Journal of High Energy Physics

, 2014:71 | Cite as

Sequestered de Sitter string scenarios: soft-terms

  • Luis Aparicio
  • Michele Cicoli
  • Sven Krippendorf
  • Anshuman Maharana
  • Francesco Muia
  • Fernando Quevedo
Open Access
Regular Article - Theoretical Physics


We analyse soft supersymmetry breaking in type IIB de Sitter string vacua after moduli stabilisation, focussing on models in which the Standard Model is sequestered from the supersymmetry breaking sources and the spectrum of soft-terms is hierarchically smaller than the gravitino mass m 3/2. Due to this feature, these models are compatible with gauge coupling unification and TeV scale supersymmetry with no cosmological moduli problem. We determine the influence on soft-terms of concrete realisations of de Sitter vacua constructed from supersymmetric effective actions. One of these scenarios provides the first study of soft-terms for consistent string models embedded in a compact Calabi-Yau manifold with all moduli stabilised. Depending on the moduli dependence of the Kähler metric for matter fields and on the mechanism responsible to obtain a de Sitter vacuum, we find two scenarios for phenomenology: (i) a split-supersymmetry scenario where gaugino masses are suppressed with respect to scalar masses: M 1/2m 3/2 ϵm 0m 3/2 \( \sqrt{\epsilon } \)m 3/2 for ϵm 3/2 /M P ≪ 1; (ii) a typical MSSM scenario where all soft-terms are of the same order: M 1/2m 0m 3/2 ϵm 3/2. Background fluxes determine the numerical coefficients of the soft-terms allowing for small variations of parameters as is necessary to confront data and to interpolate between different scenarios. We comment on different stringy origins of the μ-term and potential sources of desequestering.


Strings and branes phenomenology 


Open Access

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  1. [1]
    N. Craig, The state of supersymmetry after run I of the LHC, arXiv:1309.0528 [INSPIRE].
  2. [2]
    R. Kitano and Y. Nomura, Dark matter before the LHC in a natural supersymmetric standard model, Phys. Lett. B 632 (2006) 162 [hep-ph/0509221] [INSPIRE].
  3. [3]
    M. Papucci, J.T. Ruderman and A. Weiler, Natural SUSY endures, JHEP 09 (2012) 035 [arXiv:1110.6926] [INSPIRE].ADSCrossRefGoogle Scholar
  4. [4]
    C. Brust, A. Katz, S. Lawrence and R. Sundrum, SUSY, the third generation and the LHC, JHEP 03 (2012) 103 [arXiv:1110.6670] [INSPIRE].ADSCrossRefGoogle Scholar
  5. [5]
    O. Lebedev, H.P. Nilles and M. Ratz, A note on fine-tuning in mirage mediation, hep-ph/0511320 [INSPIRE].
  6. [6]
    T.J. LeCompte and S.P. Martin, Large Hadron Collider reach for supersymmetric models with compressed mass spectra, Phys. Rev. D 84 (2011) 015004 [arXiv:1105.4304] [INSPIRE].ADSGoogle Scholar
  7. [7]
    B.C. Allanach and B. Gripaios, Hide and seek with natural supersymmetry at the LHC, JHEP 05 (2012) 062 [arXiv:1202.6616] [INSPIRE].ADSCrossRefGoogle Scholar
  8. [8]
    J.A. Evans and Y. Kats, LHC coverage of RPV MSSM with light stops, JHEP 04 (2013) 028 [arXiv:1209.0764] [INSPIRE].ADSCrossRefGoogle Scholar
  9. [9]
    G.G. Ross, K. Schmidt-Hoberg and F. Staub, The generalised NMSSM at one loop: fine tuning and phenomenology, JHEP 08 (2012) 074 [arXiv:1205.1509] [INSPIRE].ADSCrossRefGoogle Scholar
  10. [10]
    R. Bousso and J. Polchinski, Quantization of four form fluxes and dynamical neutralization of the cosmological constant, JHEP 06 (2000) 006 [hep-th/0004134] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  11. [11]
    N. Arkani-Hamed and S. Dimopoulos, Supersymmetric unification without low energy supersymmetry and signatures for fine-tuning at the LHC, JHEP 06 (2005) 073 [hep-th/0405159] [INSPIRE].ADSCrossRefGoogle Scholar
  12. [12]
    S. Krippendorf, H.P. Nilles, M. Ratz and M.W. Winkler, Hidden SUSY from precision gauge unification, Phys. Rev. D 88 (2013) 035022 [arXiv:1306.0574] [INSPIRE].ADSGoogle Scholar
  13. [13]
    S. Krippendorf, H.P. Nilles, M. Ratz and M.W. Winkler, The heterotic string yields natural supersymmetry, Phys. Lett. B 712 (2012) 87 [arXiv:1201.4857] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  14. [14]
    M. Badziak, S. Krippendorf, H.P. Nilles and M.W. Winkler, The heterotic MiniLandscape and the 126 GeV Higgs boson, JHEP 03 (2013) 094 [arXiv:1212.0854] [INSPIRE].ADSCrossRefGoogle Scholar
  15. [15]
    BICEP2 collaboration, P.A.R. Ade et al., Detection of B-mode polarization at degree angular scales by BICEP2, Phys. Rev. Lett. 112 (2014) 241101 [arXiv:1403.3985] [INSPIRE].ADSCrossRefGoogle Scholar
  16. [16]
    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] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  17. [17]
    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].ADSCrossRefMathSciNetGoogle Scholar
  18. [18]
    J.P. Conlon and F. Quevedo, Gaugino and scalar masses in the landscape, JHEP 06 (2006) 029 [hep-th/0605141] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  19. [19]
    J.P. Conlon, S.S. AbdusSalam, F. Quevedo and K. Suruliz, Soft SUSY breaking terms for chiral matter in IIB string compactifications, JHEP 01 (2007) 032 [hep-th/0610129] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  20. [20]
    V. Lowen and H.P. Nilles, Mirage pattern from the heterotic string, Phys. Rev. D 77 (2008) 106007 [arXiv:0802.1137] [INSPIRE].ADSMathSciNetGoogle Scholar
  21. [21]
    S.P. de Alwis, Classical and quantum SUSY breaking effects in IIB local models, JHEP 03 (2010) 078 [arXiv:0912.2950] [INSPIRE].CrossRefGoogle Scholar
  22. [22]
    M. Cicoli, S. de Alwis and A. Westphal, Heterotic moduli stabilisation, JHEP 10 (2013) 199 [arXiv:1304.1809] [INSPIRE].ADSCrossRefGoogle Scholar
  23. [23]
    B.S. Acharya, K. Bobkov, G.L. Kane, J. Shao and P. Kumar, The G 2 -MSSM: an M-theory motivated model of particle physics, Phys. Rev. D 78 (2008) 065038 [arXiv:0801.0478] [INSPIRE].ADSGoogle Scholar
  24. [24]
    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].ADSCrossRefMathSciNetGoogle Scholar
  25. [25]
    M. Cicoli, C. Mayrhofer and R. Valandro, Moduli stabilisation for chiral global models, JHEP 02 (2012) 062 [arXiv:1110.3333] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  26. [26]
    M. Cicoli, S. Krippendorf, C. Mayrhofer, F. Quevedo and R. Valandro, D-branes at del Pezzo singularities: global embedding and moduli stabilisation, JHEP 09 (2012) 019 [arXiv:1206.5237] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  27. [27]
    M. Cicoli, S. Krippendorf, C. Mayrhofer, F. Quevedo and R. Valandro, D3/D7 branes at singularities: constraints from global embedding and moduli stabilisation, JHEP 07 (2013) 150 [arXiv:1304.0022] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  28. [28]
    M. Cicoli et al., Explicit de Sitter flux vacua for global string models with chiral matter, JHEP 05 (2014) 001 [arXiv:1312.0014] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  29. [29]
    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
  30. [30]
    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].ADSCrossRefMathSciNetGoogle Scholar
  31. [31]
    G. Aldazabal, L.E. Ibáñez, F. Quevedo and A.M. Uranga, D-branes at singularities: a bottom up approach to the string embedding of the standard model, JHEP 08 (2000) 002 [hep-th/0005067] [INSPIRE].ADSCrossRefGoogle Scholar
  32. [32]
    R. Blumenhagen, S. Moster and E. Plauschinn, Moduli stabilisation versus chirality for MSSM like type IIB orientifolds, JHEP 01 (2008) 058 [arXiv:0711.3389] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  33. [33]
    R. Blumenhagen, J.P. Conlon, S. Krippendorf, S. Moster and F. Quevedo, SUSY breaking in local string/F-theory models, JHEP 09 (2009) 007 [arXiv:0906.3297] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  34. [34]
    J.P. Conlon and F.G. Pedro, Moduli redefinitions and moduli stabilisation, JHEP 06 (2010) 082 [arXiv:1003.0388] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  35. [35]
    K. Choi, H.P. Nilles, C.S. Shin and M. Trapletti, Sparticle spectrum of large volume compactification, JHEP 02 (2011) 047 [arXiv:1011.0999] [INSPIRE].ADSCrossRefGoogle Scholar
  36. [36]
    C.S. Shin, Anomalous U(1) mediation in large volume compactification, JHEP 01 (2012) 084 [arXiv:1108.5740] [INSPIRE].ADSCrossRefGoogle Scholar
  37. [37]
    G.D. Coughlan, W. Fischler, E.W. Kolb, S. Raby and G.G. Ross, Cosmological problems for the Polonyi potential, Phys. Lett. B 131 (1983) 59 [INSPIRE].ADSCrossRefGoogle Scholar
  38. [38]
    T. Banks, D.B. Kaplan and A.E. Nelson, Cosmological implications of dynamical supersymmetry breaking, Phys. Rev. D 49 (1994) 779 [hep-ph/9308292] [INSPIRE].ADSGoogle Scholar
  39. [39]
    B. de Carlos, J.A. Casas, F. Quevedo and E. Roulet, Model independent properties and cosmological implications of the dilaton and moduli sectors of 4D strings, Phys. Lett. B 318 (1993) 447 [hep-ph/9308325] [INSPIRE].ADSCrossRefGoogle Scholar
  40. [40]
    G. Aldazabal, L.E. Ibáñez and F. Quevedo, A D brane alternative to the MSSM, JHEP 02 (2000) 015 [hep-ph/0001083] [INSPIRE].ADSCrossRefGoogle Scholar
  41. [41]
    M.J. Dolan, S. Krippendorf and F. Quevedo, Towards a systematic construction of realistic D-brane models on a del Pezzo singularity, JHEP 10 (2011) 024 [arXiv:1106.6039] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  42. [42]
    J.P. Conlon, C.H. Kom, K. Suruliz, B.C. Allanach and F. Quevedo, Sparticle spectra and LHC signatures for large volume string compactifications, JHEP 08 (2007) 061 [arXiv:0704.3403] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  43. [43]
    J.P. Conlon, Gauge threshold corrections for local string models, JHEP 04 (2009) 059 [arXiv:0901.4350] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  44. [44]
    J.P. Conlon and E. Palti, Gauge threshold corrections for local orientifolds, JHEP 09 (2009) 019 [arXiv:0906.1920] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  45. [45]
    M. Berg, D. Marsh, L. McAllister and E. Pajer, Sequestering in string compactifications, JHEP 06 (2011) 134 [arXiv:1012.1858] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  46. [46]
    J.P. Conlon and L.T. Witkowski, Scattering and sequestering of blow-up moduli in local string models, JHEP 12 (2011) 028 [arXiv:1109.4153] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  47. [47]
    M. Berg, J.P. Conlon, D. Marsh and L.T. Witkowski, Superpotential de-sequestering in string models, JHEP 02 (2013) 018 [arXiv:1207.1103] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  48. [48]
    S. Krippendorf and F. Quevedo, Metastable SUSY breaking, de Sitter moduli stabilisation and Kähler moduli inflation, JHEP 11 (2009) 039 [arXiv:0901.0683] [INSPIRE].ADSCrossRefGoogle Scholar
  49. [49]
    L. Aparicio, M. Cicoli, S. Krippendorf, A. Maharana, F. Muia and F. Quevedo, Sequestered de Sitter string models: LHC phenomenology, to appear.Google Scholar
  50. [50]
    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].ADSCrossRefMathSciNetGoogle Scholar
  51. [51]
    S. Gukov, C. Vafa and E. Witten, CFT’s from Calabi-Yau four folds, Nucl. Phys. B 584 (2000) 69 [Erratum ibid. B 608 (2001) 477] [hep-th/9906070] [INSPIRE].
  52. [52]
    D. Baumann et al., On D3-brane potentials in compactifications with fluxes and wrapped D-branes, JHEP 11 (2006) 031 [hep-th/0607050] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  53. [53]
    J.P. Conlon, A. Maharana and F. Quevedo, Towards realistic string vacua, JHEP 05 (2009) 109 [arXiv:0810.5660] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  54. [54]
    J.P. Conlon, Mirror mediation, JHEP 03 (2008) 025 [arXiv:0710.0873] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  55. [55]
    P.G. Camara, L.E. Ibáñez and I. Valenzuela, The string origin of SUSY flavor violation, JHEP 10 (2013) 092 [arXiv:1307.3104] [INSPIRE].ADSCrossRefGoogle Scholar
  56. [56]
    M. Cicoli, M. Goodsell, J. Jaeckel and A. Ringwald, Testing string vacua in the lab: from a hidden CMB to dark forces in flux compactifications, JHEP 07 (2011) 114 [arXiv:1103.3705] [INSPIRE].ADSCrossRefGoogle Scholar
  57. [57]
    J.P. Conlon, D. Cremades and F. Quevedo, Kähler potentials of chiral matter fields for Calabi-Yau string compactifications, JHEP 01 (2007) 022 [hep-th/0609180] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  58. [58]
    L. Aparicio, D.G. Cerdeno and L.E. Ibáñez, Modulus-dominated SUSY-breaking soft terms in F-theory and their test at LHC, JHEP 07 (2008) 099 [arXiv:0805.2943] [INSPIRE].ADSCrossRefGoogle Scholar
  59. [59]
    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
  60. [60]
    A. Brignole, L.E. Ibáñez and C. Muñoz, Towards a theory of soft terms for the supersymmetric standard model, Nucl. Phys. B 422 (1994) 125 [Erratum ibid. B 436 (1995) 747] [hep-ph/9308271] [INSPIRE].
  61. [61]
    E. Dudas and S.K. Vempati, Large D-terms, hierarchical soft spectra and moduli stabilisation, Nucl. Phys. B 727 (2005) 139 [hep-th/0506172] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  62. [62]
    J.E. Kim and H.P. Nilles, The μ problem and the strong CP problem, Phys. Lett. B 138 (1984) 150 [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  63. [63]
    G.F. Giudice and A. Masiero, A natural solution to the μ problem in supergravity theories, Phys. Lett. B 206 (1988) 480 [INSPIRE].ADSCrossRefGoogle Scholar
  64. [64]
    G. Lopes Cardoso, D. Lüst and T. Mohaupt, Moduli spaces and target space duality symmetries in (0, 2) Z N orbifold theories with continuous Wilson lines, Nucl. Phys. B 432 (1994) 68 [hep-th/9405002] [INSPIRE].ADSCrossRefGoogle Scholar
  65. [65]
    I. Antoniadis, E. Gava, K.S. Narain and T.R. Taylor, Effective μ term in superstring theory, Nucl. Phys. B 432 (1994) 187 [hep-th/9405024] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  66. [66]
    A. Brignole, L.E. Ibáñez, C. Muñoz and C. Scheich, Some issues in soft SUSY breaking terms from dilaton/moduli sectors, Z. Phys. C 74 (1997) 157 [hep-ph/9508258] [INSPIRE].Google Scholar
  67. [67]
    A. Brignole, L.E. Ibáñez and C. Muñoz, Orbifold induced μ term and electroweak symmetry breaking, Phys. Lett. B 387 (1996) 769 [hep-ph/9607405] [INSPIRE].ADSCrossRefGoogle Scholar
  68. [68]
    A. Hebecker, A.K. Knochel and T. Weigand, A shift symmetry in the Higgs sector: experimental hints and stringy realizations, JHEP 06 (2012) 093 [arXiv:1204.2551] [INSPIRE].ADSCrossRefGoogle Scholar
  69. [69]
    L.E. Ibáñez and A.M. Uranga, Instanton induced open string superpotentials and branes at singularities, JHEP 02 (2008) 103 [arXiv:0711.1316] [INSPIRE].ADSCrossRefGoogle Scholar
  70. [70]
    D. Berenstein, C.P. Herzog, P. Ouyang and S. Pinansky, Supersymmetry breaking from a Calabi-Yau singularity, JHEP 09 (2005) 084 [hep-th/0505029] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  71. [71]
    M. Graña, MSSM parameters from supergravity backgrounds, Phys. Rev. D 67 (2003) 066006 [hep-th/0209200] [INSPIRE].ADSGoogle Scholar
  72. [72]
    P.G. Camara, L.E. Ibáñez and A.M. Uranga, Flux induced SUSY breaking soft terms, Nucl. Phys. B 689 (2004) 195 [hep-th/0311241] [INSPIRE].ADSCrossRefGoogle Scholar
  73. [73]
    M. Graña, T.W. Grimm, H. Jockers and J. Louis, Soft supersymmetry breaking in Calabi-Yau orientifolds with D-branes and fluxes, Nucl. Phys. B 690 (2004) 21 [hep-th/0312232] [INSPIRE].ADSCrossRefGoogle Scholar
  74. [74]
    M. Schmaltz and W. Skiba, Minimal gaugino mediation, Phys. Rev. D 62 (2000) 095005 [hep-ph/0001172] [INSPIRE].ADSGoogle Scholar
  75. [75]
    T.T. Yanagida and N. Yokozaki, Focus point in gaugino mediation — reconsideration of the fine-tuning problem, Phys. Lett. B 722 (2013) 355 [arXiv:1301.1137] [INSPIRE].ADSCrossRefGoogle Scholar
  76. [76]
    H. Baer, V. Barger, P. Huang and X. Tata, Natural supersymmetry: LHC, dark matter and ILC searches, JHEP 05 (2012) 109 [arXiv:1203.5539] [INSPIRE].ADSCrossRefGoogle Scholar
  77. [77]
    O. Loaiza-Brito, J. Martin, H.P. Nilles and M. Ratz, log(M Pl /m 3/2), AIP Conf. Proc. 805 (2006) 198 [hep-th/0509158] [INSPIRE].ADSCrossRefGoogle Scholar
  78. [78]
    K. Choi, K.S. Jeong, T. Kobayashi and K.-I. Okumura, Little SUSY hierarchy in mixed modulus-anomaly mediation, Phys. Lett. B 633 (2006) 355 [hep-ph/0508029] [INSPIRE].ADSCrossRefGoogle Scholar
  79. [79]
    C.P. Burgess, A. Maharana and F. Quevedo, Über-naturalness: unexpectedly light scalars from supersymmetric extra dimensions, JHEP 05 (2011) 010 [arXiv:1005.1199] [INSPIRE].ADSCrossRefGoogle Scholar
  80. [80]
    J.R. Ellis, A.B. Lahanas, D.V. Nanopoulos, M. Quirós and F. Zwirner, Supersymmetry breaking in the observable sector of superstring models, Phys. Lett. B 188 (1987) 408 [INSPIRE].ADSCrossRefGoogle Scholar
  81. [81]
    I. Antoniadis and M. Quirós, Supersymmetry breaking in M-theory and gaugino condensation, Nucl. Phys. B 505 (1997) 109 [hep-th/9705037] [INSPIRE].ADSCrossRefGoogle Scholar
  82. [82]
    J.Y. Lee, Gaugino masses from gravitino at one loop, arXiv:1302.5846 [INSPIRE].
  83. [83]
    J.A. Bagger, T. Moroi and E. Poppitz, Anomaly mediation in supergravity theories, JHEP 04 (2000) 009 [hep-th/9911029] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  84. [84]
    S.P. de Alwis, On anomaly mediated SUSY breaking, Phys. Rev. D 77 (2008) 105020 [arXiv:0801.0578] [INSPIRE].ADSGoogle Scholar
  85. [85]
    J.P. Conlon, M. Goodsell and E. Palti, Anomaly mediation in superstring theory, Fortsch. Phys. 59 (2011) 5 [arXiv:1008.4361] [INSPIRE].ADSCrossRefzbMATHMathSciNetGoogle Scholar
  86. [86]
    T.W. Grimm, J. Keitel, R. Savelli and M. Weissenbacher, From M-theory higher curvature terms to α corrections in F-theory, arXiv:1312.1376 [INSPIRE].
  87. [87]
    D. Junghans and G. Shiu, Brane curvature corrections to the \( \mathcal{N} \) =1 type II/F-theory effective action, arXiv:1407.0019 [INSPIRE].
  88. [88]
    S. Krippendorf, M.J. Dolan, A. Maharana and F. Quevedo, D-branes at toric singularities: model building, Yukawa couplings and flavour physics, JHEP 06 (2010) 092 [arXiv:1002.1790] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  89. [89]
    A. Maharana, Symmetry breaking bulk effects in local D-brane models, JHEP 06 (2012) 002 [arXiv:1111.3047] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar

Copyright information

© The Author(s) 2014

Authors and Affiliations

  • Luis Aparicio
    • 1
  • Michele Cicoli
    • 1
    • 2
    • 3
  • Sven Krippendorf
    • 4
  • Anshuman Maharana
    • 5
  • Francesco Muia
    • 2
    • 3
  • Fernando Quevedo
    • 1
    • 6
  1. 1.ICTPTriesteItaly
  2. 2.Dipartimento di Fisica e AstronomiaUniversità di BolognaBolognaItaly
  3. 3.INFN, Sezione di BolognaBolognaItaly
  4. 4.Bethe Center for Theoretical Physics and Physikalisches Institut der Universität BonnBonnGermany
  5. 5.Harish Chandra Research InstituteAllahabadIndia
  6. 6.DAMTP, Centre for Mathematical SciencesCambridgeU.K.

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