ADE string chains and mirror symmetry

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Regular Article - Theoretical Physics
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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.

Keywords

F-Theory Field Theories in Higher Dimensions Supersymmetric Gauge Theory Topological Strings 

Notes

Open Access

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Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.Yau Mathematical Sciences CenterTsinghua UniversityBeijingChina
  2. 2.Center of Mathematical Sciences and ApplicationsHarvard UniversityCambridgeU.S.A.
  3. 3.Department of MathematicsHarvard UniversityCambridgeU.S.A.

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