Skip to main content
SpringerLink
Log in

Higgs Bundles and UV Completion in F-Theory

  • Published:
Communications in Mathematical Physics Aims and scope Submit manuscript

Abstract

F-theory admits 7-branes with exceptional gauge symmetries, which can be compactified to give phenomenological four-dimensional GUT models. Here we study general supersymmetric compactifications of eight-dimensional Yang–Mills theory. They are mathematically described by meromorphic Higgs bundles, and therefore admit a spectral cover description. This allows us to give a rigorous and intrinsic construction of local models in F-theory. We use our results to prove a no-go theorem showing that local SU(5) models with three generations do not exist for generic moduli. However we show that three-generation models do exist on the Noether–Lefschetz locus. We explain how F-theory models can be mapped to non-perturbative orientifold models using a scaling limit proposed by Sen. Further we address the construction of global models that do not have heterotic duals, considering models with base CP 3 or a blow-up thereof as examples. We show how one may obtain a contractible worldvolume with a two-cycle not inherited from the bulk, a necessary condition for implementing GUT breaking using fluxes.

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

Access this article

Log in via an institution

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. Donagi, R., Wijnholt, M.: Model building with F-theory. Adv. Theor. Math. Phys. 15, 1237. http://arXiv.org/abs/0802.2969v3 [hep-th], 2012

  2. Beasley C., Heckman J.J., Vafa C.: GUTs and exceptional branes in F-theory—I. JHEP 0901, 058 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  3. Hayashi H., Tatar R., Toda Y., Watari T., Yamazaki M.: New aspects of heterotic—F theory Duality. Nucl. Phys. B 806, 224 (2009)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  4. Vafa C.: Evidence for F-theory. Nucl. Phys. B 469, 403 (1996)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  5. Donagi, R., Wijnholt, M.: Breaking GUT groups in F-theory. Adv. Theor. Math. Phys. 15, 1523 http://arXiv.org/abs/0808.2223v1 [hep-th], 2008

  6. Beasley C., Heckman J.J., Vafa C.: GUTs and exceptional branes in F-theory—II: experimental predictions. JHEP 0901, 059 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  7. Tatar R., Watari T.: GUT relations from string theory compactifications. Nucl. Phys. B 810, 316 (2009)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  8. Heckman, J.J., Vafa, C.: Flavor hierarchy from F-theory, http://arXiv.org/abs/0811.2417v3 [hep-th], 2009

  9. Heckman, J.J., Kane, G.L., Shao, J., Vafa, C.: The footprint of F-theory at the LHC, http://arXiv.org/abs/0903.3609v1 [hep-ph], 2009

  10. Hayashi, H., Kawano, T., Tatar, R., Watari, T.: Codimension-3 singularities and Yukawa couplings in F-theory, http://arXiv.org/abs/0901.4941v3 [hep-th], 2009

  11. Andreas, B., Curio, G.: From local to global in F-theory model building, http://arXiv.org/abs/0902.4143v1 [hep-th], 2009

  12. Blumenhagen R., Braun V., Grimm T.W., Weigand T.: GUTs in type IIB orientifold compactifications. Nucl. phys. B 815, 1–94 (2009)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  13. Font A., Ibanez L.E.: Yukawa structure from U(1) fluxes in F-theory grand unification. JHEP 0902, 016 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  14. Blumenhagen R.: Gauge coupling unification in F-theory grand unified theories. Phys. Rev. Lett. 102, 071601 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  15. Bourjaily, J.L.: Local models in F-theory and M-theory with three generations, http://arXiv.org/abs/0901.3785v2 [hep-th], 2009

  16. Jiang J., Li T., Nanopoulos D.V., Xie D.: F-SU(5). Phys. Lett. B 677, 322 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  17. Collinucci A.: New F-theory lifts. JHEP 0908, 076 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  18. Collinucci A., Denef F., Esole M.: D-brane deconstructions in IIB orientifolds. JHEP 0902, 005 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  19. Heckman, J.J., Marsano, J., Saulina, N., Schafer-Nameki, S., Vafa, C.: Instantons and SUSY breaking in F-theory, http://arXiv.org/abs/v20808.1286 [hep-th], 2009

  20. Marsano J., Saulina N., Schafer-Nameki S.: An instanton toolbox for F-theory model building. JHEP 1001, 128 (2010)

    Article  ADS  MathSciNet  Google Scholar 

  21. Clingher, A., Donagi, R., Wijnholt, M.: The Sen limit, http://arXiv.org/abs/1212.4505v1 [hep-th], 2012

  22. Pantev T., Wijnholt M.: Hitchin’s equations and M-theory phenomenology. J. Geom. Phys. 61, 1223 (2011)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  23. Donagi, R., Katz, S., Wijnholt, M. Weak coupling, degeneration and log Calabi–Yau spaces, http://arXiv.org/abs/1212.0553v1 [hep-th], 2012

  24. Tate, J.: Algorithm for determining the type of a singular fiber in an elliptic pencil. In: Modular functions of one variable IV, Lecture Notes in Mathematics, Vol. 476, Berlin, Springer, 1975, pp. 33–52

  25. Bershadsky M., Intriligator K.A., Kachru S., Morrison D.R., Sadov V., Vafa C.: Geometric singularities and enhanced gauge symmetries. Nucl. Phys. B 481, 215 (1996)

    Article  ADS  MathSciNet  Google Scholar 

  26. Sen A.: Orientifold limit of F-theory vacua. Phys. Rev. D 55, 7345 (1997)

    Article  ADS  MathSciNet  Google Scholar 

  27. Sen A.: F-theory and orientifolds. Nucl. Phys. B 475, 562 (1996)

    Article  ADS  MATH  Google Scholar 

  28. Dasgupta K., Mukhi S.: F-theory at constant coupling. Phys. Lett. B 385, 125 (1996)

    Article  ADS  MathSciNet  Google Scholar 

  29. Sadov V.: Generalized Green–Schwarz mechanism in F theory. Phys. Lett. B 388, 45 (1996)

    Article  ADS  MathSciNet  Google Scholar 

  30. Tatar R., Watari T.: Proton decay, Yukawa couplings and underlying gauge symmetry in string theory. Nucl. Phys. B 747, 212 (2006)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  31. Cheung Y.K., Yin Z.: Anomalies, branes, and currents. Nucl. Phys. B 517, 69 (1998)

    Article  ADS  MathSciNet  Google Scholar 

  32. Minasian R., Moore G.W.: K-theory and Ramond–Ramond charge. JHEP 9711, 002 (1997)

    Article  ADS  MathSciNet  Google Scholar 

  33. Witten, E.: Anomaly cancellation on G(2) manifolds, http://arXiv.org/abs/hepth-th/0108165v1, 2001

  34. Hitchin N.J.: The self-duality equations on a Riemann surface. Proc. Lond. Math. Soc. (55) 3, 59–126 (1987)

    Article  MathSciNet  Google Scholar 

  35. Simpson C.T.: Higgs bundles and local systems. Publications Mathématiques de l’IHES 75, 5–95 (1992)

    Article  MATH  Google Scholar 

  36. Donagi, R.: Spectral covers, http://arXiv.org/abs/alg-geom/9505009v1, 1995

  37. Donagi R., Wijnholt M.: Gluing Branes- I. JHEP 1305, 068. http://arXiv.org/abs/arXiv:1104.2610 [hep-th], (2013)

  38. Donagi R., He Y.H., Ovrut B.A., Reinbacher R.: The particle spectrum of heterotic compactifications. JHEP 0412, 054 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  39. Blumenhagen R., Moster S., Reinbacher R., Weigand T.: Massless spectra of three generation U(N) heterotic string vacua. JHEP 0705, 041 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  40. Curio G.: Chiral matter and transitions in heterotic string models. Phys. Lett. B 435, 39 (1998)

    Article  ADS  MathSciNet  Google Scholar 

  41. Grauert H.: Ueber Modifikationen und exzeptionelle analytische Mengen. Math. Ann. 146, 331–368 (1962)

    Article  MATH  MathSciNet  Google Scholar 

  42. Ancona V.: Faisceaux amples sur les espaces analytiques. Trans. Am. Math. Soc. 274(1), 89–100 (1982) (French English summary) [Ample sheaves on analytic spaces]

    Article  MATH  MathSciNet  Google Scholar 

  43. Peternell, T.: Manuscripta Math. 37, 19–26 (1982); Erratum, ibid. 42, 259–263 (1983)

  44. Donagi, R., Wijnholt, M.: Gluing branes II: flavour physics and string duality. JHEP 1305, 092. http://arXiv.org/abs/arXiv:1112.4854v1 [hep-th], 2013

  45. Denef F., Douglas M.R.: Computational complexity of the landscape I. Ann. Phys 322, 1096 (2007)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  46. Verlinde H., Wijnholt M.: Building the standard model on a D3-brane. JHEP 0701, 106 (2007)

    Article  ADS  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Pennsylvania, Philadelphia, PA, 19104-6395, USA

    Ron Donagi

  2. Max Planck Institute (Albert Einstein Institute), Am Mühlenberg 1, 14476, Potsdam-Golm, Germany

    Martijn Wijnholt

Authors
  1. Ron Donagi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Martijn Wijnholt
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Martijn Wijnholt.

Additional information

Communicated by N. A. Nekrasov

Rights and permissions

Reprints and permissions

About this article

Cite this article

Donagi, R., Wijnholt, M. Higgs Bundles and UV Completion in F-Theory. Commun. Math. Phys. 326, 287–327 (2014). https://doi.org/10.1007/s00220-013-1878-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00220-013-1878-8

Keywords

Search

Navigation