A universal tachyon in nearly no-scale de Sitter compactifications

  • Daniel Junghans
  • Marco Zagermann
Open Access
Regular Article - Theoretical Physics


We investigate de Sitter solutions of \( \mathcal{N}=1 \) supergravity with an F-term scalar potential near a no-scale Minkowski point, as they may in particular arise from flux compactifications in string theory. We show that a large class of such solutions has a universal tachyon with \( \eta \le -\frac{4}{3} \) at positive vacuum energies, thus forbidding meta-stable de Sitter vacua and slow-roll inflation. The tachyon aligns with the sgoldstino in the Minkowski limit, whereas the sgoldstino itself is generically stable in the de Sitter vacuum due to mass mixing effects. We specify necessary conditions for the superpotential and the Kähler potential to avoid the instability. Our result may also help to explain why the program of classical de Sitter hunting has remained unsuccessful, while constructions involving instantons or non-geometric fluxes have led to various examples of meta-stable de Sitter vacua.


Flux compactifications Superstring Vacua 


Open Access

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  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].ADSMathSciNetzbMATHGoogle Scholar
  2. [2]
    C.P. Burgess, R. Kallosh and F. Quevedo, De Sitter string vacua from supersymmetric D terms, JHEP 10 (2003) 056 [hep-th/0309187] [INSPIRE].ADSMathSciNetGoogle Scholar
  3. [3]
    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
  4. [4]
    M. Rummel and A. Westphal, A sufficient condition for de Sitter vacua in type IIB string theory, JHEP 01 (2012) 020 [arXiv:1107.2115] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    J. Louis, M. Rummel, R. Valandro and A. Westphal, Building an explicit de Sitter, JHEP 10 (2012) 163 [arXiv:1208.3208] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  6. [6]
    M. Cicoli, A. Maharana, F. Quevedo and C.P. Burgess, De Sitter string vacua from dilaton-dependent non-perturbative effects, JHEP 06 (2012) 011 [arXiv:1203.1750] [INSPIRE].ADSCrossRefGoogle Scholar
  7. [7]
    M. Cicoli, D. Klevers, S. Krippendorf, C. Mayrhofer, F. Quevedo and R. Valandro, Explicit de Sitter flux vacua for global string models with chiral matter, JHEP 05 (2014) 001 [arXiv:1312.0014] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  8. [8]
    J. Blåbäck, D. Roest and I. Zavala, De Sitter vacua from nonperturbative flux compactifications, Phys. Rev. D 90 (2014) 024065 [arXiv:1312.5328] [INSPIRE].ADSGoogle Scholar
  9. [9]
    U. Danielsson and G. Dibitetto, An alternative to anti-branes and O-planes?, JHEP 05 (2014) 013 [arXiv:1312.5331] [INSPIRE].ADSCrossRefGoogle Scholar
  10. [10]
    M. Rummel and Y. Sumitomo, De Sitter vacua from a D-term generated racetrack uplift, JHEP 01 (2015) 015 [arXiv:1407.7580] [INSPIRE].zbMATHGoogle Scholar
  11. [11]
    A.P. Braun, M. Rummel, Y. Sumitomo and R. Valandro, De Sitter vacua from a D-term generated racetrack potential in hypersurface Calabi-Yau compactifications, JHEP 12 (2015) 033 [arXiv:1509.06918] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  12. [12]
    R. Kallosh, A. Linde, B. Vercnocke and T. Wrase, Analytic classes of metastable de Sitter vacua, JHEP 10 (2014) 011 [arXiv:1406.4866] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  13. [13]
    M.C.D. Marsh, B. Vercnocke and T. Wrase, Decoupling and de Sitter vacua in approximate no-scale supergravities, JHEP 05 (2015) 081 [arXiv:1411.6625] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  14. [14]
    A. Guarino and G. Inverso, Single-step de Sitter vacua from nonperturbative effects with matter, Phys. Rev. D 93 (2016) 066013 [arXiv:1511.07841] [INSPIRE].ADSMathSciNetGoogle Scholar
  15. [15]
    A. Retolaza and A. Uranga, De Sitter uplift with dynamical SUSY breaking, JHEP 04 (2016) 137 [arXiv:1512.06363] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  16. [16]
    X. Dong, B. Horn, E. Silverstein and G. Torroba, Micromanaging de Sitter holography, Class. Quant. Grav. 27 (2010) 245020 [arXiv:1005.5403] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  17. [17]
    M. Dodelson, X. Dong, E. Silverstein and G. Torroba, New solutions with accelerated expansion in string theory, JHEP 12 (2014) 050 [arXiv:1310.5297] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  18. [18]
    B. de Carlos, A. Guarino and J.M. Moreno, Flux moduli stabilisation, supergravity algebras and no-go theorems, JHEP 01 (2010) 012 [arXiv:0907.5580] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  19. [19]
    B. de Carlos, A. Guarino and J.M. Moreno, Complete classification of Minkowski vacua in generalised flux models, JHEP 02 (2010) 076 [arXiv:0911.2876] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  20. [20]
    G. Dibitetto, R. Linares and D. Roest, Flux compactifications, gauge algebras and de Sitter, Phys. Lett. B 688 (2010) 96 [arXiv:1001.3982] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  21. [21]
    U. Danielsson and G. Dibitetto, On the distribution of stable de Sitter vacua, JHEP 03 (2013) 018 [arXiv:1212.4984] [INSPIRE].ADSCrossRefGoogle Scholar
  22. [22]
    J. Blåbäck, U. Danielsson and G. Dibitetto, Fully stable dS vacua from generalised fluxes, JHEP 08 (2013) 054 [arXiv:1301.7073] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  23. [23]
    C. Damian, L.R. Diaz-Barron, O. Loaiza-Brito and M. Sabido, Slow-roll inflation in non-geometric flux compactification, JHEP 06 (2013) 109 [arXiv:1302.0529] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  24. [24]
    C. Damian and O. Loaiza-Brito, More stable de Sitter vacua from S-dual nongeometric fluxes, Phys. Rev. D 88 (2013) 046008 [arXiv:1304.0792] [INSPIRE].ADSGoogle Scholar
  25. [25]
    F. Hassler, D. Lüst and S. Massai, On inflation and de Sitter in non-geometric string backgrounds, Fortsch. Phys. 65 (2017) 1700062 [arXiv:1405.2325] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  26. [26]
    J. Blåbäck, U.H. Danielsson, G. Dibitetto and S.C. Vargas, Universal dS vacua in STU-models, JHEP 10 (2015) 069 [arXiv:1505.04283] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  27. [27]
    M. Cicoli, S. de Alwis and A. Westphal, Heterotic moduli stabilisation, JHEP 10 (2013) 199 [arXiv:1304.1809] [INSPIRE].ADSCrossRefGoogle Scholar
  28. [28]
    S.L. Parameswaran and A. Westphal, De Sitter string vacua from perturbative Kähler corrections and consistent D-terms, JHEP 10 (2006) 079 [hep-th/0602253] [INSPIRE].ADSCrossRefGoogle Scholar
  29. [29]
    C. Kounnas, D. Lüst and N. Toumbas, R 2 inflation from scale invariant supergravity and anomaly free superstrings with fluxes, Fortsch. Phys. 63 (2015) 12 [arXiv:1409.7076] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  30. [30]
    A. Achúcarro, P. Ortiz and K. Sousa, A new class of de Sitter vacua in string theory compactifications, Phys. Rev. D 94 (2016) 086012 [arXiv:1510.01273] [INSPIRE].ADSMathSciNetGoogle Scholar
  31. [31]
    M. Cicoli, F. Quevedo and R. Valandro, De Sitter from T-branes, JHEP 03 (2016) 141 [arXiv:1512.04558] [INSPIRE].ADSCrossRefGoogle Scholar
  32. [32]
    I. Ben-Dayan, S. Jing, A. Westphal and C. Wieck, Accidental inflation from Kähler uplifting, JCAP 03 (2014) 054 [arXiv:1309.0529] [INSPIRE].ADSCrossRefGoogle Scholar
  33. [33]
    R. Blumenhagen et al., A flux-scaling scenario for high-scale moduli stabilization in string theory, Nucl. Phys. B 897 (2015) 500 [arXiv:1503.07634] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  34. [34]
    R. Blumenhagen, C. Damian, A. Font, D. Herschmann and R. Sun, The flux-scaling scenario: de Sitter uplift and axion inflation, Fortsch. Phys. 64 (2016) 536 [arXiv:1510.01522] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  35. [35]
    Y. Sumitomo and S.-H. Henry Tye, A stringy mechanism for a small cosmological constant, JCAP 08 (2012) 032 [arXiv:1204.5177] [INSPIRE].ADSCrossRefGoogle Scholar
  36. [36]
    Y. Sumitomo and S.-H. Henry Tye, A stringy mechanism for a small cosmological constantmulti-moduli cases, JCAP 02 (2013) 006 [arXiv:1209.5086] [INSPIRE].ADSCrossRefGoogle Scholar
  37. [37]
    S.-H. Henry Tye and S.S.C. Wong, Linking light scalar modes with a small positive cosmological constant in string theory, JHEP 06 (2017) 094 [arXiv:1611.05786] [INSPIRE].MathSciNetGoogle Scholar
  38. [38]
    G.W. Gibbons, Aspects of supergravity theories, in Supersymmetry, supergravity and related topics, F. del Aguila, J.A. de Azcárraga and L.E. Ibáñez eds., World Scientific, (1985), pg. 346 [INSPIRE].
  39. [39]
    B. de Wit, D.J. Smit and N.D. Hari Dass, Residual supersymmetry of compactified D = 10 supergravity, Nucl. Phys. B 283 (1987) 165 [INSPIRE].ADSCrossRefGoogle Scholar
  40. [40]
    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
  41. [41]
    M.P. Hertzberg, S. Kachru, W. Taylor and M. Tegmark, Inflationary constraints on type IIA string theory, JHEP 12 (2007) 095 [arXiv:0711.2512] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  42. [42]
    E. Silverstein, Simple de Sitter solutions, Phys. Rev. D 77 (2008) 106006 [arXiv:0712.1196] [INSPIRE].ADSMathSciNetGoogle Scholar
  43. [43]
    S.S. Haque, G. Shiu, B. Underwood and T. Van Riet, Minimal simple de Sitter solutions, Phys. Rev. D 79 (2009) 086005 [arXiv:0810.5328] [INSPIRE].ADSMathSciNetGoogle Scholar
  44. [44]
    P.J. Steinhardt and D. Wesley, Dark energy, inflation and extra dimensions, Phys. Rev. D 79 (2009) 104026 [arXiv:0811.1614] [INSPIRE].ADSGoogle Scholar
  45. [45]
    C. Caviezel, P. Koerber, S. Körs, D. Lüst, T. Wrase and M. Zagermann, On the cosmology of type IIA compactifications on SU(3)-structure manifolds, JHEP 04 (2009) 010 [arXiv:0812.3551] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  46. [46]
    R. Flauger, S. Paban, D. Robbins and T. Wrase, Searching for slow-roll moduli inflation in massive type IIA supergravity with metric fluxes, Phys. Rev. D 79 (2009) 086011 [arXiv:0812.3886] [INSPIRE].ADSGoogle Scholar
  47. [47]
    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
  48. [48]
    C. Caviezel, T. Wrase and M. Zagermann, Moduli stabilization and cosmology of type IIB on SU(2)-structure orientifolds, JHEP 04 (2010) 011 [arXiv:0912.3287] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  49. [49]
    T. Wrase and M. Zagermann, On classical de Sitter vacua in string theory, Fortsch. Phys. 58 (2010) 906 [arXiv:1003.0029] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  50. [50]
    T. Van Riet, On classical de Sitter solutions in higher dimensions, Class. Quant. Grav. 29 (2012) 055001 [arXiv:1111.3154] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  51. [51]
    D. Andriot and J. Blåbäck, Refining the boundaries of the classical de Sitter landscape, JHEP 03 (2017) 102 [Erratum ibid. 03 (2018) 083] [arXiv:1609.00385] [INSPIRE].
  52. [52]
    S.R. Green, E.J. Martinec, C. Quigley and S. Sethi, Constraints on string cosmology, Class. Quant. Grav. 29 (2012) 075006 [arXiv:1110.0545] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  53. [53]
    F.F. Gautason, D. Junghans and M. Zagermann, On cosmological constants from α-corrections, JHEP 06 (2012) 029 [arXiv:1204.0807] [INSPIRE].ADSCrossRefGoogle Scholar
  54. [54]
    D. Kutasov, T. Maxfield, I. Melnikov and S. Sethi, Constraining de Sitter space in string theory, Phys. Rev. Lett. 115 (2015) 071305 [arXiv:1504.00056] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  55. [55]
    C. Quigley, Gaugino condensation and the cosmological constant, JHEP 06 (2015) 104 [arXiv:1504.00652] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  56. [56]
    F. Denef and M.R. Douglas, Distributions of nonsupersymmetric flux vacua, JHEP 03 (2005) 061 [hep-th/0411183] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  57. [57]
    D. Marsh, L. McAllister and T. Wrase, The wasteland of random supergravities, JHEP 03 (2012) 102 [arXiv:1112.3034] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  58. [58]
    X. Chen, G. Shiu, Y. Sumitomo and S.-H. Henry Tye, A global view on the search for de Sitter vacua in (type IIA) string theory, JHEP 04 (2012) 026 [arXiv:1112.3338] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  59. [59]
    T.C. Bachlechner, D. Marsh, L. McAllister and T. Wrase, Supersymmetric vacua in random supergravity, JHEP 01 (2013) 136 [arXiv:1207.2763] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  60. [60]
    U.H. Danielsson, P. Koerber and T. Van Riet, Universal de Sitter solutions at tree-level, JHEP 05 (2010) 090 [arXiv:1003.3590] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  61. [61]
    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].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  62. [62]
    G. Shiu and Y. Sumitomo, Stability constraints on classical de Sitter vacua, JHEP 09 (2011) 052 [arXiv:1107.2925] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  63. [63]
    U.H. Danielsson, G. Shiu, T. Van Riet and T. Wrase, A note on obstinate tachyons in classical dS solutions, JHEP 03 (2013) 138 [arXiv:1212.5178] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  64. [64]
    L. Covi, M. Gómez-Reino, C. Gross, J. Louis, G.A. Palma and C.A. Scrucca, De Sitter vacua in no-scale supergravities and Calabi-Yau string models, JHEP 06 (2008) 057 [arXiv:0804.1073] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  65. [65]
    L. Covi, M. Gomez-Reino, C. Gross, J. Louis, G.A. Palma and C.A. Scrucca, Constraints on modular inflation in supergravity and string theory, JHEP 08 (2008) 055 [arXiv:0805.3290] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  66. [66]
    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] [INSPIRE].ADSMathSciNetGoogle Scholar
  67. [67]
    M. Gomez-Reino and C.A. Scrucca, Locally stable non-supersymmetric Minkowski vacua in supergravity, JHEP 05 (2006) 015 [hep-th/0602246] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  68. [68]
    M. Gomez-Reino and C.A. Scrucca, Constraints for the existence of flat and stable non-supersymmetric vacua in supergravity, JHEP 09 (2006) 008 [hep-th/0606273] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  69. [69]
    M. Gomez-Reino and C.A. Scrucca, Metastable supergravity vacua with F and D supersymmetry breaking, JHEP 08 (2007) 091 [arXiv:0706.2785] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  70. [70]
    I. Ben-Dayan, R. Brustein and S.P. de Alwis, Models of modular inflation and their phenomenological consequences, JCAP 07 (2008) 011 [arXiv:0802.3160] [INSPIRE].ADSCrossRefGoogle Scholar
  71. [71]
    M. Badziak and M. Olechowski, Volume modulus inflation and a low scale of SUSY breaking, JCAP 07 (2008) 021 [arXiv:0802.1014] [INSPIRE].ADSCrossRefGoogle Scholar
  72. [72]
    A. Hetz and G.A. Palma, Sound speed of primordial fluctuations in supergravity inflation, Phys. Rev. Lett. 117 (2016) 101301 [arXiv:1601.05457] [INSPIRE].ADSCrossRefGoogle Scholar
  73. [73]
    D. Junghans, Tachyons in classical de Sitter vacua, JHEP 06 (2016) 132 [arXiv:1603.08939] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  74. [74]
    E. Cremmer, S. Ferrara, C. Kounnas and D.V. Nanopoulos, Naturally vanishing cosmological constant in N = 1 supergravity, Phys. Lett. B 133 (1983) 61 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  75. [75]
    J.R. Ellis, A.B. Lahanas, D.V. Nanopoulos and K. Tamvakis, No-scale supersymmetric Standard Model, Phys. Lett. B 134 (1984) 429 [INSPIRE].ADSCrossRefGoogle Scholar
  76. [76]
    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
  77. [77]
    P.G. Camara and M. Graña, No-scale supersymmetry breaking vacua and soft terms with torsion, JHEP 02 (2008) 017 [arXiv:0710.4577] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  78. [78]
    E. Palti, G. Tasinato and J. Ward, Weakly-coupled IIA flux compactifications, JHEP 06 (2008) 084 [arXiv:0804.1248] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  79. [79]
    J. Blåbäck, U.H. Danielsson, D. Junghans, T. Van Riet, T. Wrase and M. Zagermann, Smeared versus localised sources in flux compactifications, JHEP 12 (2010) 043 [arXiv:1009.1877] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  80. [80]
    D. Andriot, J. Blåbäck and T. Van Riet, Minkowski flux vacua of type-II supergravities, Phys. Rev. Lett. 118 (2017) 011603 [Erratum ibid. 120 (2018) 169901] [arXiv:1609.00729] [INSPIRE].
  81. [81]
    K. Becker, M. Becker, M. Haack and J. Louis, Supersymmetry breaking and αcorrections to flux induced potentials, JHEP 06 (2002) 060 [hep-th/0204254] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  82. [82]
    F. Bonetti and M. Weissenbacher, The Euler characteristic correction to the Kähler potentialrevisited, JHEP 01 (2017) 003 [arXiv:1608.01300] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  83. [83]
    M. Berg, M. Haack and E. Pajer, Jumping through loops: on soft terms from large volume compactifications, JHEP 09 (2007) 031 [arXiv:0704.0737] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  84. [84]
    M. Cicoli, J.P. Conlon and F. Quevedo, Systematics of string loop corrections in type IIB Calabi-Yau flux compactifications, JHEP 01 (2008) 052 [arXiv:0708.1873] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  85. [85]
    T. House and E. Palti, Effective action of (massive) IIA on manifolds with SU(3) structure, Phys. Rev. D 72 (2005) 026004 [hep-th/0505177] [INSPIRE].ADSMathSciNetGoogle Scholar
  86. [86]
    M. Graña, J. Louis and D. Waldram, Hitchin functionals in N = 2 supergravity, JHEP 01 (2006) 008 [hep-th/0505264] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  87. [87]
    M. Graña, J. Louis and D. Waldram, SU(3) × SU(3) compactification and mirror duals of magnetic fluxes, JHEP 04 (2007) 101 [hep-th/0612237] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  88. [88]
    I. Benmachiche and T.W. Grimm, Generalized N = 1 orientifold compactifications and the Hitchin functionals, Nucl. Phys. B 748 (2006) 200 [hep-th/0602241] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  89. [89]
    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
  90. [90]
    O. DeWolfe, A. Giryavets, S. Kachru and W. Taylor, Type IIA moduli stabilization, JHEP 07 (2005) 066 [hep-th/0505160] [INSPIRE].ADSMathSciNetGoogle Scholar
  91. [91]
    G. Villadoro and F. Zwirner, Beyond twisted tori, Phys. Lett. B 652 (2007) 118 [arXiv:0706.3049] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  92. [92]
    R. Kallosh and T. Wrase, Emergence of spontaneously broken supersymmetry on an anti-D3-brane in KKLT dS vacua, JHEP 12 (2014) 117 [arXiv:1411.1121] [INSPIRE].ADSCrossRefGoogle Scholar
  93. [93]
    E.A. Bergshoeff, K. Dasgupta, R. Kallosh, A. Van Proeyen and T. Wrase, \( \overline{\mathrm{D}3} \) and dS, JHEP 05 (2015) 058 [arXiv:1502.07627] [INSPIRE].ADSCrossRefGoogle Scholar

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© The Author(s) 2018

Authors and Affiliations

  1. 1.Arnold-Sommerfeld-Center für Theoretische Physik, Department für PhysikLudwig-Maximilians-Universität MünchenMünchenGermany
  2. 2.Institut für Theoretische PhysikLeibniz Universität HannoverHannoverGermany
  3. 3.Riemann Center for Geometry and PhysicsLeibniz Universität HannoverHannoverGermany

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