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Abstract

F-theory is a non-perturbative formulation of type IIB superstring theory which allows for the decoupling of gravity and for the formulation of GUT theories based on the gauge group E 6. In this paper we explore F-theory models in which the low energy supersymmetric theory contains the particle content of three 27 dimensional representations of the underlying E 6 gauge group, plus two extra right-handed neutrinos predicted from F and D flatness. The resulting TeV scale effective theory resembles either the E6SSM or the NMSSM+, depending on whether an additional Abelian gauge group does or does not survive. However there are novel features compared to both these models as follows: (i) If the additional Abelian gauge group is unbroken then it can have a weaker gauge coupling than in the E6SSM; (ii) If the additional Abelian gauge group is broken then non-perturbative effects can violate the scale invariance of the NMSSM+ leading to a generalised model; (iii) Unification is achieved not at the field theory level but at the F-theory level since the gauge couplings are split by flux effects, negating the need for any additional doublet states which are usually required; (iv) Proton decay is suppressed by the geometric coupling suppression of a singlet state, a mechanism peculiar to F-theory, which effectively suppresses the coupling of the exotic charge −1/3 colour triplet state D to quarks and leptons; (v) The \( \overline{D} \) decays as a chiral leptoquark with couplings to left-handed quarks and leptons, providing characteristic and striking signatures at the LHC.

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References

  1. H. Georgi and S. Glashow, Unity of all elementary particle forces, Phys. Rev. Lett. 32 (1974) 438 [INSPIRE].

    Article  ADS  Google Scholar 

  2. J.J. Heckman, A. Tavanfar and C. Vafa, The point of E 8 in F-theory GUTs, JHEP 08 (2010) 040 [arXiv:0906.0581] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  3. R. Donagi and M. Wijnholt, Model building with F-theory, Adv. Theor. Math. Phys. 15 (2011) 1237 [arXiv:0802.2969] [INSPIRE].

    Article  MathSciNet  MATH  Google Scholar 

  4. C. Beasley, J.J. Heckman and C. Vafa, GUTs and exceptional branes in F-theoryI, JHEP 01 (2009) 058 [arXiv:0802.3391] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  5. R. Donagi and M. Wijnholt, Breaking GUT groups in F-theory, Adv. Theor. Math. Phys. 15 (2011) 1523 [arXiv:0808.2223] [INSPIRE].

    Article  MathSciNet  MATH  Google Scholar 

  6. C. Beasley, J.J. Heckman and C. Vafa, GUTs and exceptional branes in F-theoryII: experimental predictions, JHEP 01 (2009) 059 [arXiv:0806.0102] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  7. R. Blumenhagen, T.W. Grimm, B. Jurke and T. Weigand, Global F-theory GUTs, Nucl. Phys. B 829 (2010) 325 [arXiv:0908.1784] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  8. 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 

  9. B. Andreas and G. Curio, From local to global in F-theory model building, J. Geom. Phys. 60 (2010) 1089 [arXiv:0902.4143] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  10. E. Dudas and E. Palti, Froggatt-Nielsen models from E 8 in F-theory GUTs, JHEP 01 (2010) 127 [arXiv:0912.0853] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  11. E. Dudas and E. Palti, On hypercharge flux and exotics in F-theory GUTs, JHEP 09 (2010) 013 [arXiv:1007.1297] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  12. S.F. King, G. Leontaris and G. Ross, Family symmetries in F-theory GUTs, Nucl. Phys. B 838 (2010) 119 [arXiv:1005.1025] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  13. J.C. Callaghan, S.F. King, G.K. Leontaris and G.G. Ross, Towards a realistic F-theory GUT, JHEP 04 (2012) 094 [arXiv:1109.1399] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  14. C. Lüdeling, H.P. Nilles and C.C. Stephan, The potential fate of local model building, Phys. Rev. D 83 (2011) 086008 [arXiv:1101.3346] [INSPIRE].

    ADS  Google Scholar 

  15. S.F. King, S. Moretti and R. Nevzorov, Theory and phenomenology of an exceptional supersymmetric standard model, Phys. Rev. D 73 (2006) 035009 [hep-ph/0510419] [INSPIRE].

    ADS  Google Scholar 

  16. S.F. King, S. Moretti and R. Nevzorov, Exceptional supersymmetric standard model, Phys. Lett. B 634 (2006) 278 [hep-ph/0511256] [INSPIRE].

    Article  ADS  Google Scholar 

  17. S.F. King, S. Moretti and R. Nevzorov, Gauge coupling unification in the exceptional supersymmetric standard model, Phys. Lett. B 650 (2007) 57 [hep-ph/0701064] [INSPIRE].

    Article  ADS  Google Scholar 

  18. R. Howl and S.F. King, Minimal E 6 supersymmetric standard model, JHEP 01 (2008) 030 [arXiv:0708.1451] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  19. R. Howl and S.F. King, Planck scale unification in a supersymmetric standard model, Phys. Lett. B 652 (2007) 331 [arXiv:0705.0301] [INSPIRE].

    Article  ADS  Google Scholar 

  20. J.P. Hall and S.F. King, Neutralino dark matter with inert higgsinos and singlinos, JHEP 08 (2009) 088 [arXiv:0905.2696] [INSPIRE].

    Article  ADS  Google Scholar 

  21. J.P. Hall and S.F. King, NMSSM+, JHEP 01 (2013) 076 [arXiv:1209.4657] [INSPIRE].

    Article  ADS  Google Scholar 

  22. M. Kuntzler and S. Schäfer-Nameki, G-flux and spectral divisors, JHEP 11 (2012) 025 [arXiv:1205.5688] [INSPIRE].

    Article  ADS  Google Scholar 

  23. M. Cvetič, R. Donagi, J. Halverson and J. Marsano, On seven-brane dependent instanton prefactors in F-theory, JHEP 11 (2012) 004 [arXiv:1209.4906] [INSPIRE].

    Article  ADS  Google Scholar 

  24. C.-M. Chen and Y.-C. Chung, On F-theory E 6 GUTs, JHEP 03 (2011) 129 [arXiv:1010.5536] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  25. J.J. Heckman, F-theory and experiment, Contemp. Phys. 51 (2010) 331.

    Article  ADS  Google Scholar 

  26. 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] [INSPIRE].

    Article  ADS  Google Scholar 

  27. G.K. Leontaris, Aspects of F-theory GUTs, PoS (CORFU2011) 095 [arXiv:1203.6277] [INSPIRE].

  28. S. Katz, D.R. Morrison, S. Schäfer-Nameki and J. Sully, Tates algorithm and F-theory, JHEP 08 (2011) 094 [arXiv:1106.3854] [INSPIRE].

    Article  ADS  Google Scholar 

  29. J. Tate, Algorithm for determining the type of a singular fiber in an elliptic pencil, in Modular functions of one variable IV, Lect. Notes Math. 476 (1975) 33, Springer-Verlag, Berlin Germany (1975).

  30. M. Bershadsky et al., Geometric singularities and enhanced gauge symmetries, Nucl. Phys. B 481 (1996) 215 [hep-th/9605200] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  31. M. Cvetič, I. Garcia-Etxebarria and J. Halverson, Global F-theory models: instantons and gauge dynamics, JHEP 01 (2011) 073 [arXiv:1003.5337] [INSPIRE].

    Article  ADS  Google Scholar 

  32. S. Cecotti, C. Cordova, J.J. Heckman and C. Vafa, T-branes and monodromy, JHEP 07 (2011) 030 [arXiv:1010.5780] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  33. G. Leontaris and G. Ross, Yukawa couplings and fermion mass structure in F-theory GUTs, JHEP 02 (2011) 108 [arXiv:1009.6000] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  34. R. Donagi and M. Wijnholt, Higgs bundles and UV completion in F-theory, arXiv:0904.1218 [INSPIRE].

  35. J. Marsano, N. Saulina and S. Schäfer-Nameki, Monodromies, fluxes and compact three-generation F-theory GUTs, JHEP 08 (2009) 046 [arXiv:0906.4672] [INSPIRE].

    Article  ADS  Google Scholar 

  36. K.-S. Choi, SU(3) × SU(2) × U(1) vacua in F-theory, Nucl. Phys. B 842 (2011) 1 [arXiv:1007.3843] [INSPIRE].

    Article  ADS  Google Scholar 

  37. J. Marsano, Hypercharge flux, exotics and anomaly cancellation in F-theory GUTs, Phys. Rev. Lett. 106 (2011) 081601 [arXiv:1011.2212] [INSPIRE].

    Article  ADS  Google Scholar 

  38. T.W. Grimm and T. Weigand, On Abelian gauge symmetries and proton decay in global F-theory GUTs, Phys. Rev. D 82 (2010) 086009 [arXiv:1006.0226] [INSPIRE].

    ADS  Google Scholar 

  39. P.G. Camara, E. Dudas and E. Palti, Massive wavefunctions, proton decay and FCNCs in local F-theory GUTs, JHEP 12 (2011) 112 [arXiv:1110.2206] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  40. L. Aparicio, A. Font, L.E. Ibáñez and F. Marchesano, Flux and instanton effects in local F-theory models and hierarchical fermion masses, JHEP 08 (2011) 152 [arXiv:1104.2609] [INSPIRE].

    Article  ADS  Google Scholar 

  41. S. Cecotti, M.C. Cheng, J.J. Heckman and C. Vafa, Yukawa couplings in F-theory and non-commutative geometry, arXiv:0910.0477 [INSPIRE].

  42. S.F. King, Large mixing angle MSW and atmospheric neutrinos from single right-handed neutrino dominance and U(1) family symmetry, Nucl. Phys. B 576 (2000) 85 [hep-ph/9912492] [INSPIRE].

    Article  ADS  Google Scholar 

  43. S.F. King, Neutrino mass models, Rept. Prog. Phys. 67 (2004) 107 [hep-ph/0310204] [INSPIRE].

    Article  ADS  Google Scholar 

  44. R. Blumenhagen, Gauge coupling unification in F-theory grand unified theories, Phys. Rev. Lett. 102 (2009) 071601 [arXiv:0812.0248] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  45. 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] [INSPIRE].

    ADS  Google Scholar 

  46. G. Leontaris and N. Tracas, Gauge coupling flux thresholds, exotic matter and the unification scale in F-SU(5) GUT, Eur. Phys. J. C 67 (2010) 489 [arXiv:0912.1557] [INSPIRE].

    Article  ADS  Google Scholar 

  47. G. Leontaris, N. Tracas and G. Tsamis, Unification, KK-thresholds and the top Yukawa coupling in F-theory GUTs, Eur. Phys. J. C 71 (2011) 1768 [arXiv:1102.5244] [INSPIRE].

    Article  ADS  Google Scholar 

  48. G. Leontaris and N. Vlachos, On the GUT scale of F-theory SU(5), Phys. Lett. B 704 (2011) 620 [arXiv:1105.1858] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  49. J.R. Ellis, K. Enqvist, D.V. Nanopoulos and K. Tamvakis, Gaugino masses and grand unification, Phys. Lett. B 155 (1985) 381 [INSPIRE].

    Article  ADS  Google Scholar 

  50. H. Georgi, Lie algebras in particle physics, Westview press, U.S.A. (1999).

  51. H. Murayama and D. Kaplan, Family symmetries and proton decay, Phys. Lett. B 336 (1994) 221 [hep-ph/9406423] [INSPIRE].

    Article  ADS  Google Scholar 

  52. K. Babu, J.C. Pati and F. Wilczek, Fermion masses, neutrino oscillations and proton decay in the light of Super-Kamiokande, Nucl. Phys. B 566 (2000) 33 [hep-ph/9812538] [INSPIRE].

    Article  ADS  Google Scholar 

  53. T. Goto and T. Nihei, Effect of RRRR dimension five operator on the proton decay in the minimal SU(5) SUGRA GUT model, Phys. Rev. D 59 (1999) 115009 [hep-ph/9808255] [INSPIRE].

    ADS  Google Scholar 

  54. R. Dermisek, A. Mafi and S. Raby, SUSY GUTs under siege: proton decay, Phys. Rev. D 63 (2001) 035001 [hep-ph/0007213] [INSPIRE].

    ADS  Google Scholar 

  55. H. Murayama and A. Pierce, Not even decoupling can save minimal supersymmetric SU(5), Phys. Rev. D 65 (2002) 055009 [hep-ph/0108104] [INSPIRE].

    ADS  Google Scholar 

  56. U. Ellwanger, C. Hugonie and A.M. Teixeira, The next-to-minimal supersymmetric standard model, Phys. Rept. 496 (2010) 1 [arXiv:0910.1785] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  57. S.F. King and P. White, Nonminimal supersymmetric Higgs bosons at LEP-2, Phys. Rev. D 53 (1996) 4049 [hep-ph/9508346] [INSPIRE].

    ADS  Google Scholar 

  58. 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].

    Article  ADS  Google Scholar 

  59. E. Palti, A note on hypercharge flux, anomalies and U(1)s in F-theory GUTs, arXiv:1209.4421 [INSPIRE].

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Correspondence to James C. Callaghan.

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ArXiv ePrint: 1210.6913

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Callaghan, J.C., King, S.F. E6 models from F-theory. J. High Energ. Phys. 2013, 34 (2013). https://doi.org/10.1007/JHEP04(2013)034

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