Flavor structure in F-theory compactifications View Full Text


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Article Info

DATE

2010-08-09

AUTHORS

Hirotaka Hayashi, Teruhiko Kawano, Yoichi Tsuchiya, Taizan Watari

ABSTRACT

F-theory is one of frameworks in string theory where supersymmetric grand unification is accommodated, and all the Yukawa couplings and Majorana masses of righthanded neutrinos are generated. Yukawa couplings of charged fermions are generated at codimension-3 singularities, and a contribution from a given singularity point is known to be approximately rank 1. Thus, the approximate rank of Yukawa matrices in low-energy effective theory of generic F-theory compactifications are minimum of either the number of generations Ngen = 3 or the number of singularity points of certain types. If there is a geometry with only one E6 type point and one D6 type point over the entire 7-brane for SU(5) gauge fields, F-theory compactified on such a geometry would reproduce approximately rank-1 Yukawa matrices in the real world. We found, however, that there is no such geometry. Thus, it is a problem how to generate hierarchical Yukawa eigenvalues in F-theory compactifications. A solution in the literature so far is to take an appropriate factorization limit. In this article, we propose an alternative solution to the hierarchical structure problem (which requires to tune some parameters) by studying how zero mode wavefunctions depend on complex structure moduli. In this solution, the Ngen × Ngen CKM matrix is predicted to have only Ngen entries of order unity without an extra tuning of parameters, and the lepton flavor anarchy is predicted for the lepton mixing matrix. The hierarchy among the Yukawa eigenvalues of the down-type and charged lepton sector is predicted to be smaller than that of the up-type sector, and the Majorana masses of left-handed neutrinos generated through the see-saw mechanism have small hierarchy. All of these predictions agree with what we observe in the real world. We also obtained a precise description of zero mode wavefunctions near the E6 type singularity points, where the up-type Yukawa couplings are generated. More... »

PAGES

36

References to SciGraph publications

  • 2009-01-23. GUTs and exceptional branes in F-theory — I in JOURNAL OF HIGH ENERGY PHYSICS
  • 2005-06-13. Loop-corrected compactifications of the heterotic string with line bundles in JOURNAL OF HIGH ENERGY PHYSICS
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  • 2004-01-14. SU(4) instantons on Calabi-Yau threefolds with ℤ2 × ℤ2 fundamental group in JOURNAL OF HIGH ENERGY PHYSICS
  • 2003-05-16. Torus-Fibered Calabi-Yau threefolds with non-trivial fundamental group in JOURNAL OF HIGH ENERGY PHYSICS
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  • 2010-01-15. F-theory and neutrinos: Kaluza-Klein dilution of flavor hierarchy in JOURNAL OF HIGH ENERGY PHYSICS
  • 2007-05-15. Massless spectra of three generation U(N) heterotic string vacua in JOURNAL OF HIGH ENERGY PHYSICS
  • 2004-06-02. Computing Yukawa couplings from magnetized extra dimensions in JOURNAL OF HIGH ENERGY PHYSICS
  • 2009-01-23. GUTs and exceptional branes in F-theory — II. Experimental predictions in JOURNAL OF HIGH ENERGY PHYSICS
  • 1998-12-18. Toric geometry and F-theory/heterotic duality in four dimensions in JOURNAL OF HIGH ENERGY PHYSICS
  • 2004-12-23. The particle spectrum of heterotic compactifications in JOURNAL OF HIGH ENERGY PHYSICS
  • 1997-08. Vector Bundles and F Theory in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2007-01-31. D-branes at singularities, compactification, and hypercharge in JOURNAL OF HIGH ENERGY PHYSICS
  • 2009-08-10. F-theory compactifications for supersymmetric GUTs in JOURNAL OF HIGH ENERGY PHYSICS
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