# ADE String Chains and Mirror Symmetry

## TL;DR

This paper constructs mirror Calabi-Yau geometries for 6d SCFTs with base geometries determined by ADE Dynkin diagrams, linking them to Seiberg-Witten curves and extending mirror symmetry results beyond the A case.

## Contribution

It derives mirror geometries for ADE-based 6d SCFTs, including D and E types, and connects these to Seiberg-Witten curves and little string theory.

## Key findings

- Mirror curves are explicitly constructed for ADE SCFTs.
- The construction extends mirror symmetry beyond the A case.
- Connections to Seiberg-Witten curves and little string theory are established.

## Abstract

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 $-2$ 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.