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General F-theory models with tuned (SU(3) × SU(2) × U(1))/ℤ6 symmetry

  • Regular Article - Theoretical Physics
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  • Published: 01 April 2020
  • volume 2020, Article number: 8 (2020)
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General F-theory models with tuned (SU(3) × SU(2) × U(1))/ℤ6 symmetry
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  • Nikhil Raghuram1,
  • Washington Taylor2 &
  • Andrew P. Turner  ORCID: orcid.org/0000-0003-0022-92702 

  • 214 Accesses

  • 8 Citations

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A preprint version of the article is available at arXiv.

Abstract

We construct a general form for an F-theory Weierstrass model over a general base giving a 6D or 4D supergravity theory with gauge group (SU(3) × SU(2) × U(1))/ℤ6 and generic associated matter, which includes the matter content of the standard model. The Weierstrass model is identified by unHiggsing a model with U(1) gauge symmetry and charges q ≤ 4 previously found by the first author. This model includes two distinct branches that were identified in earlier work, and includes as a special case the class of models recently studied by Cvetič, Halverson, Lin, Liu, and Tian, for which we demonstrate explicitly the possibility of unification through an SU(5) unHiggsing. We develop a systematic methodology for checking that a parameterized class of F-theory Weierstrass models with a given gauge group G and fixed matter content is generic (contains all allowed moduli) and confirm that this holds for the models constructed here.

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References

  1. L.B. Anderson, A. Constantin, J. Gray, A. Lukas and E. Palti, A Comprehensive Scan for Heterotic SU(5) GUT models, JHEP01 (2014) 047 [arXiv:1307.4787] [INSPIRE].

  2. A. Constantin, Y.-H. He and A. Lukas, Counting String Theory Standard Models, Phys. Lett.B 792 (2019) 258 [arXiv:1810.00444] [INSPIRE].

  3. M. Cvetič, J. Halverson, L. Lin, M. Liu and J. Tian, Quadrillion F-Theory Compactifications with the Exact Chiral Spectrum of the Standard Model, Phys. Rev. Lett.123 (2019) 101601 [arXiv:1903.00009] [INSPIRE].

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

  5. 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].

  6. 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].

  7. L. Lin and T. Weigand, Towards the Standard Model in F-theory, Fortsch. Phys.63 (2015) 55 [arXiv:1406.6071] [INSPIRE].

  8. M. Cvetič, D. Klevers, D.K.M. Peña, P.-K. Oehlmann and J. Reuter, Three-Family Particle Physics Models from Global F-theory Compactifications, JHEP08 (2015) 087 [arXiv:1503.02068] [INSPIRE].

  9. L. Lin and T. Weigand, G 4 -flux and standard model vacua in F-theory, Nucl. Phys.B 913 (2016) 209 [arXiv:1604.04292] [INSPIRE].

  10. M. Cvetič, L. Lin, M. Liu and P.-K. Oehlmann, An F-theory Realization of the Chiral MSSM with ℤ2-Parity, JHEP09 (2018) 089 [arXiv:1807.01320] [INSPIRE].

  11. D. Klevers, D.K. Mayorga Pena, P.-K. Oehlmann, H. Piragua and J. Reuter, F-Theory on all Toric Hypersurface Fibrations and its Higgs Branches, JHEP01 (2015) 142 [arXiv:1408.4808] [INSPIRE].

  12. C. Lawrie, S. Schäfer-Nameki and J.-M. Wong, F-theory and All Things Rational: Surveying U(1) Symmetries with Rational Sections, JHEP09 (2015) 144 [arXiv:1504.05593] [INSPIRE].

  13. T.W. Grimm, A. Kapfer and D. Klevers, The Arithmetic of Elliptic Fibrations in Gauge Theories on a Circle, JHEP06 (2016) 112 [arXiv:1510.04281] [INSPIRE].

  14. M. Cvetič and L. Lin, The Global Gauge Group Structure of F-theory Compactification with U(1)s, JHEP01 (2018) 157 [arXiv:1706.08521] [INSPIRE].

  15. W. Taylor and A.P. Turner, Generic construction of the Standard Model gauge group and matter representations in F-theory, arXiv:1906.11092 [INSPIRE].

  16. W. Taylor and A.P. Turner, Generic matter representations in 6D supergravity theories, JHEP05 (2019) 081 [arXiv:1901.02012] [INSPIRE].

  17. D.R. Morrison and D.S. Park, F-Theory and the Mordell-Weil Group of Elliptically-Fibered Calabi-Yau Threefolds, JHEP10 (2012) 128 [arXiv:1208.2695] [INSPIRE].

  18. T. Weigand, F-theory, PoS(TASI2017)016 (2018) [arXiv:1806.01854] [INSPIRE].

  19. D.R. Morrison and W. Taylor, Classifying bases for 6D F-theory models, Central Eur. J. Phys.10 (2012) 1072 [arXiv:1201.1943] [INSPIRE].

  20. D.R. Morrison and W. Taylor, Non-Higgsable clusters for 4D F-theory models, JHEP05 (2015) 080 [arXiv:1412.6112] [INSPIRE].

  21. S. Lang and A. Neron, Rational points of abelian varieties over function fields, Am. J. Math.81 (1959) 95.

  22. M. Bershadsky, K.A. Intriligator, S. Kachru, D.R. Morrison, V. Sadov and C. Vafa, Geometric singularities and enhanced gauge symmetries, Nucl. Phys.B 481 (1996) 215 [hep-th/9605200] [INSPIRE].

  23. R. Donagi and M. Wijnholt, Breaking GUT Groups in F-theory, Adv. Theor. Math. Phys.15 (2011) 1523 [arXiv:0808.2223] [INSPIRE].

  24. R. Donagi and M. Wijnholt, Model Building with F-theory, Adv. Theor. Math. Phys.15 (2011) 1237 [arXiv:0802.2969] [INSPIRE].

  25. C. Beasley, J.J. Heckman and C. Vafa, GUTs and Exceptional Branes in F-theory — I, JHEP01 (2009) 058 [arXiv:0802.3391] [INSPIRE].

  26. C. Beasley, J.J. Heckman and C. Vafa, GUTs and Exceptional Branes in F-theory — II: Experimental Predictions, JHEP01 (2009) 059 [arXiv:0806.0102] [INSPIRE].

  27. J.J. Heckman, Particle Physics Implications of F-theory, Ann. Rev. Nucl. Part. Sci.60 (2010) 237 [arXiv:1001.0577] [INSPIRE].

  28. T. Weigand, Lectures on F-theory compactifications and model building, Class. Quant. Grav.27 (2010) 214004 [arXiv:1009.3497] [INSPIRE].

  29. A. Maharana and E. Palti, Models of Particle Physics from Type IIB String Theory and F-theory: A Review, Int. J. Mod. Phys.A 28 (2013) 1330005 [arXiv:1212.0555] [INSPIRE].

  30. A. Grassi, J. Halverson, J. Shaneson and W. Taylor, Non-Higgsable QCD and the Standard Model Spectrum in F-theory, JHEP01 (2015) 086 [arXiv:1409.8295] [INSPIRE].

  31. G. Martini and W. Taylor, 6D F-theory models and elliptically fibered Calabi-Yau threefolds over semi-toric base surfaces, JHEP06 (2015) 061 [arXiv:1404.6300] [INSPIRE].

  32. Y.-N. Wang, Tuned and Non-Higgsable U(1)s in F-theory, JHEP03 (2017) 140 [arXiv:1611.08665] [INSPIRE].

  33. W. Taylor and Y.-N. Wang, A Monte Carlo exploration of threefold base geometries for 4d F-theory vacua, JHEP01 (2016) 137 [arXiv:1510.04978] [INSPIRE].

  34. J. Halverson, C. Long and B. Sung, Algorithmic universality in F-theory compactifications, Phys. Rev.D 96 (2017) 126006 [arXiv:1706.02299] [INSPIRE].

  35. W. Taylor and Y.-N. Wang, Scanning the skeleton of the 4D F-theory landscape, JHEP01 (2018) 111 [arXiv:1710.11235] [INSPIRE].

  36. W. Taylor and Y.-N. Wang, The F-theory geometry with most flux vacua, JHEP12 (2015) 164 [arXiv:1511.03209] [INSPIRE].

  37. J. Tian and Y.-N. Wang, E-string spectrum and typical F-theory geometry, arXiv:1811.02837 [INSPIRE].

  38. M.R. Douglas, The Statistics of string/M theory vacua, JHEP05 (2003) 046 [hep-th/0303194] [INSPIRE].

  39. S. Ashok and M.R. Douglas, Counting flux vacua, JHEP01 (2004) 060 [hep-th/0307049] [INSPIRE].

  40. F. Denef and M.R. Douglas, Distributions of flux vacua, JHEP05 (2004) 072 [hep-th/0404116] [INSPIRE].

  41. F. Denef, Les Houches Lectures on Constructing String Vacua, Les Houches87 (2008) 483 [arXiv:0803.1194] [INSPIRE].

  42. M.C.N. Cheng, G.W. Moore and N.M. Paquette, Flux vacua: A voluminous recount, arXiv:1909.04666 [INSPIRE].

  43. A.P. Braun and T. Watari, Distribution of the Number of Generations in Flux Compactifications, Phys. Rev.D 90 (2014) 121901 [arXiv:1408.6156] [INSPIRE].

  44. S. Katz, D.R. Morrison, S. Schäfer-Nameki and J. Sully, Tate’s algorithm and F-theory, JHEP08 (2011) 094 [arXiv:1106.3854] [INSPIRE].

  45. N. Raghuram, Abelian F-theory Models with Charge-3 and Charge-4 Matter, JHEP05 (2018) 050 [arXiv:1711.03210] [INSPIRE].

  46. D.S. Park, Anomaly Equations and Intersection Theory, JHEP01 (2012) 093 [arXiv:1111.2351] [INSPIRE].

  47. J.J. Heckman and T. Rudelius, Top Down Approach to 6D SCFTs, J. Phys.A 52 (2019) 093001 [arXiv:1805.06467] [INSPIRE].

  48. F. Baume, M. Cvetič, C. Lawrie and L. Lin, When rational sections become cyclic — Gauge enhancement in F-theory via Mordell-Weil torsion, JHEP03 (2018) 069 [arXiv:1709.07453] [INSPIRE].

  49. H. Georgi and S.L. Glashow, Unity of All Elementary Particle Forces, Phys. Rev. Lett.32 (1974) 438 [INSPIRE].

  50. P.S. Aspinwall and D.R. Morrison, Nonsimply connected gauge groups and rational points on elliptic curves, JHEP07 (1998) 012 [hep-th/9805206] [INSPIRE].

  51. D.R. Morrison and W. Taylor, Charge completeness and the massless charge lattice in F-theory models of supergravity, UCSB-MATH-2020-01, MIT-CTP-5169.

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

  53. D.R. Morrison and W. Taylor, Matter and singularities, JHEP01 (2012) 022 [arXiv:1106.3563] [INSPIRE].

  54. D. Klevers, D.R. Morrison, N. Raghuram and W. Taylor, Exotic matter on singular divisors in F-theory, JHEP11 (2017) 124 [arXiv:1706.08194] [INSPIRE].

  55. M. Cvetič, D. Klevers and H. Piragua, F-Theory Compactifications with Multiple U(1)-Factors: Constructing Elliptic Fibrations with Rational Sections, JHEP06 (2013) 067 [arXiv:1303.6970] [INSPIRE].

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

  57. L.B. Anderson, J. Gray, N. Raghuram and W. Taylor, Matter in transition, JHEP04 (2016) 080 [arXiv:1512.05791] [INSPIRE].

  58. Y.-C. Huang and W. Taylor, Comparing elliptic and toric hypersurface Calabi-Yau threefolds at large Hodge numbers, JHEP02 (2019) 087 [arXiv:1805.05907] [INSPIRE].

  59. C. Vafa, The String landscape and the swampland, hep-th/0509212 [INSPIRE].

  60. D.R. Morrison and W. Taylor, Toric bases for 6D F-theory models, Fortsch. Phys.60 (2012) 1187 [arXiv:1204.0283] [INSPIRE].

  61. W. Taylor and Y.-N. Wang, Non-toric bases for elliptic Calabi-Yau threefolds and 6D F-theory vacua, Adv. Theor. Math. Phys.21 (2017) 1063 [arXiv:1504.07689] [INSPIRE].

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Authors and Affiliations

  1. Department of Physics, Robeson Hall, 0435, Virginia Tech, 850 West Campus Drive, Blacksburg, VA, 24061, USA

    Nikhil Raghuram

  2. Center for Theoretical Physics, Department of Physics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA, 02139, USA

    Washington Taylor & Andrew P. Turner

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  1. Nikhil Raghuram
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  2. Washington Taylor
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Correspondence to Andrew P. Turner.

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ArXiv ePrint: 1912.10991

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Cite this article

Raghuram, N., Taylor, W. & Turner, A.P. General F-theory models with tuned (SU(3) × SU(2) × U(1))/ℤ6 symmetry. J. High Energ. Phys. 2020, 8 (2020). https://doi.org/10.1007/JHEP04(2020)008

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  • Received: 10 January 2020

  • Accepted: 07 March 2020

  • Published: 01 April 2020

  • DOI: https://doi.org/10.1007/JHEP04(2020)008

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Keywords

  • F-Theory
  • Supergravity Models
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