On ADE quiver models and F-theory compactification

Based on mirror symmetry, we discuss geometric engineering of N = 1 ADE quiver models from F-theory compactifications on elliptic K3 surfaces fibred over certain four-dimensional base spaces. The latter are constructed as intersecting 4-cycles according to ADE Dynkin diagrams, thereby mimicking the construction of Calabi–Yau threefolds used in geometric engineering in type II superstring theory. Matter is incorporated by considering D7-branes wrapping these 4-cycles. Using a geometric procedure referred to as folding, we discuss how the corresponding physics can be converted into a scenario with D5-branes wrapping 2-cycles of ALE spaces.