The Geometry of SO(3), SO(5), and SO(6) models

Understand

SO(3), SO(5), and SO(6)-models are singular elliptic fibrations with Mordell--Weil torsion Z/2Z and singular fibers whose dual fibers correspond to affine Dynkin diagrams of type A1, C2, and A3 respectively, where we emphasize the distinction between SO(n) and its universal cover Spin(n).

• While the SO(3)-model has been studied before, the SO(5) and SO(6)-models are studied here for the first time.
• By computing crepant resolutions of their Weierstrass models, we study their fiber structures and topological invariants.
• In the special case that the SO(n)-model is an elliptically fibered Calabi-Yau threefold, we compute the Chern-Simons couplings and matter content of a 5D N=1 supergravity theory with gauge group SO(n), which is related to M-theory compactified on this Calabi-Yau threefold.