist and S. Sethi, M-theory and Type IIA Flux Compactifications, JHEP 12 (2012) 122 [arXiv:1208.0261] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  12. [12]
    K. Dasgupta, R. Gwyn, E. McDonough, M. Mia and R. Tatar, de Sitter Vacua in Type IIB String Theory: Classical Solutions and Quantum Corrections, JHEP 07 (2014) 054 [arXiv:1402.5112] [INSPIRE].
  13. [13]
    I. Bena, M. Graña, S. Kuperstein and S. Massai, Giant Tachyons in the Landscape, JHEP 02 (2015) 146 [arXiv:1410.7776] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  14. [14]
    C. Quigley, Gaugino Condensation and the Cosmological Constant, JHEP 06 (2015) 104 [arXiv:1504.00652] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  15. [15]
    D. Cohen-Maldonado, J. Diaz, T. van Riet and B. Vercnocke, Observations on fluxes near anti-branes, JHEP 01 (2016) 126 [arXiv:1507.01022] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  16. [16]
    D. Junghans and M. Zagermann, A Universal Tachyon in Nearly No-scale de Sitter Compactifications, JHEP 07 (2018) 078 [arXiv:1612.06847] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  17. [17]
    S. Sethi, Supersymmetry Breaking by Fluxes, JHEP 10 (2018) 022 [arXiv:1709.03554] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  18. [18]
    U.H. Danielsson and T. Van Riet, What if string theory has no de Sitter vacua?, Int. J. Mod. Phys. D 27 (2018) 1830007 [arXiv:1804.01120] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  19. [19]
    J. Moritz and T. Van Riet, Racing through the swampland: de Sitter uplift vs weak gravity, JHEP 09 (2018) 099 [arXiv:1805.00944] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  20. [20]
    M. Cicoli, S. De Alwis, A. Maharana, F. Muia and F. Quevedo, de Sitter vs Quintessence in String Theory, Fortsch. Phys. 67 (2019) 1800079 [arXiv:1808.08967] [INSPIRE].
  21. [21]
    S. Kachru and S.P. Trivedi, A comment on effective field theories of flux vacua, Fortsch. Phys. 67 (2019) 1800086 [arXiv:1808.08971] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  22. [22]
    R. Kallosh and T. Wrase, dS Supergravity from 10d, Fortsch. Phys. 67 (2019) 1800071 [arXiv:1808.09427] [INSPIRE].CrossRefGoogle Scholar
  23. [23]
    Y. Akrami, R. Kallosh, A. Linde and V. Vardanyan, The Landscape, the Swampland and the Era of Precision Cosmology, Fortsch. Phys. 67 (2019) 1800075 [arXiv:1808.09440] [INSPIRE].CrossRefGoogle Scholar
  24. [24]
    J. Moritz, A. Retolaza and A. Westphal, On uplifts by warped anti-D3-branes, Fortsch. Phys. 67 (2019) 1800098 [arXiv:1809.06618] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  25. [25]
    I. Bena, E. Dudas, M. Graña and S. Lüst, Uplifting Runaways, Fortsch. Phys. 67 (2019) 1800100 [arXiv:1809.06861] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  26. [26]
    R. Kallosh, A. Linde, E. McDonough and M. Scalisi, 4D models of de Sitter uplift, Phys. Rev. D 99 (2019) 046006 [arXiv:1809.09018] [INSPIRE].ADSGoogle Scholar
  27. [27]
    J. Armas, N. Nguyen, V. Niarchos, N.A. Obers and T. Van Riet, Meta-stable non-extremal anti-branes, Phys. Rev. Lett. 122 (2019) 181601 [arXiv:1812.01067] [INSPIRE].ADSCrossRefGoogle Scholar
  28. [28]
    A. Hebecker and T. Wrase, The Asymptotic dS Swampland Conjecturea Simplified Derivation and a Potential Loophole, Fortsch. Phys. 67 (2019) 1800097 [arXiv:1810.08182] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  29. [29]
    J.J. Heckman, C. Lawrie, L. Lin and G. Zoccarato, F-theory and Dark Energy, arXiv:1811.01959 [INSPIRE].
  30. [30]
    D. Junghans, Weakly Coupled de Sitter Vacua with Fluxes and the Swampland, JHEP 03 (2019) 150 [arXiv:1811.06990] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  31. [31]
    R. Kallosh, A. Linde, E. McDonough and M. Scalisi, dS Vacua and the Swampland, JHEP 03 (2019) 134 [arXiv:1901.02022] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  32. [32]
    J.J. Heckman, C. Lawrie, L. Lin, J. Sakstein and G. Zoccarato, Pixelated Dark Energy, arXiv:1901.10489 [INSPIRE].
  33. [33]
    J.M. Maldacena and C. Núñez, Supergravity description of field theories on curved manifolds and a no go theorem, Int. J. Mod. Phys. A 16 (2001) 822 [hep-th/0007018] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  34. [34]
    S.B. Giddings and A. Maharana, Dynamics of warped compactifications and the shape of the warped landscape, Phys. Rev. D 73 (2006) 126003 [hep-th/0507158] [INSPIRE].ADSMathSciNetGoogle Scholar
  35. [35]
    J.P. Derendinger, L.E. Ibáñez and H.P. Nilles, On the Low-Energy d = 4, N = 1 Supergravity Theory Extracted from the d = 10, N = 1 Superstring, Phys. Lett. 155B (1985) 65 [INSPIRE].ADSCrossRefGoogle Scholar
  36. [36]
    M. Dine, R. Rohm, N. Seiberg and E. Witten, Gluino Condensation in Superstring Models, Phys. Lett. 156B (1985) 55 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  37. [37]
    P.G. Camara, L.E. Ibáñez and A.M. Uranga, Flux-induced SUSY-breaking soft terms on D7-D3 brane systems, Nucl. Phys. B 708 (2005) 268 [hep-th/0408036] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  38. [38]
    D. Baumann, A. Dymarsky, I.R. Klebanov, J.M. Maldacena, L.P. McAllister and A. Murugan, On D3-brane Potentials in Compactifications with Fluxes and Wrapped D-branes, JHEP 11 (2006) 031 [hep-th/0607050] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  39. [39]
    P. Koerber and L. Martucci, From ten to four and back again: How to generalize the geometry, JHEP 08 (2007) 059 [arXiv:0707.1038] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  40. [40]
    D. Baumann, A. Dymarsky, S. Kachru, I.R. Klebanov and L. McAllister, Compactification Effects in D-brane Inflation, Phys. Rev. Lett. 104 (2010) 251602 [arXiv:0912.4268] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  41. [41]
    D. Baumann, A. Dymarsky, S. Kachru, I.R. Klebanov and L. McAllister, D3-brane Potentials from Fluxes in AdS/CFT, JHEP 06 (2010) 072 [arXiv:1001.5028] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  42. [42]
    A. Dymarsky and L. Martucci, D-brane non-perturbative effects and geometric deformations, JHEP 04 (2011) 061 [arXiv:1012.4018] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  43. [43]
    S.B. Giddings, S. Kachru and J. Polchinski, Hierarchies from fluxes in string compactifications, Phys. Rev. D 66 (2002) 106006 [hep-th/0105097] [INSPIRE].ADSMathSciNetGoogle Scholar
  44. [44]
    P. Hořava and E. Witten, Heterotic and type-I string dynamics from eleven-dimensions, Nucl. Phys. B 460 (1996) 506 [hep-th/9510209] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  45. [45]
    P. Hořava and E. Witten, Eleven-dimensional supergravity on a manifold with boundary, Nucl. Phys. B 475 (1996) 94 [hep-th/9603142] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  46. [46]
    P. Hořava, Gluino condensation in strongly coupled heterotic string theory, Phys. Rev. D 54 (1996) 7561 [hep-th/9608019] [INSPIRE].ADSMathSciNetGoogle Scholar
  47. [47]
    H.P. Nilles, M. Olechowski and M. Yamaguchi, Supersymmetry breaking and soft terms in M-theory, Phys. Lett. B 415 (1997) 24 [hep-th/9707143] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  48. [48]
    E.A. Mirabelli and M.E. Peskin, Transmission of supersymmetry breaking from a four-dimensional boundary, Phys. Rev. D 58 (1998) 065002 [hep-th/9712214] [INSPIRE].ADSMathSciNetGoogle Scholar
  49. [49]
    S.P. de Alwis, On Potentials from fluxes, Phys. Rev. D 68 (2003) 126001 [hep-th/0307084] [INSPIRE].ADSMathSciNetGoogle Scholar
  50. [50]
    J. Polchinski, Brane/antibrane dynamics and KKLT stability, arXiv:1509.05710 [INSPIRE].
  51. [51]
    U.H. Danielsson, S.S. Haque, G. Shiu and T. Van Riet, Towards Classical de Sitter Solutions in String Theory, JHEP 09 (2009) 114 [arXiv:0907.2041] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  52. [52]
    U.H. Danielsson, S.S. Haque, P. Koerber, G. Shiu, T. Van Riet and T. Wrase, de Sitter hunting in a classical landscape, Fortsch. Phys. 59 (2011) 897 [arXiv:1103.4858] [INSPIRE].
  53. [53]
    V.S. Kaplunovsky and J. Louis, Model independent analysis of soft terms in effective supergravity and in string theory, Phys. Lett. B 306 (1993) 269 [hep-th/9303040] [INSPIRE].ADSCrossRefGoogle Scholar
  54. [54]
    V. Kaplunovsky and J. Louis, Field dependent gauge couplings in locally supersymmetric effective quantum field theories, Nucl. Phys. B 422 (1994) 57 [hep-th/9402005] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  55. [55]
    S. Kachru, R. Kallosh, A.D. Linde, J.M. Maldacena, L.P. McAllister and S.P. Trivedi, Towards inflation in string theory, JCAP 10 (2003) 013 [hep-th/0308055] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  56. [56]
    G. von Gersdorff and A. Hebecker, Kähler corrections for the volume modulus of flux compactifications, Phys. Lett. B 624 (2005) 270 [hep-th/0507131] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  57. [57]
    M. Berg, M. Haack and B. Körs, String loop corrections to Kähler potentials in orientifolds, JHEP 11 (2005) 030 [hep-th/0508043] [INSPIRE].ADSCrossRefGoogle Scholar
  58. [58]
    F. Carta, J. Moritz and A. Westphal, Gaugino condensation and small uplifts in KKLT, arXiv:1902.01412 [INSPIRE].
  59. [59]
    F.F. Gautason, V. Van Hemelryck, T. Van Riet and G. Venken, A 10d view on the KKLT AdS vacuum and uplifting, arXiv:1902.01415 [INSPIRE].
  60. [60]
    M. Nakahara, Geometry, topology and physics, Taylor & Francis (2003) [INSPIRE].

Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Crete Center for Theoretical Physics, Institute for Theoretical and Computational Physics, Department of PhysicsUniversity of CreteHeraklionGreece
  2. 2.Institute for Theoretical PhysicsUniversity of HeidelbergHeidelbergGermany
  3. 3.Department of PhysicsUniversity of WisconsinMadisonU.S.A.

Personalised recommendations