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Flux and instanton effects in local F-theory models and hierarchical fermion masses

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Abstract

We study the deformation induced by fluxes and instanton effects on Yukawa couplings involving 7-brane intersections in local F-theory constructions. In the absence of non-perturbative effects, holomorphic Yukawa couplings do not depend on open string fluxes. On the other hand instanton effects (or gaugino condensation on distant 7-branes) do induce corrections to the Yukawas. The leading order effect may also be captured by the presence of closed string (1,2) IASD fluxes, which give rise to a non-commutative structure. We check that even in the presence of these non-perturbative effects the holomorphic Yukawas remain independent of magnetic fluxes. Although fermion mass hierarchies may be obtained from these non-perturbative effects, they would give identical Yukawa couplings for D-quark and Lepton masses in SU(5) F-theory GUT’s, in contradiction with experiment. We point out that this problem may be solved by appropriately normalizing the wavefunctions. We show in a simple toy model how the presence of hypercharge flux may then be responsible for the difference between D-quarks and Lepton masses in local SU(5) GUT’s.

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Authors and Affiliations

  1. Departamento de Física Teórica, Universidad Autónoma de Madrid, Cantoblanco, 28049, Madrid, Spain

    L. Aparicio & L. E. Ibáñez

  2. Instituto de Física Teórica UAM-CSIC, C/ Nicolás Cabrera 13-15, Cantoblanco, 28049, Madrid, Spain

    L. Aparicio, L. E. Ibáñez & F. Marchesano

  3. Departamento de Física, Centro de Física Teórica y Computacional, Facultad de Ciencias, Universidad Central de Venezuela, Avenida los Ilustres, A.P. 20513, Caracas, 1020–A, Venezuela

    A. Font

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  1. L. Aparicio
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ArXiv ePrint: 1104.2609

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Aparicio, L., Font, A., Ibáñez, L.E. et al. Flux and instanton effects in local F-theory models and hierarchical fermion masses. J. High Energ. Phys. 2011, 152 (2011). https://doi.org/10.1007/JHEP08(2011)152

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