ADE String Chains and Mirror Symmetry

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.

version 2: typos corrected, 30 pages, 8 figures

References in corpus (3)

• 6d Conformal Matter
• Anomaly of strings of 6d $\mathcal{N}=(1,0)$ theories
• Little strings on $D_n$ orbifolds

Cited by in corpus (13)

• Universal Features of BPS Strings in Six-dimensional SCFTs
• Topological Strings on Singular Elliptic Calabi-Yau 3-folds and Minimal 6d SCFTs
• Revisiting the classifications of 6d SCFTs and LSTs
• Blowup Equations for Refined Topological Strings
• Elliptic Blowup Equations for 6d SCFTs. III: E-strings, M-strings and Chains
• Green-Schwarz Automorphisms and 6D SCFTs
• D-type fiber-base duality
• Elliptic Blowup Equations for 6d SCFTs. IV: Matters
• M5 branes and Theta Functions
• Computing the elliptic genus of higher rank E-strings from genus 0 GW invariants
• Elliptic Quantum Curves of Class ${\mathcal{S}}_k$
• $DE$-type little strings from glued brane webs
• Bootstrapping ADE M-strings