Geometric Engineering, Mirror Symmetry and 6d (1,0) -> 4d, N=2

Understand

We study compactification of 6 dimensional (1,0) theories on T^2.

• We use geometric engineering of these theories via F-theory and employ mirror symmetry technology to solve for the effective 4d N=2 geometry for a large number of the (1,0) theories including those associated with conformal matter.
• Using this we show that for a given 6d theory we can obtain many inequivalent 4d N=2 SCFTs.
• Some of these respect the global symmetries of the 6d theory while others exhibit SL(2,Z) duality symmetry inherited from global diffeomorphisms of the T^2.