Skip to main content

Advertisement

Springer Nature Link
Log in

Anomaly cancellation and abelian gauge symmetries in F-theory

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

Abstract

We study 4D F-theory compactifications on singular Calabi-Yau fourfolds with fluxes. The resulting \(\mathcal{N}=1\) effective theories can admit non-Abelian and U(1) gauge groups as well as charged chiral matter. In these setups we analyze anomaly cancellation and the generalized Green-Schwarz mechanism. This requires the study of 3D \(\mathcal{N}=2\) theories obtained by a circle compactification and their M-theory duals. Reducing M- theory on resolved Calabi-Yau fourfolds corresponds to considering the effective theory on the 3D Coulomb branch in which certain massive states are integrated out. Both 4D gaugings and 3D one-loop corrections of these massive states induce Chern-Simons terms. All 4D anomalies are captured by the one-loop terms. The ones corresponding to the mixed gauge-gravitational anomalies depend on the Kaluza-Klein vector and are induced by integrating out Kaluza-Klein modes of the U(1) charged matter. In M-theory all Chern-Simons terms classically arise from G 4-flux. We find that F-theory fluxes implement automatically the 4D Green-Schwarz mechanism if non-trivial geometric relations for the resolved Calabi-Yau fourfold are satisfied. We confirm these relations in various explicit examples and elucidate the general construction of U(1) symmetries in F-theory. We also compare anomaly cancellation in F-theory with its analog in Type IIB orientifold setups.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Explore related subjects

Discover the latest articles and news from researchers in related subjects, suggested using machine learning.

References

  1. S. Weinberg, The quantum theory of fields. Volume 2, Cambridge University Press, Cambridge U.K. (1996), chapter 22.

    Book  Google Scholar 

  2. J. Zinn-Justin, Chiral anomalies and topology, Lect. Notes Phys. 659 (2005) 167 [hep-th/0201220] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  3. J.A. Harvey, TASI 2003 lectures on anomalies, hep-th/0509097 [INSPIRE].

  4. A. Bilal, Lectures on anomalies, arXiv:0802.0634 [INSPIRE].

  5. M.B. Green and J.H. Schwarz, Anomaly cancellation in supersymmetric D = 10 gauge theory and superstring theory, Phys. Lett. B 149 (1984) 117 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  6. A. Sagnotti, A note on the Green-Schwarz mechanism in open string theories, Phys. Lett. B 294 (1992) 196 [hep-th/9210127] [INSPIRE].

    Article  ADS  Google Scholar 

  7. C. Vafa, Evidence for F-theory, Nucl. Phys. B 469 (1996) 403 [hep-th/9602022] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  8. D.R. Morrison and C. Vafa, Compactifications of F-theory on Calabi-Yau threefolds. 2, Nucl. Phys. B 476 (1996) 437 [hep-th/9603161] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  9. T.W. Grimm and H. Hayashi, F-theory fluxes, chirality and Chern-Simons theories, JHEP 03 (2012) 027 [arXiv:1111.1232] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  10. 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 

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

    Article  MathSciNet  ADS  Google Scholar 

  12. 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] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  13. 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] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  14. A.P. Braun, A. Collinucci and R. Valandro, G-flux in F-theory and algebraic cycles, Nucl. Phys. B 856 (2012) 129 [arXiv:1107.5337] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  15. J. Marsano and S. Schäfer-Nameki, Yukawas, G-flux and spectral covers from resolved Calabi-Yau’s, JHEP 11 (2011) 098 [arXiv:1108.1794] [INSPIRE].

    Article  ADS  Google Scholar 

  16. S. Krause, C. Mayrhofer and T. Weigand, G 4 flux, chiral matter and singularity resolution in F-theory compactifications, Nucl. Phys. B 858 (2012) 1 [arXiv:1109.3454] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  17. S. Krause, C. Mayrhofer and T. Weigand, Gauge fluxes in F-theory and type IIB orientifolds, JHEP 08 (2012) 119 [arXiv:1202.3138] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  19. M. Cvetič, G. Shiu and A.M. Uranga, Chiral four-dimensional N = 1 supersymmetric type 2A orientifolds from intersecting D6 branes, Nucl. Phys. B 615 (2001) 3 [hep-th/0107166] [INSPIRE].

    Article  ADS  Google Scholar 

  20. F.G. Marchesano Buznego, Intersecting D-brane models, hep-th/0307252 [INSPIRE].

  21. 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 

  22. R. Blumenhagen, B. Körs, D. Lüst and S. Stieberger, Four-dimensional string compactifications with D-branes, orientifolds and fluxes, Phys. Rept. 445 (2007) 1 [hep-th/0610327] [INSPIRE].

    Article  ADS  Google Scholar 

  23. E. Plauschinn, The generalized Green-Schwarz mechanism for type IIB orientifolds with D3- and D7-branes, JHEP 05 (2009) 062 [arXiv:0811.2804] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  24. M. Cvetič and J. Halverson, TASI lectures: particle physics from perturbative and non-perturbative effects in D-braneworlds, arXiv:1101.2907 [INSPIRE].

  25. P.S. Aspinwall and D.R. Morrison, Nonsimply connected gauge groups and rational points on elliptic curves, JHEP 07 (1998) 012 [hep-th/9805206] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  26. D.S. Park, Anomaly equations and intersection theory, JHEP 01 (2012) 093 [arXiv:1111.2351] [INSPIRE].

    Article  ADS  Google Scholar 

  27. D.R. Morrison and D.S. Park, F-theory and the Mordell-Weil group of elliptically-fibered Calabi-Yau threefolds, JHEP 10 (2012) 128 [arXiv:1208.2695] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  28. 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 

  29. 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 

  30. 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 

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

  32. T.W. Grimm, M. Kerstan, E. Palti and T. Weigand, Massive abelian gauge symmetries and fluxes in F-theory, JHEP 12 (2011) 004 [arXiv:1107.3842] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  33. L. Álvarez-Gaumé and E. Witten, Gravitational anomalies, Nucl. Phys. B 234 (1984) 269 [INSPIRE].

    Article  ADS  Google Scholar 

  34. P. Anastasopoulos, M. Bianchi, E. Dudas and E. Kiritsis, Anomalies, anomalous U(1)’s and generalized Chern-Simons terms, JHEP 11 (2006) 057 [hep-th/0605225] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  35. P. Candelas and A. Font, Duality between the webs of heterotic and type-II vacua, Nucl. Phys. B 511 (1998) 295 [hep-th/9603170] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  36. P. Candelas, E. Perevalov and G. Rajesh, Toric geometry and enhanced gauge symmetry of F-theory/heterotic vacua, Nucl. Phys. B 507 (1997) 445 [hep-th/9704097] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  37. 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 

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

    Article  MathSciNet  ADS  Google Scholar 

  39. 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 

  40. C.-M. Chen, J. Knapp, M. Kreuzer and C. Mayrhofer, Global SO(10) F-theory GUTs, JHEP 10 (2010) 057 [arXiv:1005.5735] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  41. J. Knapp, M. Kreuzer, C. Mayrhofer and N.-O. Walliser, Toric construction of global F-theory GUTs, JHEP 03 (2011) 138 [arXiv:1101.4908] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  42. V. Braun, Toric elliptic fibrations and F-theory compactifications, JHEP 01 (2013) 016 [arXiv:1110.4883] [INSPIRE].

    Article  ADS  Google Scholar 

  43. M. Esole and S.-T. Yau, Small resolutions of SU(5)-models in F-theory, arXiv:1107.0733 [INSPIRE].

  44. T.W. Grimm and R. Savelli, Gravitational instantons and fluxes from M/F-theory on Calabi-Yau fourfolds, Phys. Rev. D 85 (2012) 026003 [arXiv:1109.3191] [INSPIRE].

    ADS  Google Scholar 

  45. F. Bonetti and T.W. Grimm, Six-dimensional (1,0) effective action of F-theory via M-theory on Calabi-Yau threefolds, JHEP 05 (2012) 019 [arXiv:1112.1082] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  46. T. Shioda, Mordell-Weil lattices and Galois representation. I, P. Jpn. Acad. 65A (1989) 268.

    Article  MathSciNet  Google Scholar 

  47. T. Shioda, On the Mordell-Weil lattices, Comment. Math. Univ. St. Paul 39 (1990) 211.

    MathSciNet  MATH  Google Scholar 

  48. T.W. Grimm, The N = 1 effective action of F-theory compactifications, Nucl. Phys. B 845 (2011) 48 [arXiv:1008.4133] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  49. E. Witten, On flux quantization in M-theory and the effective action, J. Geom. Phys. 22 (1997) 1 [hep-th/9609122] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  50. A. Collinucci and R. Savelli, On flux quantization in F-theory, JHEP 02 (2012) 015 [arXiv:1011.6388] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  51. A. Collinucci and R. Savelli, On flux quantization in F-theory II: unitary and symplectic gauge groups, JHEP 08 (2012) 094 [arXiv:1203.4542] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  52. B.R. Greene, D.R. Morrison and M.R. Plesser, Mirror manifolds in higher dimension, Commun. Math. Phys. 173 (1995) 559 [hep-th/9402119] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  53. P. Mayr, Mirror symmetry, N = 1 superpotentials and tensionless strings on Calabi-Yau four folds, Nucl. Phys. B 494 (1997) 489 [hep-th/9610162] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  54. A. Klemm, B. Lian, S. Roan and S.-T. Yau, Calabi-Yau fourfolds for M-theory and F-theory compactifications, Nucl. Phys. B 518 (1998) 515 [hep-th/9701023] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  55. S. Gukov, C. Vafa and E. Witten, CFT’s from Calabi-Yau four folds, Nucl. Phys. B 584 (2000) 69 [Erratum ibid. B 608 (2001) 477-478] [hep-th/9906070] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  56. D. Lüst, P. Mayr, S. Reffert and S. Stieberger, F-theory flux, destabilization of orientifolds and soft terms on D7-branes, Nucl. Phys. B 732 (2006) 243 [hep-th/0501139] [INSPIRE].

    Article  ADS  Google Scholar 

  57. 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] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  58. 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] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  59. H. Jockers, P. Mayr and J. Walcher, On N = 1 4D effective couplings for F-theory and Heterotic Vacua, Adv. Theor. Math. Phys. 14 (2010) 1433 [arXiv:0912.3265] [INSPIRE].

    Article  MathSciNet  Google Scholar 

  60. M. Alim et al., Type II/F-theory superpotentials with several deformations and N = 1 mirror symmetry, JHEP 06 (2011) 103 [arXiv:1010.0977] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  61. D. Klevers, Holomorphic couplings in non-perturbative string compactifications, Fortsch. Phys. 60 (2012) 3 [arXiv:1106.6259] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  62. K. Intriligator, H. Jockers, P. Mayr, D.R. Morrison and M.R. Plesser, Conifold transitions in M-theory on Calabi-Yau fourfolds with background fluxes, arXiv:1203.6662 [INSPIRE].

  63. M. Haack and J. Louis, M theory compactified on Calabi-Yau fourfolds with background flux, Phys. Lett. B 507 (2001) 296 [hep-th/0103068] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  64. T.W. Grimm and W. Taylor, Structure in 6D and 4D N = 1 supergravity theories from F-theory, JHEP 10 (2012) 105 [arXiv:1204.3092] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  65. V. Sadov, Generalized Green-Schwarz mechanism in F-theory, Phys. Lett. B 388 (1996) 45 [hep-th/9606008] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  66. H.-C. Kao, K.-M. Lee and T. Lee, The Chern-Simons coefficient in supersymmetric Yang-Mills Chern-Simons theories, Phys. Lett. B 373 (1996) 94 [hep-th/9506170] [INSPIRE].

    Article  MathSciNet  Google Scholar 

  67. A.J. Niemi and G.W. Semenoff, Axial anomaly induced fermion fractionization and effective gauge theory actions in odd dimensional space-times, Phys. Rev. Lett. 51 (1983) 2077 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  68. A.N. Redlich, Parity violation and gauge noninvariance of the effective gauge field action in three-dimensions, Phys. Rev. D 29 (1984) 2366 [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  69. O. Aharony, A. Hanany, K.A. Intriligator, N. Seiberg and M. Strassler, Aspects of N = 2 supersymmetric gauge theories in three-dimensions, Nucl. Phys. B 499 (1997) 67 [hep-th/9703110] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  70. F. Bonetti, T.W. Grimm and S. Hohenegger, A Kaluza-Klein inspired action for chiral p-forms and their anomalies, arXiv:1206.1600 [INSPIRE].

  71. J. Wess and J. Bagger, Supersymmetry and supergravity, Princeton University Press, Princeton U.S.A. (1992).

    Google Scholar 

  72. W. Taylor, TASI lectures on supergravity and string vacua in various dimensions, arXiv:1104.2051 [INSPIRE].

  73. H. Jockers and J. Louis, The effective action of D7-branes in N = 1 Calabi-Yau orientifolds, Nucl. Phys. B 705 (2005) 167 [hep-th/0409098] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  74. H. Jockers and J. Louis, D-terms and F-terms from D7-brane fluxes, Nucl. Phys. B 718 (2005) 203 [hep-th/0502059] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  75. K.A. Intriligator, D.R. Morrison and N. Seiberg, Five-dimensional supersymmetric gauge theories and degenerations of Calabi-Yau spaces, Nucl. Phys. B 497 (1997) 56 [hep-th/9702198] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, PA, 19104-6396, U.S.A.

    Mirjam Cvetič & Denis Klevers

  2. Center for Applied Mathematics and Theoretical Physics, University of Maribor, Maribor, Slovenia

    Mirjam Cvetič

  3. Max-Planck-Institut für Physik, Föhringer Ring 6, 80805, Munich, Germany

    Thomas W. Grimm

Authors
  1. Mirjam Cvetič
    View author publications

    Search author on:PubMed Google Scholar

  2. Thomas W. Grimm
    View author publications

    Search author on:PubMed Google Scholar

  3. Denis Klevers
    View author publications

    Search author on:PubMed Google Scholar

Corresponding author

Correspondence to Denis Klevers.

Additional information

ArXiv ePrint: 1210.6034

Rights and permissions

Reprints and permissions

About this article

Cite this article

Cvetič, M., Grimm, T.W. & Klevers, D. Anomaly cancellation and abelian gauge symmetries in F-theory. J. High Energ. Phys. 2013, 101 (2013). https://doi.org/10.1007/JHEP02(2013)101

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP02(2013)101

Keywords