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Journal of High Energy Physics

, 2013:32 | Cite as

New examples of flux vacua

  • Travis Maxfield
  • Jock McOrist
  • Daniel Robbins
  • Savdeep SethiEmail author
Article

Abstract

Type IIB toroidal orientifolds are among the earliest examples of flux vacua. By applying T-duality, we construct the first examples of massive IIA flux vacua with Minkowski space-times, along with new examples of type IIA flux vacua. The backgrounds are surprisingly simple with no four-form flux at all. They serve as illustrations of the ingredients needed to build type IIA and massive IIA solutions with scale separation. To check that these backgrounds are actually solutions, we formulate the complete set of type II supergravity equations of motion in a very useful form that treats the R-R fields democratically.

Keywords

Flux compactifications D-branes Supergravity Models Superstring Vacua 

References

  1. [1]
    G.W. Gibbons, Aspects of supergravity theories, three lectures given at GIFT Seminar on Theoretical Physics, June 4-11, San Feliu de Guixols, Spain (1984).Google Scholar
  2. [2]
    K. Dasgupta, G. Rajesh and S. Sethi, M theory, orientifolds and G-flux, JHEP 08 (1999) 023 [hep-th/9908088] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    M.B. Schulz, Calabi-Yau duals of torus orientifolds, JHEP 05 (2006) 023 [hep-th/0412270] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  4. [4]
    M. Graña, R. Minasian, M. Petrini and A. Tomasiello, A scan for new N = 1 vacua on twisted tori, JHEP 05 (2007) 031 [hep-th/0609124] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  5. [5]
    L. Romans, Massive N = 2a supergravity in ten-dimensions, Phys. Lett. B 169 (1986) 374 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  6. [6]
    K. Behrndt and M. Cvetič, General N = 1 supersymmetric flux vacua of (massive) type IIA string theory, Phys. Rev. Lett. 95 (2005) 021601 [hep-th/0403049] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  7. [7]
    A. Tomasiello, New string vacua from twistor spaces, Phys. Rev. D 78 (2008) 046007 [arXiv:0712.1396] [INSPIRE].ADSMathSciNetGoogle Scholar
  8. [8]
    M. Petrini and A. Zaffaroni, N = 2 solutions of massive type IIA and their Chern-Simons duals, JHEP 09 (2009) 107 [arXiv:0904.4915] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  9. [9]
    D. Lüst and D. Tsimpis, New supersymmetric AdS 4 type-II vacua, JHEP 09 (2009) 098 [arXiv:0906.2561] [INSPIRE].CrossRefGoogle Scholar
  10. [10]
    D. Tsimpis, Supersymmetric AdS vacua and separation of scales, JHEP 08 (2012) 142 [arXiv:1206.5900] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  11. [11]
    J. McOrist and S. Sethi, M-theory and type IIA flux compactifications, JHEP 12 (2012) 122 [arXiv:1208.0261] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  12. [12]
    M.R. Garousi, T-duality of curvature terms in D-brane actions, JHEP 02 (2010) 002 [arXiv:0911.0255] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  13. [13]
    M.R. Garousi and M. Mir, On RR couplings on D-branes at order O(α ′2), JHEP 02 (2011) 008 [arXiv:1012.2747] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  14. [14]
    M.R. Garousi, Ramond-Ramond field strength couplings on D-branes, JHEP 03 (2010) 126 [arXiv:1002.0903] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  15. [15]
    K. Becker, G. Guo and D. Robbins, Higher derivative brane couplings from T-duality, JHEP 09 (2010) 029 [arXiv:1007.0441] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  16. [16]
    M.R. Garousi, T-duality of anomalous Chern-Simons couplings, Nucl. Phys. B 852 (2011) 320 [arXiv:1007.2118] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  17. [17]
    K. Becker, G.-Y. Guo and D. Robbins, Disc amplitudes, picture changing and space-time actions, JHEP 01 (2012) 127 [arXiv:1106.3307] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  18. [18]
    K. Becker, G. Guo and D. Robbins, Four-derivative brane couplings from string amplitudes, JHEP 12 (2011) 050 [arXiv:1110.3831] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  19. [19]
    M.R. Garousi, S-duality of D-brane action at order O(α ′2), Phys. Lett. B 701 (2011) 465 [arXiv:1103.3121] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  20. [20]
    M.R. Garousi and M. Mir, Towards extending the Chern-Simons couplings at order O(α ′2), JHEP 05 (2011) 066 [arXiv:1102.5510] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  21. [21]
    A. Basu, Supersymmetry constraints on the R 4 multiplet in type IIB on T 2, Class. Quant. Grav. 28 (2011) 225018 [arXiv:1107.3353] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  22. [22]
    M.R. Garousi, T-duality of the Riemann curvature corrections to supergravity, Phys. Lett. B 718 (2013) 1481 [arXiv:1208.4459] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  23. [23]
    M.R. Garousi, Ricci curvature corrections to type-II supergravity, Phys. Rev. D 87 (2013) 025006 [arXiv:1210.4379] [INSPIRE].ADSGoogle Scholar
  24. [24]
    E. Hatefi and I. Park, Universality in all-order α corrections to BPS/non-BPS brane world volume theories, Nucl. Phys. B 864 (2012) 640 [arXiv:1205.5079] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  25. [25]
    E. Hatefi and I. Park, More on closed string induced higher derivative interactions on D-branes, Phys. Rev. D 85 (2012) 125039 [arXiv:1203.5553] [INSPIRE].ADSGoogle Scholar
  26. [26]
    E. Hatefi, On higher derivative corrections to Wess-Zumino and tachyonic actions in type-II super string theory, Phys. Rev. D 86 (2012) 046003 [arXiv:1203.1329] [INSPIRE].ADSGoogle Scholar
  27. [27]
    E. Hatefi, Shedding light on new Wess-Zumino couplings with their corrections to all orders in α , JHEP 04 (2013) 070 [arXiv:1211.2413] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  28. [28]
    E. Hatefi, All order α higher derivative corrections to non-BPS branes of type IIB Super string theory, JHEP 07 (2013) 002 [arXiv:1304.3711] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  29. [29]
    J.T. Liu and R. Minasian, Higher-derivative couplings in string theory: dualities and the B-field, arXiv:1304.3137 [INSPIRE].
  30. [30]
    H. Godazgar and M. Godazgar, Duality completion of higher derivative corrections, JHEP 09 (2013) 140 [arXiv:1306.4918] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  31. [31]
    M.R. Garousi, Ramond-Ramond corrections to type-II supergravity at order α ′3, JHEP 06 (2013) 030 [arXiv:1302.7275] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  32. [32]
    A. Basu, The structure of the \( {{\mathcal{R}}^8} \) term in type IIB string theory, Class. Quant. Grav. 30 (2013) 235028 [arXiv:1306.2501] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  33. [33]
    A. Basu, Constraining gravitational interactions in the M-theory effective action, arXiv:1308.2564 [INSPIRE].
  34. [34]
    J. Shelton, W. Taylor and B. Wecht, Nongeometric flux compactifications, JHEP 10 (2005) 085 [hep-th/0508133] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  35. [35]
    D. Lüst, F. Marchesano, L. Martucci and D. Tsimpis, Generalized non-supersymmetric flux vacua, JHEP 11 (2008) 021 [arXiv:0807.4540] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  36. [36]
    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
  37. [37]
    D. Andriot, E. Goi, R. Minasian and M. Petrini, Supersymmetry breaking branes on solvmanifolds and de Sitter vacua in string theory, JHEP 05 (2011) 028 [arXiv:1003.3774] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  38. [38]
    J. Blaback et al., Smeared versus localised sources in flux compactifications, JHEP 12 (2010) 043 [arXiv:1009.1877] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  39. [39]
    J. Blaback, B. Janssen, T. Van Riet and B. Vercnocke, Fractional branes, warped compactifications and backreacted orientifold planes, JHEP 10 (2012) 139 [arXiv:1207.0814] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  40. [40]
    C. Caviezel et al., The effective theory of type IIA AdS 4 compactifications on nilmanifolds and cosets, Class. Quant. Grav. 26 (2009) 025014 [arXiv:0806.3458] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  41. [41]
    M. Petrini, G. Solard and T. Van Riet, AdS vacua with scale separation from IIB supergravity, JHEP 11 (2013) 010 [arXiv:1308.1265] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  42. [42]
    F. Saracco and A. Tomasiello, Localized O6-plane solutions with Romans mass, JHEP 07 (2012) 077 [arXiv:1201.5378] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  43. [43]
    K. Becker and M. Becker, M theory on eight manifolds, Nucl. Phys. B 477 (1996) 155 [hep-th/9605053] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  44. [44]
    S. Kachru, M.B. Schulz and S. Trivedi, Moduli stabilization from fluxes in a simple IIB orientifold, JHEP 10 (2003) 007 [hep-th/0201028] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  45. [45]
    K. Becker and S. Sethi, Torsional heterotic geometries, Nucl. Phys. B 820 (2009) 1 [arXiv:0903.3769] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  46. [46]
    S. Sethi, C. Vafa and E. Witten, Constraints on low dimensional string compactifications, Nucl. Phys. B 480 (1996) 213 [hep-th/9606122] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  47. [47]
    E. Witten, On flux quantization in M-theory and the effective action, J. Geom. Phys. 22 (1997) 1 [hep-th/9609122] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  48. [48]
    C. Angelantonj, M. Bianchi, G. Pradisi, A. Sagnotti and Y. Stanev, Chiral asymmetry in four-dimensional open string vacua, Phys. Lett. B 385 (1996) 96 [hep-th/9606169] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  49. [49]
    A. Sen and S. Sethi, The mirror transform of type-I vacua in six-dimensions, Nucl. Phys. B 499 (1997) 45 [hep-th/9703157] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  50. [50]
    M. Berkooz et al., Anomalies, dualities and topology of D = 6 N = 1 superstring vacua, Nucl. Phys. B 475 (1996) 115 [hep-th/9605184] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  51. [51]
    M. Fukuma, T. Oota and H. Tanaka, Comments on T dualities of Ramond-Ramond potentials on tori, Prog. Theor. Phys. 103 (2000) 425 [hep-th/9907132] [INSPIRE].ADSCrossRefGoogle Scholar
  52. [52]
    E. Bergshoeff et al., New formulations of D = 10 supersymmetry and D8-O8 domain walls, Class. Quant. Grav. 18 (2001) 3359 [hep-th/0103233] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  53. [53]
    P. Koerber, Lectures on generalized complex geometry for physicists, Fortsch. Phys. 59 (2011) 169 [arXiv:1006.1536] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  54. [54]
    D. Belov and G.W. Moore, Holographic action for the self-dual field, hep-th/0605038 [INSPIRE].
  55. [55]
    D.M. Belov and G.W. Moore, Type II actions from 11-dimensional Chern-Simons theories, hep-th/0611020 [INSPIRE].
  56. [56]
    S. Fidanza, R. Minasian and A. Tomasiello, Mirror symmetric SU(3) structure manifolds with NS fluxes, Commun. Math. Phys. 254 (2005) 401 [hep-th/0311122] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  57. [57]
    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
  58. [58]
    A.R. Frey and J. Polchinski, N = 3 warped compactifications, Phys. Rev. D 65 (2002) 126009 [hep-th/0201029] [INSPIRE].ADSMathSciNetGoogle Scholar
  59. [59]
    C. Hull, Massive string theories from M-theory and F-theory, JHEP 11 (1998) 027 [hep-th/9811021] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  60. [60]
    J. Polchinski, String theory. Volume 2: superstring theory and beyond, Cambridge University Press, Cambridge U.K. (1998).Google Scholar
  61. [61]
    E. Bergshoeff, M. de Roo, M.B. Green, G. Papadopoulos and P. Townsend, Duality of type-II 7 branes and 8 branes, Nucl. Phys. B 470 (1996) 113 [hep-th/9601150] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  62. [62]
    E. Bergshoeff and M. De Roo, D-branes and T duality, Phys. Lett. B 380 (1996) 265 [hep-th/9603123] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  63. [63]
    M.B. Green, C.M. Hull and P.K. Townsend, D-brane Wess-Zumino actions, t duality and the cosmological constant, Phys. Lett. B 382 (1996) 65 [hep-th/9604119] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  64. [64]
    S. Hassan, T duality, space-time spinors and RR fields in curved backgrounds, Nucl. Phys. B 568 (2000) 145 [hep-th/9907152] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar

Copyright information

© The Author(s) 2013

Authors and Affiliations

  • Travis Maxfield
    • 1
  • Jock McOrist
    • 2
  • Daniel Robbins
    • 3
  • Savdeep Sethi
    • 1
    Email author
  1. 1.Enrico Fermi InstituteUniversity of ChicagoChicagoUnited States
  2. 2.Department of MathematicsUniversity of SurreyGuildfordUnited Kingdom
  3. 3.Institute for Theoretical PhysicsUniversity of AmsterdamAmsterdamThe Netherlands

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