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Classifying bases for 6D F-theory models

  • Research Article
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Central European Journal of Physics

Abstract

We classify six-dimensional F-theory compactifications in terms of simple features of the divisor structure of the base surface of the elliptic fibration. This structure controls the minimal spectrum of the theory. We determine all irreducible configurations of divisors (“clusters”) that are required to carry nonabelian gauge group factors based on the intersections of the divisors with one another and with the canonical class of the base. All 6D F-theory models are built from combinations of these irreducible configurations. Physically, this geometric structure characterizes the gauge algebra and matter that can remain in a 6D theory after maximal Higgsing. These results suggest that all 6D supergravity theories realized in F-theory have a maximally Higgsed phase in which the gauge algebra is built out of summands of the types su(3), so(8), f4, e6, e8, e8, (g2 ⊕ su(2)); and su(2) ⊕ so(7) ⊕ su(2), with minimal matter content charged only under the last three types of summands, corresponding to the non-Higgsable cluster types identified through F-theory geometry. Although we have identified all such geometric clusters, we have not proven that there cannot be an obstruction to Higgsing to the minimal gauge and matter configuration for any possible F-theory model. We also identify bounds on the number of tensor fields allowed in a theory with any fixed gauge algebra; we use this to bound the size of the gauge group (or algebra) in a simple class of F-theory bases.

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References

  1. A. Grassi, D.R. Morrison, arXiv:math/0005196

  2. V. Kumar, W. Taylor, arXiv:0906.0987 [hep-th]

  3. V. Kumar, W. Taylor, arXiv:0910.1586 [hep-th]

  4. V. Kumar, D.R. Morrison, W. Taylor, arXiv:0911.3393 [hep-th]

  5. V. Kumar, D.R. Morrison, W. Taylor, arXiv:1008.1062 [hep-th]

  6. V. Kumar, D. Park, W. Taylor, arXiv:1011.0726 [hepth]

  7. N. Seiberg, W. Taylor, arXiv:1103.0019 [hep-th]

  8. D.R. Morrison, W. Taylor, arXiv:1106.3563 [hep-th]

  9. A. Grassi, D.R. Morrison, arXiv:1109.0042 [hep-th]

  10. V. Braun, arXiv:1110.4883 [hep-th]

  11. D.S. Park, W. Taylor, arXiv:1110.5916 [hep-th]

  12. D.S. Park, arXiv:1111.2351 [hep-th]

  13. F. Bonetti, T.W. Grimm, arXiv:1112.1082 [hep-th]

  14. C. Vafa, arXiv:hep-th/9602022

  15. D.R. Morrison, C. Vafa, arXiv:hep-th/9602114

  16. D.R. Morrison, C. Vafa, arXiv:hep-th/9603161

  17. A. Grassi, Math. Ann. 290, 287 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  18. M. Gross, Duke Math. Jour. 74, 271 (1994)

    Article  MATH  Google Scholar 

  19. M.J. Duff, R. Minasian, E. Witten, arXiv:hep-th/9601036

  20. N. Seiberg, E. Witten, arXiv:hep-th/9603003

  21. A. Sagnotti, arXiv:hep-th/9210127

  22. V. Sadov, arXiv:hep-th/9606008

  23. P. Candelas, E. Perevalov, G. Rajesh, arXiv:hep-th/9704097

  24. P. S. Aspinwall, D.R. Morrison, arXiv:hep-th/9705104

  25. D.R. Morrison, W. Taylor, to appear

  26. D.R. Morrison, arXiv:hep-th/0411120

  27. F. Denef, arXiv:0803.1194 [hep-th]

  28. W. Taylor, arXiv:1104.2051 [hep-th]

  29. J. de Boer et al., arXiv:hep-th/0103170

  30. P.S. Aspinwall, D.R. Morrison, arXiv:hep-th/9805206

  31. K. Kodaira, Ann. Math. 77, 563 (1963)

    Article  MATH  Google Scholar 

  32. K. Kodaira, Ann. Math. 78, 1 (1963)

    Article  MathSciNet  MATH  Google Scholar 

  33. M. Bershadsky et al., arXiv:hep-th/9605200

  34. S. Katz, D.R. Morrison, S. Schafer-Nameki, J. Sully, arXiv:1106.3854 [hep-th]

  35. S.H. Katz, C. Vafa, arXiv:hep-th/9606086

  36. M. Esole, S.-T. Yau, arXiv:1107.0733 [hep-th]

  37. M. Esole, J. Fullwood, S.-T. Yau, arXiv:1110.6177 [hep-th]

  38. C. Cordova, arXiv:0910.2955 [hep-th]

  39. S. Kachru, C. Vafa, arXiv:hep-th/9505105]

  40. K.A. Intriligator, arXiv:hep-th/9708117]

  41. U.H. Danielsson, P. Stjernberg, arXiv:hep-th/9603082

  42. M. Demazure, H.C. Pinkham, B. Teissier, eds., Seminaire sur les singularités des surfaces, Lecture Notes in Math. vol. 777 (Springer, 1980)

  43. H.C. Pinkham, Simple elliptic singularities, Del Pezzo surfaces and Cremona transformations, Proc. Sympos. Pure Math., Vol. XXX, Part 1, 69 (Amer. Math. Soc., 1977)

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Authors and Affiliations

  1. Departments of Mathematics and Physics, University of California, Santa Barbara, CA, 93106, USA

    David R. Morrison

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

    Washington Taylor

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  1. David R. Morrison
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  2. Washington Taylor
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Correspondence to David R. Morrison.

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Morrison, D.R., Taylor, W. Classifying bases for 6D F-theory models. centr.eur.j.phys. 10, 1072–1088 (2012). https://doi.org/10.2478/s11534-012-0065-4

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  • DOI: https://doi.org/10.2478/s11534-012-0065-4

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