ADE String Chains and Mirror Symmetry

Haghighat, Babak; Yan, Wenbin; Yau, Shing-Tung

doi:10.1007/JHEP01(2018)043

ADE String Chains and Mirror Symmetry

May 15, 2017

28 pages

Published in:

JHEP 01 (2018) 043

Published: Jan 10, 2018

e-Print:

1705.05199 [hep-th]

DOI:

10.1007/JHEP01(2018)043

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Abstract: (Springer)

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.

Note:

version 2: typos corrected, 30 pages, 8 figures

F-Theory
Field Theories in Higher Dimensions
Supersymmetric Gauge Theory
Topological Strings
symmetry: mirror
space: Calabi-Yau
geometry: mirror
compactification: torus
string model
Seiberg-Witten model

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Figures(8)

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