Advertisement

Higher-derivative supergravity and moduli stabilization

  • David CiupkeEmail author
  • Jan Louis
  • Alexander Westphal
Open Access
Regular Article - Theoretical Physics

Abstract

We review the ghost-free four-derivative terms for chiral superfields in \( \mathcal{N}=1 \) supersymmetry and supergravity. These terms induce cubic polynomial equations of motion for the chiral auxiliary fields and correct the scalar potential. We discuss the different solutions and argue that only one of them is consistent with the principles of effective field theory. Special attention is paid to the corrections along flat directions which can be stabilized or destabilized by the higher-derivative terms. We then compute these higher-derivative terms explicitly for the type IIB string compactified on a Calabi-Yau orientifold with fluxes via Kaluza-Klein reducing the (α′)3 R 4 corrections in ten dimensions for the respective \( \mathcal{N}=1 \) Kähler moduli sector. We prove that together with flux and the known (α′)3-corrections the higher-derivative term stabilizes all Calabi-Yau manifolds with positive Euler number, provided the sign of the new correction is negative.

Keywords

Flux compactifications Superstring Vacua Supersymmetric Effective Theories Supergravity Models 

Notes

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.

References

  1. [1]
    S. Cecotti, S. Ferrara and L. Girardello, Structure of the Scalar Potential in General N = 1 Higher Derivative Supergravity in Four-dimensions, Phys. Lett. B 187 (1987) 321 [INSPIRE].MathSciNetCrossRefADSGoogle Scholar
  2. [2]
    J. Khoury, J.-L. Lehners and B. Ovrut, Supersymmetric P (X, ϕ) and the Ghost Condensate, Phys. Rev. D 83 (2011) 125031 [arXiv:1012.3748] [INSPIRE].ADSGoogle Scholar
  3. [3]
    M. Koehn, J.-L. Lehners and B.A. Ovrut, Higher-Derivative Chiral Superfield Actions Coupled to N = 1 Supergravity, Phys. Rev. D 86 (2012) 085019 [arXiv:1207.3798] [INSPIRE].ADSGoogle Scholar
  4. [4]
    F. Farakos and A. Kehagias, Emerging Potentials in Higher-Derivative Gauged Chiral Models Coupled to N = 1 Supergravity, JHEP 11 (2012) 077 [arXiv:1207.4767] [INSPIRE].CrossRefADSGoogle Scholar
  5. [5]
    F. Farakos, S. Ferrara, A. Kehagias and M. Porrati, Supersymmetry Breaking by Higher Dimension Operators, Nucl. Phys. B 879 (2014) 348 [arXiv:1309.1476] [INSPIRE].MathSciNetCrossRefADSGoogle Scholar
  6. [6]
    S. Sasaki, M. Yamaguchi and D. Yokoyama, Supersymmetric DBI inflation, Phys. Lett. B 718 (2014) 1 [arXiv:1205.1353] [INSPIRE].ADSGoogle Scholar
  7. [7]
    M. Koehn, J.-L. Lehners and B.A. Ovrut, DBI Inflation in N = 1 Supergravity, Phys. Rev. D 86 (2012) 123510 [arXiv:1208.0752] [INSPIRE].ADSGoogle Scholar
  8. [8]
    F. Farakos, A. Kehagias and A. Riotto, On the Starobinsky Model of Inflation from Supergravity, Nucl. Phys. B 876 (2013) 187 [arXiv:1307.1137] [INSPIRE].MathSciNetCrossRefADSGoogle Scholar
  9. [9]
    M. Koehn, J.-L. Lehners and B.A. Ovrut, Cosmological super-bounce, Phys. Rev. D 90 (2014) 025005 [arXiv:1310.7577] [INSPIRE].ADSGoogle Scholar
  10. [10]
    R. Gwyn and J.-L. Lehners, Non-Canonical Inflation in Supergravity, JHEP 05 (2014) 050 [arXiv:1402.5120] [INSPIRE].MathSciNetCrossRefADSGoogle Scholar
  11. [11]
    I. Antoniadis, E. Dudas and D.M. Ghilencea, Supersymmetric Models with Higher Dimensional Operators, JHEP 03 (2008) 045 [arXiv:0708.0383] [INSPIRE].MathSciNetCrossRefADSGoogle Scholar
  12. [12]
    E. Dudas and D.M. Ghilencea, Effective operators in SUSY, superfield constraints and searches for a UV completion, JHEP 06 (2015) 124 [arXiv:1503.08319] [INSPIRE].MathSciNetCrossRefADSGoogle Scholar
  13. [13]
    I.L. Buchbinder, S. Kuzenko and Z. Yarevskaya, Supersymmetric effective potential: Superfield approach, Nucl. Phys. B 411 (1994) 665 [INSPIRE].CrossRefADSGoogle Scholar
  14. [14]
    A. Pickering and P.C. West, The One loop effective superpotential and nonholomorphicity, Phys. Lett. B 383 (1996) 54 [hep-th/9604147] [INSPIRE].MathSciNetCrossRefADSGoogle Scholar
  15. [15]
    S.M. Kuzenko and S.J. Tyler, The one-loop effective potential of the Wess-Zumino model revisited, JHEP 09 (2014) 135 [arXiv:1407.5270] [INSPIRE].CrossRefADSGoogle Scholar
  16. [16]
    J.Z. Simon, Higher Derivative Lagrangians, Nonlocality, Problems and Solutions, Phys. Rev. D 41 (1990) 3720 [INSPIRE].ADSGoogle Scholar
  17. [17]
    S.B. Giddings, S. Kachru and J. Polchinski, Hierarchies from fluxes in string compactifications, Phys. Rev. D 66 (2002) 106006 [hep-th/0105097] [INSPIRE].MathSciNetADSGoogle Scholar
  18. [18]
    K. Dasgupta, G. Rajesh and S. Sethi, M-theory, orientifolds and G-flux, JHEP 08 (1999) 023 [hep-th/9908088] [INSPIRE].MathSciNetCrossRefADSGoogle Scholar
  19. [19]
    K. Becker, M. Becker, M. Haack and J. Louis, Supersymmetry breaking and alpha-prime corrections to flux induced potentials, JHEP 06 (2002) 060 [hep-th/0204254] [INSPIRE].MathSciNetCrossRefADSGoogle Scholar
  20. [20]
    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].
  21. [21]
    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].MathSciNetCrossRefADSGoogle Scholar
  22. [22]
    M.R. Douglas and S. Kachru, Flux compactification, Rev. Mod. Phys. 79 (2007) 733 [hep-th/0610102] [INSPIRE].zbMATHMathSciNetCrossRefADSGoogle Scholar
  23. [23]
    F. Denef, Les Houches Lectures on Constructing String Vacua, arXiv:0803.1194 [INSPIRE].
  24. [24]
    D. Baumann and L. McAllister, Inflation and String Theory, arXiv:1404.2601.
  25. [25]
    I. Antoniadis, S. Ferrara, R. Minasian and K.S. Narain, R 4 couplings in M and type-II theories on Calabi-Yau spaces, Nucl. Phys. B 507 (1997) 571 [hep-th/9707013] [INSPIRE].MathSciNetCrossRefADSGoogle Scholar
  26. [26]
    I. Antoniadis, R. Minasian, S. Theisen and P. Vanhove, String loop corrections to the universal hypermultiplet, Class. Quant. Grav. 20 (2003) 5079 [hep-th/0307268] [INSPIRE].zbMATHMathSciNetCrossRefADSGoogle Scholar
  27. [27]
    J. Wess and J. Bagger, Supersymmetry and Supergravity, Princeton Series in Physics, Princeton University Press (1992).Google Scholar
  28. [28]
    C.P. Burgess, Introduction to Effective Field Theory, Ann. Rev. Nucl. Part. Sci. 57 (2007) 329 [hep-th/0701053] [INSPIRE].CrossRefADSGoogle Scholar
  29. [29]
    X. Jaén, J. Llosa and A. Molina, A Reduction of order two for infinite order lagrangians, Phys. Rev. D 34 (1986) 2302 [INSPIRE].ADSGoogle Scholar
  30. [30]
    A.E. Nelson and N. Seiberg, R-symmetry breaking versus supersymmetry breaking, Nucl. Phys. B 416 (1994) 46 [hep-ph/9309299] [INSPIRE].
  31. [31]
    D. Baumann and D. Green, Supergravity for Effective Theories, JHEP 03 (2012) 001 [arXiv:1109.0293] [INSPIRE].MathSciNetCrossRefADSGoogle Scholar
  32. [32]
    J.W. Burton, M.K. Gaillard and V. Jain, Effective one loop scalar lagrangian in no scale supergravity models, Phys. Rev. D 41 (1990) 3118 [INSPIRE].ADSGoogle Scholar
  33. [33]
    M. Berg, M. Haack and B. Körs, String loop corrections to Kähler potentials in orientifolds, JHEP 11 (2005) 030 [hep-th/0508043] [INSPIRE].CrossRefADSGoogle Scholar
  34. [34]
    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].MathSciNetCrossRefADSGoogle Scholar
  35. [35]
    J.P. Conlon, F. Quevedo and K. Suruliz, Large-volume flux compactifications: Moduli spectrum and D3/D7 soft supersymmetry breaking, JHEP 08 (2005) 007 [hep-th/0505076] [INSPIRE].MathSciNetCrossRefADSGoogle Scholar
  36. [36]
    T.W. Grimm, R. Savelli and M. Weissenbacher, On α corrections in N = 1 F-theory compactifications, Phys. Lett. B 725 (2013) 431 [arXiv:1303.3317] [INSPIRE].MathSciNetCrossRefADSGoogle Scholar
  37. [37]
    T.W. Grimm, J. Keitel, R. Savelli and M. Weissenbacher, From M-theory higher curvature terms to αcorrections in F-theory, arXiv:1312.1376 [INSPIRE].
  38. [38]
    D. Junghans and G. Shiu, Brane curvature corrections to the \( \mathcal{N} \) = 1 type-II/F-theory effective action, JHEP 03 (2015) 107 [arXiv:1407.0019] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  39. [39]
    A. Kehagias and H. Partouche, On the exact quartic effective action for the type IIB superstring, Phys. Lett. B 422 (1998) 109 [hep-th/9710023] [INSPIRE].MathSciNetCrossRefADSGoogle Scholar
  40. [40]
    G. Policastro and D. Tsimpis, R 4 , purified, Class. Quant. Grav. 23 (2006) 4753 [hep-th/0603165] [INSPIRE].zbMATHMathSciNetCrossRefADSGoogle Scholar
  41. [41]
    J.T. Liu and R. Minasian, Higher-derivative couplings in string theory: dualities and the B-field, Nucl. Phys. B 874 (2013) 413 [arXiv:1304.3137] [INSPIRE].MathSciNetCrossRefADSGoogle Scholar
  42. [42]
    M.B. Green, M. Gutperle and P. Vanhove, One loop in eleven-dimensions, Phys. Lett. B 409 (1997) 177 [hep-th/9706175] [INSPIRE].MathSciNetCrossRefADSGoogle Scholar
  43. [43]
    V. Balasubramanian and P. Berglund, Stringy corrections to Kähler potentials, SUSY breaking and the cosmological constant problem, JHEP 11 (2004) 085 [hep-th/0408054] [INSPIRE].MathSciNetCrossRefADSGoogle Scholar
  44. [44]
    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].MathSciNetCrossRefADSGoogle Scholar
  45. [45]
    J. Louis, M. Rummel, R. Valandro and A. Westphal, Building an explicit de Sitter, JHEP 10 (2012) 163 [arXiv:1208.3208] [INSPIRE].MathSciNetCrossRefADSGoogle Scholar
  46. [46]
    M. Berg, M. Haack and B. Körs, On volume stabilization by quantum corrections, Phys. Rev. Lett. 96 (2006) 021601 [hep-th/0508171] [INSPIRE].CrossRefADSGoogle Scholar
  47. [47]
    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] [INSPIRE].MathSciNetCrossRefADSGoogle Scholar
  48. [48]
    P. Candelas and X. de la Ossa, Moduli Space of Calabi-Yau Manifolds, Nucl. Phys. B 355 (1991) 455 [INSPIRE].CrossRefADSGoogle Scholar
  49. [49]
    M. Cicoli, J.P. Conlon, A. Maharana and F. Quevedo, A Note on the Magnitude of the Flux Superpotential, JHEP 01 (2014) 027 [arXiv:1310.6694] [INSPIRE].CrossRefADSGoogle Scholar
  50. [50]
    P. Candelas, A. Font, S.H. Katz and D.R. Morrison, Mirror symmetry for two parameter models. 2., Nucl. Phys. B 429 (1994) 626 [hep-th/9403187] [INSPIRE].MathSciNetCrossRefADSGoogle Scholar
  51. [51]
    F. Denef, M.R. Douglas and B. Florea, Building a better racetrack, JHEP 06 (2004) 034 [hep-th/0404257] [INSPIRE].MathSciNetCrossRefADSGoogle Scholar
  52. [52]
    T.W. Grimm, T.G. Pugh and M. Weissenbacher, The effective action of warped M-theory reductions with higher derivative termsPart I, arXiv:1412.5073 [INSPIRE].
  53. [53]
    L. Martucci, Warping the Kähler potential of F-theory/ IIB flux compactifications, JHEP 03 (2015) 067 [arXiv:1411.2623] [INSPIRE].MathSciNetCrossRefADSGoogle Scholar
  54. [54]
    S.A. Fulling, R.C. King, B.G. Wybourne and C.J. Cummins, Normal forms for tensor polynomials. 1: The Riemann tensor, Class. Quant. Grav. 9 (1992) 1151 [INSPIRE].
  55. [55]
    M.D. Freeman and C.N. Pope, β-functions and Superstring Compactifications, Phys. Lett. B 174 (1986) 48 [INSPIRE].
  56. [56]
    B.-Y. Chen and K. Ogiue, Some characterizations of complex space forms in terms of chern classes, Q. J. Math. 26 (1975) 459.zbMATHMathSciNetCrossRefGoogle Scholar
  57. [57]
    S. Kobayashi and K. Nomizu, Foundations of Differential Geometry: Vol. 2, Interscience Tracts in Pure and Applied Mathematics, Interscience Publishers (1969).Google Scholar
  58. [58]
    L. Covi, M. Gomez-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].

Copyright information

© The Author(s) 2015

Authors and Affiliations

  1. 1.Deutsches Elektronen-Synchrotron DESY, Theory GroupHamburgGermany
  2. 2.Fachbereich Physik der Universität HamburgHamburgGermany
  3. 3.Zentrum für Mathematische PhysikUniversität HamburgHamburgGermany

Personalised recommendations