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High U(1) charges in type IIB models and their F-theory lift

  • Francesco Mattia Cianci
  • Damián K. Mayorga PeñaEmail author
  • Roberto Valandro
Open Access
Regular Article - Theoretical Physics
  • 17 Downloads

Abstract

We construct models with U(1) gauge group and matter with charges up to 6, in the context of type IIB compactifications. We show explicitly that models with charges up to 4 can be derived from corresponding models in F-theory by applying the Sen weak coupling limit. We derive which type IIB models should be the limit of charge 5 and 6 F-theory models. Explicit six dimensional type IIB models with maximal charge 5 and 6 are constructed on an algebraic K3 surface that is the double cover of 2. By using type IIB results we are also able to rediscover the F-theory charge 4 model in a straightforward way.

Keywords

Anomalies in Field and String Theories D-branes Field Theories in Higher Dimensions Superstring Vacua 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

References

  1. [1]
    C. Vafa, Evidence for F-theory, Nucl. Phys. B 469 (1996) 403 [hep-th/9602022] [INSPIRE].
  2. [2]
    D.R. Morrison and C. Vafa, Compactifications of F-theory on Calabi-Yau threefolds. 1, Nucl. Phys. B 473 (1996) 74 [hep-th/9602114] [INSPIRE].
  3. [3]
    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].
  4. [4]
    C. Beasley, J.J. Heckman and C. Vafa, GUTs and exceptional branes in F-theoryI, JHEP 01 (2009) 058 [arXiv:0802.3391] [INSPIRE].
  5. [5]
    R. Donagi and M. Wijnholt, Model building with F-theory, Adv. Theor. Math. Phys. 15 (2011) 1237 [arXiv:0802.2969] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    J. Halverson, C. Long and B. Sung, Algorithmic universality in F-theory compactifications, Phys. Rev. D 96 (2017) 126006 [arXiv:1706.02299] [INSPIRE].
  7. [7]
    W. Taylor and Y.-N. Wang, Scanning the skeleton of the 4D F-theory landscape, JHEP 01 (2018) 111 [arXiv:1710.11235] [INSPIRE].
  8. [8]
    V. Braun, T.W. Grimm and J. Keitel, Complete intersection fibers in F-theory, JHEP 03 (2015) 125 [arXiv:1411.2615] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    Y. Kimura, F-theory models on K3 surfaces with various Mordell-Weil ranksConstructions that use quadratic base change of rational elliptic surfaces, JHEP 05 (2018) 048 [arXiv:1802.05195] [INSPIRE].
  10. [10]
    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].
  11. [11]
    M. Cvetič, T.W. Grimm and D. Klevers, Anomaly cancellation and abelian gauge symmetries in F-theory, JHEP 02 (2013) 101 [arXiv:1210.6034] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  12. [12]
    C. Mayrhofer, E. Palti and T. Weigand, U(1) symmetries in F-theory GUTs with multiple sections, JHEP 03 (2013) 098 [arXiv:1211.6742] [INSPIRE].
  13. [13]
    M. Cvetič, D. Klevers and H. Piragua, F-theory compactifications with multiple U(1)-factors: constructing elliptic fibrations with rational sections, JHEP 06 (2013) 067 [arXiv:1303.6970] [INSPIRE].
  14. [14]
    M. Cvetič, D. Klevers, H. Piragua and P. Song, Elliptic fibrations with rank three Mordell-Weil group: F-theory with U(1) × U(1) × U(1) gauge symmetry, JHEP 03 (2014) 021 [arXiv:1310.0463] [INSPIRE].
  15. [15]
    L.B. Anderson, I. García-Etxebarria, T.W. Grimm and J. Keitel, Physics of F-theory compactifications without section, JHEP 12 (2014) 156 [arXiv:1406.5180] [INSPIRE].
  16. [16]
    D. Klevers et al., F-theory on all toric hypersurface fibrations and its Higgs branches, JHEP 01 (2015) 142 [arXiv:1408.4808] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  17. [17]
    C. Mayrhofer, E. Palti, O. Till and T. Weigand, Discrete gauge symmetries by higgsing in four-dimensional F-theory compactifications, JHEP 12 (2014) 068 [arXiv:1408.6831] [INSPIRE].ADSCrossRefGoogle Scholar
  18. [18]
    L. Lin, C. Mayrhofer, O. Till and T. Weigand, Fluxes in F-theory compactifications on genus-one fibrations, JHEP 01 (2016) 098 [arXiv:1508.00162] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  19. [19]
    M. Cvetič, A. Grassi and M. Poretschkin, Discrete symmetries in heterotic/F-theory duality and mirror symmetry, JHEP 06 (2017) 156 [arXiv:1607.03176] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  20. [20]
    V. Kumar and W. Taylor, String universality in six dimensions, Adv. Theor. Math. Phys. 15 (2011) 325 [arXiv:0906.0987] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  21. [21]
    V. Kumar and W. Taylor, A bound on 6D N = 1 supergravities, JHEP 12 (2009) 050 [arXiv:0910.1586] [INSPIRE].
  22. [22]
    V. Kumar, D.R. Morrison and W. Taylor, Mapping 6D N = 1 supergravities to F-theory, JHEP 02 (2010) 099 [arXiv:0911.3393] [INSPIRE].
  23. [23]
    V. Kumar, D.R. Morrison and W. Taylor, Global aspects of the space of 6D N = 1 supergravities, JHEP 11 (2010) 118 [arXiv:1008.1062] [INSPIRE].
  24. [24]
    V. Kumar, D.S. Park and W. Taylor, 6D supergravity without tensor multiplets, JHEP 04 (2011) 080 [arXiv:1011.0726] [INSPIRE].
  25. [25]
    N. Seiberg and W. Taylor, Charge lattices and consistency of 6D supergravity, JHEP 06 (2011) 001 [arXiv:1103.0019] [INSPIRE].
  26. [26]
    S. Monnier, G.W. Moore and D.S. Park, Quantization of anomaly coefficients in 6D \( \mathcal{N}=\left(1,0\right) \) supergravity, JHEP 02 (2018) 020 [arXiv:1711.04777] [INSPIRE].
  27. [27]
    W. Taylor and A.P. Turner, An infinite swampland of U(1) charge spectra in 6D supergravity theories, JHEP 06 (2018) 010 [arXiv:1803.04447] [INSPIRE].
  28. [28]
    A. Grassi and D.R. Morrison, Anomalies and the Euler characteristic of elliptic Calabi-Yau threefolds, Commun. Num. Theor. Phys. 6 (2012) 51 [arXiv:1109.0042] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  29. [29]
    L.B. Anderson, J. Gray, N. Raghuram and W. Taylor, Matter in transition, JHEP 04 (2016) 080 [arXiv:1512.05791] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  30. [30]
    D. Klevers, D.R. Morrison, N. Raghuram and W. Taylor, Exotic matter on singular divisors in F-theory, JHEP 11 (2017) 124 [arXiv:1706.08194] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  31. [31]
    M. Cvetič, J.J. Heckman and L. Lin, Towards exotic matter and discrete non-Abelian symmetries in F-theory, JHEP 11 (2018) 001 [arXiv:1806.10594] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  32. [32]
    D.S. Park and W. Taylor, Constraints on 6D supergravity theories with abelian gauge symmetry, JHEP 01 (2012) 141 [arXiv:1110.5916] [INSPIRE].
  33. [33]
    N. Raghuram and W. Taylor, Large U(1) charges in F-theory, JHEP 10 (2018) 182 [arXiv:1809.01666] [INSPIRE].
  34. [34]
    N. Raghuram, Abelian F-theory models with charge-3 and charge-4 matter, JHEP 05 (2018) 050 [arXiv:1711.03210] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  35. [35]
    A. Sen, Orientifold limit of F-theory vacua, Phys. Rev. D 55 (1997) R7345 [hep-th/9702165] [INSPIRE].
  36. [36]
    D.K. Mayorga Pena and R. Valandro, Weak coupling limit of F-theory models with MSSM spectrum and massless U(1)s, JHEP 03 (2018) 107 [arXiv:1708.09452] [INSPIRE].
  37. [37]
    R.L.E. Schwarzenberger, Vector bundles on algebraic surfaces, Proc. London Math. Soc. 11 (1961) 601.MathSciNetCrossRefzbMATHGoogle Scholar
  38. [38]
    R. Friedman, Algebraic surfaces and holomorphic vector bundles, Universitext, Springer, Germany (1998).Google Scholar
  39. [39]
    S. Krause, C. Mayrhofer and T. Weigand, Gauge fluxes in F-theory and type IIB orientifolds, JHEP 08 (2012) 119 [arXiv:1202.3138] [INSPIRE].
  40. [40]
    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].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  41. [41]
    A.P. Braun, A. Collinucci and R. Valandro, The fate of U(1)’s at strong coupling in F-theory, JHEP 07 (2014) 028 [arXiv:1402.4054] [INSPIRE].
  42. [42]
    A. Collinucci and I. García-Etxebarria, E6 Yukawa couplings in F-theory as D-brane instanton effects, JHEP 03 (2017) 155 [arXiv:1612.06874] [INSPIRE].
  43. [43]
    H. Jockers and W. Lerche, Matrix factorizations, D-branes and their deformations, Nucl. Phys. Proc. Suppl. 171 (2007) 196 [arXiv:0708.0157] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  44. [44]
    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].
  45. [45]
    A. Collinucci and R. Savelli, F-theory on singular spaces, JHEP 09 (2015) 100 [arXiv:1410.4867] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  46. [46]
    A. Collinucci, M. Fazzi and R. Valandro, Geometric engineering on flops of length two, JHEP 04 (2018) 090 [arXiv:1802.00813].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  47. [47]
    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].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  48. [48]
    V.V. Batyrev, Dual polyhedra and mirror symmetry for Calabi-Yau hypersurfaces in toric varieties, J. Alg. Geom. 3 (1994) 493 [alg-geom/9310003] [INSPIRE].MathSciNetzbMATHGoogle Scholar
  49. [49]
    M. Esole and R. Savelli, Tate form and weak coupling limits in F-theory, JHEP 06 (2013) 027 [arXiv:1209.1633] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  50. [50]
    L.E. Ibáñez, R. Rabadán and A.M. Uranga, Anomalous U(1)’s in type-I and type IIB D = 4, N = 1 string vacua, Nucl. Phys. B 542 (1999) 112 [hep-th/9808139] [INSPIRE].
  51. [51]
    E. Poppitz, On the one loop Fayet-Iliopoulos term in chiral four-dimensional type-I orbifolds, Nucl. Phys. B 542 (1999) 31 [hep-th/9810010] [INSPIRE].
  52. [52]
    G. Aldazabal et al., D = 4 chiral string compactifications from intersecting branes, J. Math. Phys. 42 (2001) 3103 [hep-th/0011073] [INSPIRE].
  53. [53]
    E. Plauschinn, The generalized Green-Schwarz mechanism for type IIB orientifolds with D3- and D7-branes, JHEP 05 (2009) 062 [arXiv:0811.2804] [INSPIRE].
  54. [54]
    T.W. Grimm, M. Kerstan, E. Palti and T. Weigand, On fluxed instantons and moduli stabilisation in IIB orientifolds and F-theory, Phys. Rev. D 84 (2011) 066001 [arXiv:1105.3193] [INSPIRE].
  55. [55]
    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].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  56. [56]
    A.P. Braun, A. Collinucci and R. Valandro, Hypercharge flux in F-theory and the stable Sen limit, JHEP 07 (2014) 121 [arXiv:1402.4096] [INSPIRE].ADSCrossRefGoogle Scholar
  57. [57]
    J. Polchinski, Monopoles, duality and string theory, Int. J. Mod. Phys. A 19S1 (2004) 145 [hep-th/0304042] [INSPIRE].
  58. [58]
    T. Banks and N. Seiberg, Symmetries and strings in field theory and gravity, Phys. Rev. D 83 (2011) 084019 [arXiv:1011.5120] [INSPIRE].
  59. [59]
    A.P. Braun, S. Gerigk, A. Hebecker and H. Triendl, D7-brane moduli vs. F-theory cycles in elliptically fibred threefolds, Nucl. Phys. B 836 (2010) 1 [arXiv:0912.1596] [INSPIRE].
  60. [60]
    V.V. Nikulin, Discrete reflection groups in Lobachevsky spaces and algebraic surfaces, in the proceedings of the International Congress of Mathematicians (ICM 1986), August 3-11, Berkeley, U.S.A. (1986).Google Scholar
  61. [61]
    A. Collinucci, F. Denef and M. Esole, D-brane deconstructions in IIB orientifolds, JHEP 02 (2009) 005 [arXiv:0805.1573] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  62. [62]
    A.P. Braun, A. Hebecker and H. Triendl, D7-brane motion from M-theory cycles and obstructions in the weak coupling limit, Nucl. Phys. B 800 (2008) 298 [arXiv:0801.2163] [INSPIRE].
  63. [63]
    M. Cvetič, D. Klevers, H. Piragua and W. Taylor, General U(1) × U(1) F-theory compactifications and beyond: geometry of unHiggsings and novel matter structure, JHEP 11 (2015) 204 [arXiv:1507.05954] [INSPIRE].
  64. [64]
    Y. Kimura, Discrete gauge groups in F-theory models on genus-one fibered Calabi-Yau 4-folds without section, JHEP 04 (2017) 168 [arXiv:1608.07219] [INSPIRE].
  65. [65]
    D.S. Park, Anomaly equations and intersection theory, JHEP 01 (2012) 093 [arXiv:1111.2351] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Dipartimento di FisicaUniversità degli Studi di TriesteTriesteItaly
  2. 2.Departamento de Física, DCIUniversidad de GuanajuatoGuanajuatoMéxico
  3. 3.The Abdus Salam International Centre for Theoretical PhysicsTriesteItaly
  4. 4.INFN — Sezione di TriesteTriesteItaly

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