48 Crepant Paths to $\text{SU}(2)\!\times\!\text{SU}(3)$

Understand

We study crepant resolutions of Weierstrass models of $\text{SU}(2)\!\times\!\text{SU}(3)$-models, whose gauge group describes the non-abelian sector of the Standard Model.

• The $\text{SU}(2)\!\times\!\text{SU}(3)$-models are elliptic fibrations characterized by the collision of two Kodaira fibers with dual graphs that are affine Dynkin diagrams of type $\widetilde{\text{A}}_1$ and $\widetilde{\text{A}}_2$.
• Once we eliminate those collisions that do not have crepant resolutions, we are left with six distinct collisions that are related to each other by deformations.
• Each of these six collisions has eight distinct crepant resolutions whose flop diagram is a hexagon with two legs attached to two adjacent nodes.