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arXiv · 1705.05199

ADE String Chains and Mirror Symmetry

Babak Haghighat·Wenbin Yan·Shing-Tung Yau
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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.

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Babak Haghighat, Wenbin Yan, Shing-Tung Yau. 2017-05-15. ADE String Chains and Mirror Symmetry. https://doi.org/10.1007/jhep01(2018)043

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