Abstract
We propose a new geometric mechanism for naturally realizing unparallel three families of flavors in string theory, using the framework of F-theory. We consider a set of coalesced local 7-branes of a particular Kodaira singularity type and allow some of the branes to bend and separate from the rest, so that they meet only at an intersection point. Such a local configuration can preserve supersymmetry. Its matter spectrum is investigated by studying string junctions near the intersection, and shown to coincide, after an orbifold projection, with that of a supersymmetric coset sigma model whose target space is a homogeneous Kähler manifold associated with a corresponding painted Dynkin diagram. In particular, if one starts from the E 7 singularity, one obtains the E 7 /(SU(5) × U(1)3) model yielding precisely three generations with an unparallel family structure. Possible applications to string phenomenology are also discussed.
Highlights
Lepton flavor mixing angle was revealed to be almost maximal, ∼ 45◦
We propose a new geometric mechanism for naturally realizing unparallel three families of flavors in string theory, using the framework of F-theory
We show that a certain local 7-brane system in F-theory can realize, already at the level of six dimensions, the same quantum numbers as that of the SUSY nonlinear sigma model considered in family unification
Summary
We begin with a review of the basic idea of coset space family unification, which is what we want to achieve in string theory. The dimensions of the neutral hypermultiplet moduli spaces were compared between the two, and a perfect match was found in various cases of unbroken gauge symmetries It was found there [65] that the charged matter arose at “extra zeroes” of the discriminant of the curve (3.1) at particular values of w, where the singularities of the coinciding gauge 7-branes were (more) enhanced. The heterotic prediction of the charge matter is n + 6 hypermultiplets in 27, which is certainly implied by the extra zeroes of the discriminant (3.6) At this point, looking at the charged matter contents in the two examples, we notice an interesting fact: they are precisely the ones found in the homogeneous Kahler manifolds E8/(E7 × U(1)) and E7/(E6 × U(1)), respectively.
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