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Abelian gauge fluxes and local models in F-theory

  • Yu-Chieh Chung
Article

Abstract

We analyze the Abelian gauge fluxes in local F-theory models with G S = SU(6) and SO(10). For the case of G S = SO(10), there is a no-go theorem which states that for an exotic-free spectrum, there are no solutions for U(1)2 gauge fluxes. We explicitly construct the U(1)2 gauge fluxes with an exotic-free bulk spectrum for the case of G S = SU(6). We also analyze the conditions for the curves supporting the given field content and discuss non-minimal spectra of the MSSM with doublet-triplet splitting.

Keywords

F-Theory GUT 

References

  1. [1]
    M.B. Green, J.H. Schwarz and E. Witten, Superstring Theory, Cambridge University Press, Cambridge U.K. (1987).MATHGoogle Scholar
  2. [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] [SPIRES].CrossRefADSGoogle Scholar
  3. [3]
    H. Verlinde and M. Wijnholt, Building the Standard Model on a D3-brane, JHEP 01 (2007) 106 [hep-th/0508089] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  4. [4]
    D. Malyshev and H. Verlinde, D-branes at Singularities and String Phenomenology, Nucl. Phys. Proc. Suppl. 171 (2007) 139 [arXiv:0711.2451] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  5. [5]
    R. Blumenhagen, M. Cvetič, P. Langacker and G. Shiu, Toward realistic intersecting D-brane models, Ann. Rev. Nucl. Part. Sci. 55 (2005) 71 [hep-th/0502005] [SPIRES].CrossRefADSGoogle Scholar
  6. [6]
    R. Blumenhagen, M. Cvetič and T. Weigand, Spacetime instanton corrections in 4D string vacua — the seesaw mechanism for D-brane models, Nucl. Phys. B 771 (2007) 113 [hep-th/0609191] [SPIRES].MATHCrossRefADSGoogle Scholar
  7. [7]
    L.E. Ibáñez and A.M. Uranga, Neutrino Majorana masses from string theory instanton effects, JHEP 03 (2007) 052 [hep-th/0609213] [SPIRES].CrossRefADSGoogle Scholar
  8. [8]
    B. Florea, S. Kachru, J. McGreevy and N. Saulina, Stringy Instantons and Quiver Gauge Theories, JHEP 05 (2007) 024 [hep-th/0610003] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  9. [9]
    R. Blumenhagen, M. Cvetič, D. Lüst, R. Richter, 2 and T. Weigand, Non-perturbative Yukawa Couplings from String Instantons, Phys. Rev. Lett. 100 (2008) 061602 [arXiv:0707.1871] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  10. [10]
    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] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  11. [11]
    C. Vafa, Evidence for F-theory, Nucl. Phys. B 469 (1996) 403 [hep-th/9602022] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  12. [12]
    D.R. Morrison and C. Vafa, Compactifications of F-theory on Calabi-Yau Threefolds — I, Nucl. Phys. B 473 (1996) 74 [hep-th/9602114] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  13. [13]
    D.R. Morrison and C. Vafa, Compactifications of F-theory on Calabi-Yau Threefolds — II, Nucl. Phys. B 476 (1996) 437 [hep-th/9603161] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  14. [14]
    F. Denef, Les Houches Lectures on Constructing String Vacua, arXiv:0803.1194 [SPIRES].
  15. [15]
    M. Bershadsky et al., Geometric singularities and enhanced gauge symmetries, Nucl. Phys. B 481 (1996) 215 [hep-th/9605200] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  16. [16]
    A. Sen, F-theory and Orientifolds, Nucl. Phys. B 475 (1996) 562 [hep-th/9605150] [SPIRES].CrossRefADSGoogle Scholar
  17. [17]
    C. Beasley, J.J. Heckman and C. Vafa, GUTs and Exceptional Branes in F-theory — I, JHEP 01 (2009) 058 [arXiv:0802.3391] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  18. [18]
    C. Beasley, J.J. Heckman and C. Vafa, GUTs and Exceptional Branes in F-theory — II: Experimental Predictions, JHEP 01 (2009) 059 [arXiv:0806.0102] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  19. [19]
    R. Donagi and M. Wijnholt, Model Building with F-theory, arXiv:0802.2969 [SPIRES].
  20. [20]
    R. Donagi and M. Wijnholt, Breaking GUT Groups in F-theory, arXiv:0808.2223 [SPIRES].
  21. [21]
    M. Wijnholt, F-Theory, GUTs and Chiral Matter, arXiv:0809.3878 [SPIRES].
  22. [22]
    J.J. Heckman and C. Vafa, F-theory, GUTs and the Weak Scale, JHEP 09 (2009) 079 [arXiv:0809.1098] [SPIRES].CrossRefGoogle Scholar
  23. [23]
    J.J. Heckman and C. Vafa, From F-theory GUTs to the LHC, arXiv:0809.3452 [SPIRES].
  24. [24]
    J.J. Heckman, G.L. Kane, J. Shao and C. Vafa, The Footprint of F-theory at the LHC, JHEP 10 (2009) 039 [arXiv:0903.3609] [SPIRES].CrossRefGoogle Scholar
  25. [25]
    J.J. Heckman, A. Tavanfar and C. Vafa, The Point of E 8 in F-theory GUTs, arXiv:0906.0581 [SPIRES].
  26. [26]
    J.J. Heckman and C. Vafa, Flavor Hierarchy From F-theory, arXiv:0811.2417 [SPIRES].
  27. [27]
    V. Bouchard, J.J. Heckman, J. Seo and C. Vafa, F-theory and Neutrinos: Kaluza-Klein Dilution of Flavor Hierarchy, arXiv:0904.1419 [SPIRES].
  28. [28]
    J.J. Heckman and C. Vafa, CP Violation and F-theory GUTs, arXiv:0904.3101 [SPIRES].
  29. [29]
    A. Font and L.E. Ibáñez, Yukawa Structure from U(1) Fluxes in F-theory Grand Unification, JHEP 02 (2009) 016 [arXiv:0811.2157] [SPIRES].CrossRefADSGoogle Scholar
  30. [30]
    A. Font and L.E. Ibáñez, Matter wave functions and Yukawa couplings in F-theory Grand Unification, JHEP 09 (2009) 036 [arXiv:0907.4895] [SPIRES].CrossRefGoogle Scholar
  31. [31]
    L. Randall and D. Simmons-Duffin, Quark and Lepton Flavor Physics from F-theory, arXiv:0904.1584 [SPIRES].
  32. [32]
    J. Jiang, T. Li, D.V. Nanopoulos and D. Xie, F-SU(5), arXiv:0811.2807 [SPIRES].
  33. [33]
    J. Jiang, T. Li, D.V. Nanopoulos and D. Xie, Flipped SU(5) × U(1)X Models from F-theory, Nucl. Phys. B 830 (2010) 195 [arXiv:0905.3394] [SPIRES].CrossRefGoogle Scholar
  34. [34]
    T. Li, SU(5) and SO(10) Models from F-theory with Natural Yukawa Couplings, arXiv:0905.4563 [SPIRES].
  35. [35]
    R. Blumenhagen, Gauge Coupling Unification in F-theory Grand Unified Theories, Phys. Rev. Lett. 102 (2009) 071601 [arXiv:0812.0248] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  36. [36]
    J.L. Bourjaily, Local Models in F-theory and M-theory with Three Generations, arXiv:0901.3785 [SPIRES].
  37. [37]
    J.L. Bourjaily, Effective Field Theories for Local Models in F-theory and M-theory, arXiv:0905.0142 [SPIRES].
  38. [38]
    C.-M. Chen and Y.-C. Chung, A Note on Local GUT Models in F-theory, Nucl. Phys. B 824 (2010) 273 [arXiv:0903.3009] [SPIRES].CrossRefGoogle Scholar
  39. [39]
    J.P. Conlon and E. Palti, On Gauge Threshold Corrections for Local IIB/F-theory GUTs, Phys. Rev. D 80 (2009) 106004 [arXiv:0907.1362] [SPIRES].Google Scholar
  40. [40]
    J.P. Conlon and E. Palti, Aspects of Flavour and Supersymmetry in F-theory GUTs, JHEP 01 (2010) 029 [arXiv:0910.2413] [SPIRES].CrossRefGoogle Scholar
  41. [41]
    S. Cecotti, M.C.N. Cheng, J.J. Heckman and C. Vafa, Yukawa Couplings in F-theory and Non-Commutative Geometry, arXiv:0910.0477 [SPIRES].
  42. [42]
    J. Marsano, N. Saulina and S. Schäfer-Nameki, F-theory Compactifications for Supersymmetric GUTs, JHEP 08 (2009) 030 [arXiv:0904.3932] [SPIRES].CrossRefADSGoogle Scholar
  43. [43]
    J. Marsano, N. Saulina and S. Schäfer-Nameki, Monodromies, Fluxes and Compact Three-Generation F-theory GUTs, JHEP 08 (2009) 046 [arXiv:0906.4672] [SPIRES].CrossRefADSGoogle Scholar
  44. [44]
    R. Donagi and M. Wijnholt, Higgs Bundles and UV Completion in F-theory, arXiv:0904.1218 [SPIRES].
  45. [45]
    C. Cordova, Decoupling Gravity in F-theory, arXiv:0910.2955 [SPIRES].
  46. [46]
    H. Hayashi, R. Tatar, Y. Toda, T. Watari and M. Yamazaki, New Aspects of Heterotic-F Theory Duality, Nucl. Phys. B 806 (2009) 224 [arXiv:0805.1057] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  47. [47]
    A. Collinucci, F. Denef and M. Esole, D-brane Deconstructions in IIB Orientifolds, JHEP 02 (2009) 005 [arXiv:0805.1573] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  48. [48]
    A.P. Braun, A. Hebecker, C. Lüdeling and R. Valandro, Fixing D7 Brane Positions by F-theory Fluxes, Nucl. Phys. B 815 (2009) 256 [arXiv:0811.2416] [SPIRES].CrossRefADSGoogle Scholar
  49. [49]
    G. Aldazabal, P.G. Camara and J.A. Rosabal, Flux algebra, Bianchi identities and Freed-Witten anomalies in F-theory compactifications, Nucl. Phys. B 814 (2009) 21 [arXiv:0811.2900] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  50. [50]
    A. Collinucci, New F-theory lifts, JHEP 08 (2009) 076 [arXiv:0812.0175] [SPIRES].CrossRefADSGoogle Scholar
  51. [51]
    B. Andreas and G. Curio, From Local to Global in F-theory Model Building, arXiv:0902.4143 [SPIRES].
  52. [52]
    R. Tatar, Y. Tsuchiya and T. Watari, Right-handed Neutrinos in F-theory Compactifications, Nucl. Phys. B 823 (2009) 1 [arXiv:0905.2289] [SPIRES].CrossRefMathSciNetGoogle Scholar
  53. [53]
    A. Collinucci, New F-theory lifts II: Permutation orientifolds and enhanced singularities, arXiv:0906.0003 [SPIRES].
  54. [54]
    R. Blumenhagen, T.W. Grimm, B. Jurke and T. Weigand, F-theory uplifts and GUTs, JHEP 09 (2009) 053 [arXiv:0906.0013] [SPIRES].CrossRefGoogle Scholar
  55. [55]
    P. Aluffi and M. Esole, New Orientifold Weak Coupling Limits in F-theory, JHEP 02 (2010) 020 [arXiv:0908.1572] [SPIRES].CrossRefGoogle Scholar
  56. [56]
    R. Blumenhagen, T.W. Grimm, B. Jurke and T. Weigand, Global F-theory GUTs, Nucl. Phys. B 829 (2010) 325 [arXiv:0908.1784] [SPIRES].CrossRefGoogle Scholar
  57. [57]
    T.W. Grimm, T.-W. Ha, A. Klemm and D. Klevers, Computing Brane and Flux Superpotentials in F-theory Compactifications, arXiv:0909.2025 [SPIRES].
  58. [58]
    K.-S. Choi, Extended Gauge Symmetries in F-theory, JHEP 02 (2010) 004 [arXiv:0910.2571] [SPIRES].CrossRefGoogle Scholar
  59. [59]
    H. Hayashi, T. Kawano, R. Tatar and T. Watari, Codimension-3 Singularities and Yukawa Couplings in F- theory, Nucl. Phys. B 823 (2009) 47 [arXiv:0901.4941] [SPIRES].CrossRefMathSciNetGoogle Scholar
  60. [60]
    H. Hayashi, T. Kawano, Y. Tsuchiya and T. Watari, Flavor Structure in F-theory Compactifications, arXiv:0910.2762 [SPIRES].
  61. [61]
    E.I. Buchbinder, Dynamically SUSY Breaking SQCD on F-theory Seven-Branes, JHEP 09 (2008) 134 [arXiv:0805.3157] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  62. [62]
    J.J. Heckman, J. Marsano, N. Saulina, S. Schäfer-Nameki and C. Vafa, Instantons and SUSY breaking in F-theory, arXiv:0808.1286 [SPIRES].
  63. [63]
    J. Marsano, N. Saulina and S. Schäfer-Nameki, Gauge Mediation in F-theory GUT Models, Phys. Rev. D 80 (2009) 046006 [arXiv:0808.1571] [SPIRES].ADSGoogle Scholar
  64. [64]
    J. Marsano, N. Saulina and S. Schäfer-Nameki, An Instanton Toolbox for F-theory Model Building, JHEP 01 (2010) 128 [arXiv:0808.2450] [SPIRES].CrossRefGoogle Scholar
  65. [65]
    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] [SPIRES].CrossRefGoogle Scholar
  66. [66]
    J.J. Heckman, A. Tavanfar and C. Vafa, Cosmology of F-theory GUTs, arXiv:0812.3155 [SPIRES].
  67. [67]
    S.H. Katz and C. Vafa, Matter from geometry, Nucl. Phys. B 497 (1997) 146 [hep-th/9606086] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  68. [68]
    S. Donaldson, Anti Self-DualYang-Mills Connections over Complex Algebraic Surfaces and Stable Vector Bundles, Proc. Lond. Math. Soc. 50 (1985) 1.MATHCrossRefMathSciNetGoogle Scholar
  69. [69]
    K. Uhlenbeck and S.-T. Yau, On the existence of Hermitian Yang-Mills connections in stable bundles, Comm. Pure App. Math. 39 (1986) 257.MATHCrossRefMathSciNetGoogle Scholar
  70. [70]
    K. Uhlenbeck and S.-T. Yau, A note on our previous paper: On the existence of Hermitian Yang-Mills connections in stable bundles, Comm. Pure App. Math. 42 (1986) 703.CrossRefMathSciNetGoogle Scholar
  71. [71]
    R. Slansky, Group Theory for Unified Model Building, Phys. Rept. 79 (1981) 1 [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  72. [72]
    M. Demazure, H. Pinkham and B. Teissier, Séminaire sur les Singularités des Surfaces, Ecole Polytechnique, 1976–1977, Springer-Verlag, New York U.S.A. (1980).CrossRefGoogle Scholar
  73. [73]
    Y.I. Manin, Cubic forms: Algebra, geometry, arithmetic, second edition, translated from the Russian by M. Hazewinkel, North-Holland Publishing Co., Amsterdam, The Netherlands (1986).MATHGoogle Scholar
  74. [74]
    R. Hartshorne, Algebraic geometry, Springer-Verlag, New York U.S.A. (1977).MATHGoogle Scholar
  75. [75]
    P. Griffith and J. Harris, Principles of Algebraic Geometry, Wiley, New York U.S.A. (1994).Google Scholar
  76. [76]
    M.F. Atiyah, N.J. Hitchin, and I.M. Singer, Self-Duality in Four-Dimensional Riemannian Geometry, Proc. Roy. Soc. Lond. A 362 (1978) 425.MathSciNetADSGoogle Scholar

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© SISSA, Trieste, Italy 2010

Authors and Affiliations

  1. 1.Department of PhysicsTexas A&M UniversityCollege StationU.S.A.

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