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D-branes at del Pezzo singularities: global embedding and moduli stabilisation

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Abstract

In the context of type IIB string theory we combine moduli stabilisation and model building on branes at del Pezzo singularities in a fully consistent global compactification. By means of toric geometry, we classify all the Calabi-Yau manifolds with 3 < h 1,1 < 6 which admit two identical del Pezzo singularities mapped into each other under the orientifold involution. This effective singularity hosts the visible sector containing the Standard Model while the Kähler moduli are stabilised via a combination of D-terms, perturbative and non-perturbative effects supported on hidden sectors. We present concrete models where the visible sector, containing the Standard Model, gauge and matter content, is built via fractional D3-branes at del Pezzo singularities and all the Kähler moduli are fixed providing an explicit realisation of both KKLT and LARGE volume scenarios, the latter with D-term uplifting to de Sitter minima. We perform the consistency checks for global embedding such as tadpole, K-theory charges and Freed-Witten anomaly cancellation. We briefly discuss phenomenological and cosmological implications of our models.

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References

  1. L.E. Ibáñez and A.M. Uranga, String theory and particle physics: an introduction to string phenomenology, Cambridge University Press, Cambridge U.K. (2012) [INSPIRE].

    MATH  Google Scholar 

  2. 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].

    Article  ADS  Google Scholar 

  3. D. Berenstein, V. Jejjala and R.G. Leigh, The standard model on a D-brane, Phys. Rev. Lett. 88 (2002) 071602 [hep-ph/0105042] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  4. G. Aldazabal, L.E. Ibáñez and F. Quevedo, A D-brane alternative to the MSSM, JHEP 02 (2000) 015 [hep-ph/0001083] [INSPIRE].

    Article  ADS  Google Scholar 

  5. J. Cascales, M. Garcia del Moral, F. Quevedo and A.M. Uranga, Realistic D-brane models on warped throats: fluxes, hierarchies and moduli stabilization, JHEP 02 (2004) 031 [hep-th/0312051] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  6. H. Verlinde and M. Wijnholt, Building the standard model on a D3-brane, JHEP 01 (2007) 106 [hep-th/0508089] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  7. J.P. Conlon, A. Maharana and F. Quevedo, Towards realistic string vacua, JHEP 05 (2009) 109 [arXiv:0810.5660] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  8. 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].

    Article  MathSciNet  ADS  Google Scholar 

  9. 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].

    Article  MathSciNet  ADS  Google Scholar 

  10. C. Vafa, Geometry of grand unification, arXiv:0911.3008 [INSPIRE].

  11. J.J. Heckman, Particle physics implications of F-theory, Ann. Rev. Nucl. Part. Sci. 60 (2010) 237 [arXiv:1001.0577] [INSPIRE].

    Article  ADS  Google Scholar 

  12. T. Weigand, Lectures on F-theory compactifications and model building, Class. Quant. Grav. 27 (2010) 214004 [arXiv:1009.3497] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  13. S.B. Giddings, S. Kachru and J. Polchinski, Hierarchies from fluxes in string compactifications, Phys. Rev. D 66 (2002) 106006 [hep-th/0105097] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  14. 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].

    MathSciNet  ADS  Google Scholar 

  15. 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].

    Article  MathSciNet  ADS  Google Scholar 

  16. M. Cicoli and F. Quevedo, String moduli inflation: an overview, Class. Quant. Grav. 28 (2011) 204001 [arXiv:1108.2659] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  17. C. Burgess and L. McAllister, Challenges for string cosmology, Class. Quant. Grav. 28 (2011) 204002 [arXiv:1108.2660] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  18. 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].

    Article  MathSciNet  ADS  Google Scholar 

  19. 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].

    Article  MathSciNet  ADS  Google Scholar 

  20. R. Blumenhagen, V. Braun, T.W. Grimm and T. Weigand, GUTs in type IIB orientifold compactifications, Nucl. Phys. B 815 (2009) 1 [arXiv:0811.2936] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  21. 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].

    Article  MathSciNet  ADS  Google Scholar 

  22. M. Cicoli, M. Kreuzer and C. Mayrhofer, Toric K3-fibred Calabi-Yau manifolds with del Pezzo divisors for string compactifications, JHEP 02 (2012) 002 [arXiv:1107.0383] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  23. M. Cicoli, C. Mayrhofer and R. Valandro, Moduli stabilisation for chiral global models, JHEP 02 (2012) 062 [arXiv:1110.3333] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  24. D.-E. Diaconescu, B. Florea, S. Kachru and P. Svrček, Gauge: mediated supersymmetry breaking in string compactifications, JHEP 02 (2006) 020 [hep-th/0512170] [INSPIRE].

    Article  ADS  Google Scholar 

  25. M. Buican, D. Malyshev, D.R. Morrison, H. Verlinde and M. Wijnholt, D-branes at singularities, compactification and hypercharge, JHEP 01 (2007) 107 [hep-th/0610007] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  26. V. Balasubramanian, P. Berglund, V. Braun and I. Garcia-Etxebarria, Global embeddings for branes at toric singularities, arXiv:1201.5379 [INSPIRE].

  27. M. Kreuzer and H. Skarke, Complete classification of reflexive polyhedra in four-dimensions, Adv. Theor. Math. Phys. 4 (2002) 1209 [hep-th/0002240] [INSPIRE].

    MathSciNet  Google Scholar 

  28. M. Cicoli, C. Burgess and F. Quevedo, Fibre inflation: observable gravity waves from IIB string compactifications, JCAP 03 (2009) 013 [arXiv:0808.0691] [INSPIRE].

    Article  ADS  Google Scholar 

  29. C. Burgess et al., Non-standard primordial fluctuations and nonGaussianity in string inflation, JHEP 08 (2010) 045 [arXiv:1005.4840] [INSPIRE].

    Article  ADS  Google Scholar 

  30. M. Cicoli, F.G. Pedro and G. Tasinato, Poly-instanton inflation, JCAP 12 (2011) 022 [arXiv:1110.6182] [INSPIRE].

    Article  ADS  Google Scholar 

  31. M. Cicoli, G. Tasinato, I. Zavala, C. Burgess and F. Quevedo, Modulated reheating and large non-Gaussianity in string cosmology, JCAP 05 (2012) 039 [arXiv:1202.4580] [INSPIRE].

    Article  ADS  Google Scholar 

  32. M. Cicoli, F.G. Pedro and G. Tasinato, Natural quintessence in string theory, JCAP 07 (2012) 044 [arXiv:1203.6655] [INSPIRE].

    Article  ADS  Google Scholar 

  33. M. Cicoli, C. Burgess and F. Quevedo, Anisotropic modulus stabilisation: strings at LHC scales with micron-sized extra dimensions, JHEP 10 (2011) 119 [arXiv:1105.2107] [INSPIRE].

    Article  ADS  Google Scholar 

  34. M. Yamazaki, Brane tilings and their applications, Fortschr. Phys. 56 (2008) 555 [arXiv:0803.4474] [INSPIRE].

    Article  MathSciNet  MATH  Google Scholar 

  35. D. Malyshev and H. Verlinde, D-branes at singularities and string phenomenology, Nucl. Phys. Proc. Suppl. 171 (2007) 139 [arXiv:0711.2451] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  36. M. Kreuzer, Toric geometry and Calabi-Yau compactifications, Ukr. J. Phys. 55 (2010) 613 [hep-th/0612307] [INSPIRE].

    Google Scholar 

  37. H. Skarke, String dualities and toric geometry: an introduction, hep-th/9806059 [INSPIRE].

  38. F. Denef, Les Houches lectures on constructing string vacua, arXiv:0803.1194 [INSPIRE].

  39. http://hep.itp.tuwien.ac.at/~kreuzer/CY/.

  40. 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].

    Article  MathSciNet  ADS  Google Scholar 

  41. 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].

    Article  MathSciNet  ADS  Google Scholar 

  42. E. Witten, D-branes and k-theory, JHEP 12 (1998) 019 [hep-th/9810188] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  43. G.W. Moore and E. Witten, Selfduality, Ramond-Ramond fields and k-theory, JHEP 05 (2000) 032 [hep-th/9912279] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  44. A.M. Uranga, D-brane probes, RR tadpole cancellation and k-theory charge, Nucl. Phys. B 598 (2001) 225 [hep-th/0011048] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  45. E. Witten, An SU(2) anomaly, Phys. Lett. B 117 (1982) 324 [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  46. D.S. Freed and E. Witten, Anomalies in string theory with D-branes, Asian J. Math 3 (1999) 819 [hep-th/9907189] [INSPIRE].

    MathSciNet  MATH  Google Scholar 

  47. M. Kreuzer and H. Skarke, PALP: a package for analyzing lattice polytopes with applications to toric geometry, Comput. Phys. Commun. 157 (2004) 87 [math/0204356] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  48. A.P. Braun and N.-O. Walliser, A new offspring of PALP, arXiv:1106.4529 [INSPIRE].

  49. A.P. Braun, J. Knapp, E. Scheidegger, H. Skarke and N.-O. Walliser, PALP — a user manual, arXiv:1205.4147 [INSPIRE].

  50. V. Braun and A.Y. Novoseltsev, Toric varieties framework for Sage, http://www.sagemath.org/doc/reference/sage/schemes/toric/variety.html.

  51. D.-E. Diaconescu and J. Gomis, Fractional branes and boundary states in orbifold theories, JHEP 10 (2000) 001 [hep-th/9906242] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  52. L. Martucci, D-branes on general N = 1 backgrounds: superpotentials and D-terms, JHEP 06 (2006) 033 [hep-th/0602129] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  53. M. Bianchi, A. Collinucci and L. Martucci, Magnetized E3-brane instantons in F-theory, JHEP 12 (2011) 045 [arXiv:1107.3732] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  54. A. Collinucci, F. Denef and M. Esole, D-brane deconstructions in IIB orientifolds, JHEP 02 (2009) 005 [arXiv:0805.1573] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  55. C. Burgess, S. Krippendorf, A. Maharana and F. Quevedo, Radiative fermion masses in local D-brane models, JHEP 05 (2011) 103 [arXiv:1102.1973] [INSPIRE].

    Article  ADS  Google Scholar 

  56. A. Maharana, Symmetry breaking bulk effects in local D-brane models, arXiv:1111.3047 [INSPIRE].

  57. M. Wijnholt, Parameter space of quiver gauge theories, hep-th/0512122 [INSPIRE].

  58. A. Butti et al., On the geometry and the moduli space of beta-deformed quiver gauge theories, JHEP 07 (2008) 053 [arXiv:0712.1215] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  59. D. Baumann et al., On D3-brane potentials in compactifications with fluxes and wrapped D-branes, JHEP 11 (2006) 031 [hep-th/0607050] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  60. 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].

    Article  MathSciNet  ADS  Google Scholar 

  61. S.P. Martin, A supersymmetry primer, hep-ph/9709356 [INSPIRE].

  62. K. Becker, M. Becker, M. Haack and J. Louis, Supersymmetry breaking and α′ corrections to flux induced potentials, JHEP 06 (2002) 060 [hep-th/0204254] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  63. 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].

    Article  MathSciNet  ADS  Google Scholar 

  64. 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].

    Article  MathSciNet  ADS  Google Scholar 

  65. M. Cicoli, A. Maharana, F. Quevedo and C. Burgess, De Sitter string vacua from dilaton-dependent non-perturbative effects, JHEP 06 (2012) 011 [arXiv:1203.1750] [INSPIRE].

    Article  ADS  Google Scholar 

  66. D. Cremades, M.-P. Garcia del Moral, F. Quevedo and K. Suruliz, Moduli stabilisation and de Sitter string vacua from magnetised D7 branes, JHEP 05 (2007) 100 [hep-th/0701154] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  67. S. Krippendorf and F. Quevedo, Metastable SUSY breaking, de Sitter moduli stabilisation and Kähler moduli inflation, JHEP 11 (2009) 039 [arXiv:0901.0683] [INSPIRE].

    Article  ADS  Google Scholar 

  68. L. Aparicio, D. 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].

    Article  ADS  Google Scholar 

  69. M. Goodsell, J. Jaeckel, J. Redondo and A. Ringwald, Naturally light hidden photons in LARGE volume string compactifications, JHEP 11 (2009) 027 [arXiv:0909.0515] [INSPIRE].

    Article  ADS  Google Scholar 

  70. 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].

    Article  ADS  Google Scholar 

  71. J.P. Conlon and F. Quevedo, Gaugino and scalar masses in the landscape, JHEP 06 (2006) 029 [hep-th/0605141] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  72. 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].

    Article  MathSciNet  ADS  Google Scholar 

  73. S. de Alwis, Classical and quantum SUSY breaking effects in IIB local models, JHEP 03 (2010) 078 [arXiv:0912.2950] [INSPIRE].

    Article  Google Scholar 

  74. H. Baer, S. de Alwis, K. Givens, S. Rajagopalan and H. Summy, Gaugino anomaly mediated SUSY breaking: phenomenology and prospects for the LHC, JHEP 05 (2010) 069 [arXiv:1002.4633] [INSPIRE].

    Article  ADS  Google Scholar 

  75. J.P. Conlon and F.G. Pedro, Moduli redefinitions and moduli stabilisation, JHEP 06 (2010) 082 [arXiv:1003.0388] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  76. 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].

    Article  ADS  Google Scholar 

  77. M. Berg, D. Marsh, L. McAllister and E. Pajer, Sequestering in string compactifications, JHEP 06 (2011) 134 [arXiv:1012.1858] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  78. M. Cvetič, J. Halverson and P. Langacker, Singlet extensions of the MSSM in the quiver landscape, JHEP 09 (2010) 076 [arXiv:1006.3341] [INSPIRE].

    Article  ADS  Google Scholar 

  79. J.P. Conlon, Gauge threshold corrections for local string models, JHEP 04 (2009) 059 [arXiv:0901.4350] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  80. J.P. Conlon and E. Palti, Gauge threshold corrections for local orientifolds, JHEP 09 (2009) 019 [arXiv:0906.1920] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  81. S. Franco, A. Hanany, Y.-H. He and P. Kazakopoulos, Duality walls, duality trees and fractional branes, hep-th/0306092 [INSPIRE].

  82. R. Kallosh and A.D. Linde, Landscape, the scale of SUSY breaking and inflation, JHEP 12 (2004) 004 [hep-th/0411011] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  83. J.P. Conlon, R. Kallosh, A.D. Linde and F. Quevedo, Volume modulus inflation and the gravitino mass problem, JCAP 09 (2008) 011 [arXiv:0806.0809] [INSPIRE].

    Article  ADS  Google Scholar 

  84. D.-E. Diaconescu, R. Donagi and B. Florea, Metastable quivers in string compactifications, Nucl. Phys. B 774 (2007) 102 [hep-th/0701104] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  85. V.V. Batyrev, Dual polyhedra and mirror symmetry for Calabi-Yau hypersurfaces in toric varieties, J. Alg. Geom. 3 (1994) 493 [alg-geom/9310003] [INSPIRE].

    MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. ICTP, Strada Costiera 11, Trieste, 34014, Italy

    Michele Cicoli & Fernando Quevedo

  2. INFN, Sezione di Trieste, Trieste, Italy

    Michele Cicoli

  3. Bethe Center for Theoretical Physics and Physikalisches Institut der Universität Bonn, Nussallee 12, 53115, Bonn, Germany

    Sven Krippendorf

  4. Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 19, 69120, Heidelberg, Germany

    Christoph Mayrhofer

  5. DAMTP, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WA, U.K.

    Fernando Quevedo

  6. Institut für Theoretische Physik, Universität Hamburg, Luruper Chaussee 149, 22761, Hamburg, Germany

    Roberto Valandro

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  1. Michele Cicoli
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  4. Fernando Quevedo
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Correspondence to Sven Krippendorf.

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Cicoli, M., Krippendorf, S., Mayrhofer, C. et al. D-branes at del Pezzo singularities: global embedding and moduli stabilisation. J. High Energ. Phys. 2012, 19 (2012). https://doi.org/10.1007/JHEP09(2012)019

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