Advances in Theoretical and Mathematical Physics

Small resolutions of SU(5)-models in F-theory

Mboyo Esole and Shing-Tung Yau

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Abstract

We provide an explicit desingularization and study the resulting fiber geometry of elliptically fibered four-folds defined by Weierstrass models admitting a split $\tilde{A}_4$ 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 $\tilde{A}_4$ 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.

Article information

Source
Adv. Theor. Math. Phys., Volume 17, Number 6 (2013), 1195-1253.

Dates
First available in Project Euclid: 21 August 2014

Permanent link to this document
https://projecteuclid.org/euclid.atmp/1408626541

Mathematical Reviews number (MathSciNet)
MR3250767

Zentralblatt MATH identifier
1272.81166

Citation

Esole, Mboyo; Yau, Shing-Tung. Small resolutions of SU(5)-models in F-theory. Adv. Theor. Math. Phys. 17 (2013), no. 6, 1195--1253. https://projecteuclid.org/euclid.atmp/1408626541


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