F-theory Family Unification

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 Kahler manifold associated with a corresponding painted Dynkin diagram. In particular, if one starts from the E7 singularity, one obtains the E7/(SU(5)xU(1)^3) model yielding precisely three generations with an unparallel family structure. Possible applications to string phenomenology are also discussed.

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