6d superconformal field theories (SCFTs) are the SCFTs in the highest
possible dimension. They can be geometrically engineered in F-theory by
compactifying on non-compact elliptic Calabi-Yau manifolds. In this paper we
focus on the class of SCFTs whose base geometry is determined by β2 curves
intersecting according to ADE Dynkin diagrams and derive the corresponding
mirror Calabi-Yau manifold. The mirror geometry is uniquely determined in terms
of the mirror curve which has also an interpretation in terms of the
Seiberg-Witten curve of the four-dimensional theory arising from torus
compactification. Adding the affine node of the ADE quiver to the base
geometry, we connect to recent results on SYZ mirror symmetry for the A case
and provide a physical interpretation in terms of little string theory. Our
results, however, go beyond this case as our construction naturally covers the
D and E cases as well.Comment: version 2: typos corrected, 30 pages, 8 figure