Small resolutions of SU(5)-models in F-theory
Jul, 2011
59 pages
Published in:
- Adv.Theor.Math.Phys. 17 (2013) 6, 1195-1253
- Published: Dec, 2013
e-Print:
- 1107.0733 [hep-th]
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Abstract: (International Press)
We provide an explicit desingularization and study the resulting fiber geometry of elliptically fibered four-folds defined by Weierstrass models admitting a split singularity over a divisor of the discriminant locus. Such varieties are used to geometrically engineer SU(5) grand unified theories in F-theory. The desingularization is given by a small resolution of singularities. The fiber naturally appears after resolving the singularities in codimension-one in the base. The remaining higher codimension singularities are then beautifully described by a four-dimensional affine binomial variety which leads to six different small resolutions of the elliptically fibered four-fold. These six small resolutions define distinct four-folds connected to each other by a network of flop transitions forming a dihedral group. The location of these exotic fibers in the base is mapped to conifold points of the three-folds that defines the type IIB orientifold limit of the F-theory. The full resolution has interesting properties, specially for fibers in codimension-three: the rank of the singular fiber does not necessary increase and the fibers are not necessary in the list of Kodaira and some are not even (extended) Dynkin diagrams.Note:
- 55 pages, 18 figures, 9 tables, typo corrected, references added
- grand unified theory: SU(5)
- resolution
- singularity
- F-theory
- orientifold
- conifold
- geometry
- affine
- fibre bundle
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