Journal of High Energy Physics

, 2011:108 | Cite as

Yukawa couplings and fermion mass structure in F-theory GUTs

Open Access


The calculation of Yukawa couplings in F-theory GUTs is developed. The method is applied to the top and bottom Yukawa couplings in an SU(5) model of fermion masses based on family symmetries coming from the SU(5) factor in the underlying E(8) theory. The remaining Yukawa couplings involving the light quark generations are determined by the Froggatt Nielsen non-renormalisable terms generated by heavy messenger states. We extend the calculation of Yukawa couplings to include massive states and estimate the full up and down quark mass matrices in the SU(5) model. We discuss the new features of the resulting structure compared to what is usually assumed for Abelian family symmetry models and show how the model can give a realistic quark mass matrix structure. We extend the analysis to the neutrino sector masses and mixing where we find that tri-bi-maximal mixing is readily accommodated. Finally we discuss mechanisms for splitting the degeneracy between the charged leptons and the down quarks and the doublet triplet splitting in the Higgs sector.


F-Theory D-branes Superstring Vacua 


  1. [1]
    R. Donagi and M. Wijnholt, Model building with F-theory, arXiv:0802.2969 [SPIRES].
  2. [2]
    C. Beasley, J.J. Heckman and C. Vafa, GUTs and exceptional branes in F-theory — I, JHEP 01 (2009) 058 [arXiv:0802.3391] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  3. [3]
    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].MathSciNetADSCrossRefGoogle Scholar
  4. [4]
    R. Donagi and M. Wijnholt, Breaking GUT groups in F-theory, arXiv:0808.2223 [SPIRES].
  5. [5]
    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].MathSciNetADSCrossRefGoogle Scholar
  6. [6]
    R. Blumenhagen, T.W Grimm, B. Jurke and T. Weigand, F-theory uplifts and GUTs, JHEP 09 (2009) 053 [arXiv:0906.0013] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  7. [7]
    J.J. Heckman and C. Vafa, Flavor hierarchy from F-theory, Nucl. Phys. B 837 (2010) 137 [arXiv:0811.2417] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  8. [8]
    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].ADSCrossRefGoogle Scholar
  9. [9]
    L. Randall and D. Simmons-Duffin, Quark and lepton flavor physics from F-theory, arXiv:0904.1584 [SPIRES].
  10. [10]
    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].
  11. [11]
    J.P. Conlon and E. Palti, Aspects of flavour and supersymmetry in F-theory GUTs, JHEP 01 (2010) 029 [arXiv:0910.2413] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  12. [12]
    E. Dudas and E. Palti, Froggatt-Nielsen models from E8 in F-theory GUTs, JHEP 01 (2010) 127 [arXiv:0912.0853] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  13. [13]
    S.F. King, G.K. Leontaris and G.G. Ross, Family symmetries in F-theory GUTs, Nucl. Phys. B 838 (2010) 119 [arXiv:1005.1025] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  14. [14]
    S.H. Katz and C. Vafa, Matter from geometry, Nucl. Phys. B 497 (1997) 146 [hep-th/9606086] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  15. [15]
    R. Tatar, Y. Tsuchiya and T. Watari, Right-handed neutrinos in F-theory compactifications, Nucl. Phys. B 823 (2009) 1 [arXiv:0905.2289] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  16. [16]
    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].ADSCrossRefGoogle Scholar
  17. [17]
    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].MathSciNetADSCrossRefGoogle Scholar
  18. [18]
    F. Denef, Les Houches lectures on constructing string vacua, arXiv:0803.1194 [SPIRES].
  19. [19]
    T. Weigand, Lectures on F-theory compactifications and model building, Class. Quant. Grav. 27 (2010) 214004 [arXiv:1009.3497] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  20. [20]
    A. Strominger and E. Witten, New manifolds for superstring compactification, Commun. Math. Phys. 101 (1985) 341 [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  21. [21]
    M. Berg, M. Haack and E. Pajer, Jumping through loops: on soft terms from large volume compactifications, JHEP 09 (2007) 031 [arXiv:0704.0737] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  22. [22]
    H. Hayashi, T. Kawano, Y. Tsuchiya and T. Watari, More on dimension-4 proton decay problem in F-theory — spectral surface, discriminant locus and monodromy, Nucl. Phys. B 840 (2010) 304 [arXiv:1004.3870] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  23. [23]
    H. Hayashi, T. Kawano, Y. Tsuchiya and T. Watari, Flavor structure in F-theory compactifications, JHEP 08 (2010) 036 [arXiv:0910.2762] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  24. [24]
    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] [SPIRES].ADSGoogle Scholar
  25. [25]
    E. Kuflik and J. Marsano, Comments on flipped SU(5) (and F-theory), arXiv:1009.2510 [SPIRES].
  26. [26]
    G.F. Giudice and A. Masiero, A natural solution to the μ-problem in supergravity theories, Phys. Lett. B 206 (1988) 480 [SPIRES].ADSGoogle Scholar
  27. [27]
    D.M. Pierce, J.A. Bagger, K.T. Matchev and R.-j. Zhang, Precision corrections in the minimal supersymmetric standard model, Nucl. Phys. B 491 (1997) 3 [hep-ph/9606211] [SPIRES].ADSCrossRefGoogle Scholar
  28. [28]
    T. Blazek, S. Raby and S. Pokorski, Finite supersymmetric threshold corrections to CKM matrix elements in the large tan β regime, Phys. Rev. D 52 (1995) 4151 [hep-ph/9504364] [SPIRES].ADSGoogle Scholar
  29. [29]
    G. Ross and M. Serna, Unification and fermion mass structure, Phys. Lett. B 664 (2008) 97 [arXiv:0704.1248] [SPIRES].ADSGoogle Scholar
  30. [30]
    J. Marsano, N. Saulina and S. Schäfer-Nameki, Compact F-theory GUTs with U(1)PQ, JHEP 04 (2010) 095 [arXiv:0912.0272] [SPIRES].ADSCrossRefGoogle Scholar
  31. [31]
    V. Bouchard, J.J. Heckman, J. Seo and C. Vafa, F-theory and neutrinos: Kaluza-Klein dilution of flavor hierarchy, JHEP 01 (2010) 061 [arXiv:0904.1419] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  32. [32]
    E. Dudas and E. Palti, On hypercharge flux and exotics in F-theory GUTs, JHEP 09 (2010) 013 [arXiv:1007.1297] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  33. [33]
    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].ADSCrossRefGoogle Scholar
  34. [34]
    T.W. Grimm, The N = 1 effective action of F-theory compactifications, Nucl. Phys. B 845 (2011) 48 [arXiv:1008.4133] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  35. [35]
    R. Blumenhagen, Gauge coupling unification in F-theory grand unified theories, Phys. Rev. Lett. 102 (2009) 071601 [arXiv:0812.0248] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  36. [36]
    G.K. Leontaris and N.D. 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] [SPIRES].ADSCrossRefGoogle Scholar
  37. [37]
    W. Pokorski and G.G. Ross, Aspects of string unification, Nucl. Phys. B 526 (1998) 81 [hep-ph/9707402] [SPIRES].MathSciNetADSCrossRefGoogle Scholar

Copyright information

© The Author(s) 2011

Open Access This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

Authors and Affiliations

  1. 1.Physics Department, Theory DivisionIoannina UniversityIoanninaGreece
  2. 2.Department of PhysicsCERN Theory DivisionGeneva 23Switzerland
  3. 3.Rudolf Peierls Centre for Theoretical PhysicsUniversity of OxfordOxfordU.K.

Personalised recommendations