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

Abstract

Journal of High Energy Physics 2011.8 (2011): 152 reproduced by permission of Scuola Internazionale Superiore di Studi Avanzati (SISSA)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'sThis work has been partially supported by the grants FPA 2009-09017, FPA 2009-07908, Consolider-CPAN (CSD2007-00042) from the MICINN, HEPHACOS-S2009/ESP1473 from the C.A. de Madrid and the contract “UNILHC” PITN-GA-2009-237920 of the European Commission. F.M. is supported by the MICINN Ramón y Cajal programme through the grant RYC-2009-0509

Phenomenological implications of a minimal F-theory GUT with discrete symmetry

“…The lightest generation does not get an explicit mass from this mechanism, but we can expect a small correction to come from non-commutative fluxes or instantons [39,41,44], thus generating a small mass for the first generation. The down-type quarks contribute a further two operators to the model.…”

“…C An alternative polynomial 41 1 Introduction F-theory [1] models have attracted considerable interest over the recent years [2]- [9]. For example, Supersymmetric (SUSY) Grand Unified Theories (GUTs) based on SU(5) has been shown to emerge naturally from F-theory [10]- [26].…”

Discrete family symmetry from F-theory GUTs

“…Due to the rank theorem [37], the two lighter generations can only have one massive eigenvalue. However, corrections due to instantons and non-commutative fluxes are known as mechanisms to recover a light mass for the first generation [37,38].…”

“…We should again be able to use the Rank Theorem to argue that while the first generation should not get a mass by this mechanism, the mass may be generated by other effects [37,38]. We also expect there might be small corrections due to the higher order contributions, though we shall not consider these here.…”

“…However the remaining generation will gain a mass due to instantons and non-commutative fluxes, as in [37,38].…”