ADE string chains and mirror symmetry

• Published in: The journal of high energy physics Vol. 2018; no. 1; pp. 1 - 30
• Main Authors: Haghighat, Babak, Yan, Wenbin, Yau, Shing-Tung
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.01.2018; Springer Nature B.V; SpringerOpen
• Subjects: Classical and Quantum Gravitation; Curves; Elementary Particles; F-Theory; Field Theories in Higher Dimensions; Geometry; High energy physics; Manifolds (mathematics); Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; String Theory; Supersymmetric Gauge Theory; Symmetry; Topological Strings; Toruses; Topological Strings; Field Theories in Higher Dimensions; F-Theory; Supersymmetric Gauge Theory
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP01(2018)043

A bstract 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.