Skip to main content
Log in

Global SO(10) F-theory GUTs

  • Published:
Journal of High Energy Physics Aims and scope Submit manuscript

Abstract

Making use of toric geometry we construct a class of global F-theory GUT models. The base manifolds are blowups of Fano threefolds and the Calabi-Yau fourfold is a complete intersection of two hypersurfaces. We identify possible GUT divisors and construct SO(10) models on them using the spectral cover construction. We use a split spectral cover to generate chiral matter on the 10 curves in order to get more degrees of freedom in phenomenology. We use abelian flux to break SO(10) to SU(5) ×U(1) which is interpreted as a flipped SU(5) model. With the GUT Higgses in the SU(5) × U(1) model it is possible to further break the gauge symmetry to the Standard Model. We present several phenomenologically attractive examples in detail.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. R. Donagi and M. Wijnholt, Model building with F-theory, arXiv:0802.2969 [SPIRES].

  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].

    Article  MathSciNet  ADS  Google Scholar 

  3. 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].

    Article  MathSciNet  ADS  Google Scholar 

  4. 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].

    Article  MathSciNet  ADS  Google Scholar 

  5. 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].

    Article  MathSciNet  ADS  Google Scholar 

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

    Article  MATH  MathSciNet  ADS  Google Scholar 

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

  8. 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].

    Article  ADS  Google Scholar 

  9. J. Marsano, N. Saulina and S. Schäfer-Nameki, F-theory compactifications for supersymmetric GUTs, JHEP 08 (2009) 030 [arXiv:0904.3932] [SPIRES].

    Article  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  11. J. Marsano, N. Saulina and S. Schäfer-Nameki, Compact F-theory GUTs with U(1) PQ , JHEP 04 (2010) 095 [arXiv:0912.0272] [SPIRES].

    Article  ADS  Google Scholar 

  12. T.W. Grimm, S. Krause and T. Weigand, F-Theory GUT vacua on compact Calabi-Yau fourfolds, JHEP 07 (2010) 037 [arXiv:0912.3524] [SPIRES].

    Article  ADS  Google Scholar 

  13. C. Cordova, Decoupling gravity in F-theory, arXiv:0910.2955 [SPIRES].

  14. N.J. Hitchin, Stable bundles and integrable systems, Duke Math. J. 54 (1987) 91 [SPIRES].

    Article  MATH  MathSciNet  Google Scholar 

  15. R. Donagi, Spectral covers, MSRI Publications vol. 28, Cambridge University Press, Cambridge U.K. (1995).

    Google Scholar 

  16. R. Friedman, J. Morgan and E. Witten, Vector bundles and F-theory, Commun. Math. Phys. 187 (1997) 679 [hep-th/9701162] [SPIRES].

    Article  MATH  MathSciNet  ADS  Google Scholar 

  17. R.Y. Donagi, Principal bundles on elliptic fibrations, alg-geom/9702002.

  18. R. Blumenhagen, S. Moster, R. Reinbacher and T. Weigand, Massless spectra of three generation U(N) heterotic string vacua, JHEP 05 (2007) 041 [hep-th/0612039] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  19. S.M. Barr, A new symmetry breaking pattern for SO(10) and proton decay, Phys. Lett. B 112 (1982) 219 [SPIRES].

    MathSciNet  ADS  Google Scholar 

  20. J.P. Derendinger, J.E. Kim and D.V. Nanopoulos, Anti-SU(5), Phys. Lett. B 139 (1984) 170 [SPIRES].

    ADS  Google Scholar 

  21. I. Antoniadis, J.R. Ellis, J.S. Hagelin and D.V. Nanopoulos, Supersymmetric flipped SU(5) revitalized, Phys. Lett. B 194 (1987) 231 [SPIRES].

    ADS  Google Scholar 

  22. J. Jiang, T. Li, D.V. Nanopoulos and D. Xie, F-SU(5), Phys. Lett. B 677 (2009) 322 [SPIRES].

    MathSciNet  ADS  Google Scholar 

  23. 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].

    Article  MathSciNet  ADS  Google Scholar 

  24. 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].

    Article  ADS  Google Scholar 

  25. C.-M. Chen and Y.-C. Chung, Flipped SU(5) GUTs from E 8 singularity in F-theory, arXiv:1005.5728 [SPIRES].

  26. S. Mori and S. Mukai, Classifications of Fano 3-folds with b 2 ≥ 2, Man. Math 36 (1981) 147.

    Article  MATH  MathSciNet  Google Scholar 

  27. S. Mori and S. Mukai, On Fano 3-folds with b 2 ≥ 2, Adv. Stud. Pure Math. 1 (1983) 101.

    MathSciNet  Google Scholar 

  28. M. Kreuzer, On the statistics of lattice polytopes, arXiv:0809.1188 [SPIRES].

  29. 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].

    Article  MathSciNet  ADS  Google Scholar 

  30. T. Hubsch, Calabi-Yau manifolds — A bestiary for physicists, World Scientific P ublishing, Singapore (1992).

    Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  32. K. Kodaira, On compace analytic surfaces II, Ann. Math. 77 (1963) 563.

    Article  Google Scholar 

  33. J. Tate, Algorithm for determining the type of a singular fiber in an elliptic pencil, Lecture Notes in Mathematics, volume Modular functions of one variable IV , Springer, Berlin Germany (1975).

    Google Scholar 

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

    Google Scholar 

  35. V.V. Batyrev and L.A. Borisov, On Calabi-Yau complete intersections in toric varieties, alg-geom/9412017 [SPIRES].

  36. V.V. Batyrev and L.A. Borisov, Mirror duality and string-theoretic Hodge numbers, alg-geom/9509009 [SPIRES].

  37. M. Kreuzer, E. Riegler and D.A. Sahakyan, Toric complete intersections and weighted projective space, J. Geom. Phys. 46 (2003) 159 [math/0103214].

    Article  MATH  MathSciNet  ADS  Google Scholar 

  38. V.V. Batyrev, Dual polyhedra and mirror symmetry for Calabi-Yau hypersurfaces in toric varieties, J. Alg. Geom. 3 (1994) 493 [SPIRES].

    MATH  MathSciNet  Google Scholar 

  39. M. Kreuzer and H. Skarke, Reflexive polyhedra, weights and toric Calabi-Yau fibrations, Rev. Math. Phys. 14 (2002) 343 [math/0001106].

    Article  MATH  MathSciNet  Google Scholar 

  40. M. Kreuzer and H. Skarke, Calabi-Yau 4-folds and toric fibrations, J. Geom. Phys. 26 (1998) 272 [hep-th/9701175] [SPIRES].

    Article  MATH  MathSciNet  ADS  Google Scholar 

  41. A.C. Avram, M. Kreuzer, M. Mandelberg and H. Skarke, Searching for K3 fibrations, Nucl. Phys. B 494 (1997) 567 [hep-th/9610154] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  42. A. Klemm, M. Kreuzer, E. Riegler and E. Scheidegger, Topological string amplitudes, complete intersection Calabi-Yau spaces and threshold corrections, JHEP 05 (2005) 023 [hep-th/0410018] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  43. R. Donagi, Y.-H. He, B.A. Ovrut and R. Reinbacher, The particle spectrum of heterotic compactifications, JHEP 12 (2004) 054 [hep-th/0405014] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  44. S.H. Katz and C. Vafa, Matter from geometry, Nucl. Phys. B 497 (1997) 146 [hep-th/9606086] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  45. G. Curio, Chiral matter and transitions in heterotic string models, Phys. Lett. B 435 (1998) 39 [hep-th/9803224] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  46. D.-E. Diaconescu and G. Ionesei, Spectral covers, charged matter and bundle cohomology, JHEP 12 (1998) 001 [hep-th/9811129] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  47. T.W. Grimm and T. Weigand, On abelian gauge symmetries and proton decay in global F-theory GUTs, arXiv:1006.0226 [SPIRES].

  48. R. Donagi and M. Wijnholt, Breaking GUT groups in F-theory, arXiv:0808.2223 [SPIRES].

  49. 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].

    Article  MathSciNet  ADS  Google Scholar 

  50. Y.-C. Chung, Abelian gauge fluxes and local models in F-theory, JHEP 03 (2010) 006 [arXiv:0911.0427] [SPIRES].

    Article  ADS  Google Scholar 

  51. H. Hayashi, T. Kawano, Y. Tsuchiya and T. Watari, Flavor structure in F-theory compactifications, JHEP 08 (2010) 036 [arXiv:0910.2762] [SPIRES].

    Article  ADS  Google Scholar 

  52. D.V. Nanopoulos, F-enomenology, hep-ph/0211128 [SPIRES].

  53. H. Georgi and D.V. Nanopoulos, Ordinary predictions from grand principles: t quark mass in O(10), Nucl. Phys. B 155 (1979) 52 [SPIRES].

    Article  ADS  Google Scholar 

  54. J.J. Heckman, J. Marsano, N. Saulina, S. Schäfer-Nameki and C. Vafa, Instantons and SUSY breaking in F-theory, arXiv:0808.1286 [SPIRES].

  55. J. Marsano, N. Saulina and S. Schäfer-Nameki, An instanton toolbox for F-theory model building, JHEP 01 (2010) 128 [arXiv:0808.2450] [SPIRES].

    Article  ADS  Google Scholar 

  56. F. Marchesano and L. Martucci, Non-perturbative effects on seven-brane Yukawa couplings, Phys. Rev. Lett. 104 (2010) 231601 [arXiv:0910.5496] [SPIRES].

    Article  ADS  Google Scholar 

  57. M. Cvetič, I. Garcia-Etxebarria and R. Richter, Branes and instantons at angles and the F-theory lift of O(1) instantons, AIP Conf. Proc. 1200 (2010) 246 [arXiv:0911.0012] [SPIRES].

    Article  ADS  Google Scholar 

  58. R. Blumenhagen, A. Collinucci and B. Jurke, On instanton effects in F-theory, JHEP 08 (2010) 079 [arXiv:1002.1894] [SPIRES].

    Article  ADS  Google Scholar 

  59. M. Cvetič, I. Garcia-Etxebarria and J. Halverson, Global F-theory models: instantons and gauge dynamics, arXiv:1003.5337 [SPIRES].

  60. M. Alim et al., Hints for off-shell mirror symmetry in type-II/F-theory compactifications, Nucl. Phys. B 841 (2010) 303 [arXiv:0909.1842] [SPIRES].

    Article  ADS  Google Scholar 

  61. T.W. Grimm, T.-W. Ha, A. Klemm and D. Klevers, Computing brane and flux superpotentials in F-theory compactifications, JHEP 04 (2010) 015 [arXiv:0909.2025] [SPIRES].

    Article  ADS  Google Scholar 

  62. T.W. Grimm, T.-W. Ha, A. Klemm and D. Klevers, Five-brane superpotentials and heterotic/F-theory duality, Nucl. Phys. B 838 (2010) 458 [arXiv:0912.3250] [SPIRES].

    Article  ADS  Google Scholar 

  63. H. Jockers, P. Mayr and J. Walcher, On N = 14 Deffective couplings for F-theory and heterotic vacua, arXiv:0912.3265 [SPIRES].

  64. 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].

    Article  ADS  Google Scholar 

  65. J.J. Heckman and H. Verlinde, Evidence for F(uzz) theory, arXiv:1005.3033 [SPIRES].

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Christoph Mayrhofer.

Additional information

ArXiv ePrint: 1005.5735

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chen, CM., Knapp, J., Kreuzer, M. et al. Global SO(10) F-theory GUTs. J. High Energ. Phys. 2010, 57 (2010). https://doi.org/10.1007/JHEP10(2010)057

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP10(2010)057

Keywords

Navigation