The Superconformal Index of the E_6 SCFT

Abstract

We derive an integral representation for the superconformal index of the strongly-coupled N=2 superconformal field theory with E_6 flavor symmetry. The explicit expression of the index allows highly non-trivial checks of Argyres-Seiberg duality and of a class of S-dualities conjectured by Gaiotto.

29 pages, 7 figures

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• The superconformal index of N=1 class S fixed points
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• A "Lagrangian" for a non-Lagrangian theory
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• Reducing the 4d Index to the S^3 Partition Function
• $(0,4)$ dualities
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• Global Properties of Supersymmetric Theories and the Lens Space
• The Superconformal Index of Class S Theories of Type D
• Tri-vertices and SU(2)'s
• Counting Exceptional Instantons
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• Elliptic hypergeometric integrals and 't Hooft anomaly matching conditions
• N=2 S-duality Revisited
• 2d TQFT structure of the superconformal indices with outer-automorphism twists
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• An Exceptional Sector for F-theory GUTs
• Charting Class ${\mathcal{S}}_k$ Territory
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• More Three Dimensional Mirror Pairs
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• Elliptic Blowup Equations for 6d SCFTs. II: Exceptional Cases
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• A slow review of the AGT correspondence
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• An N=1 Lagrangian for an N=3 SCFT
• Instantons from Blow-up
• Hybrid NLIE for the Mirror AdS_5 x S^5
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• Supersymmetric Casimir Energy and $\mathrm{SL}(3,\mathbb{Z})$ Transformations
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• Peculiar Index Relations, 2D TQFT, and Universality of SUSY Enhancement
• Topological Field Theory Amplitudes for $A_{N-1}$ Fibration
• Theories of Class S and New N=1 SCFTs
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• Vanishing short multiplets in rank one 4d/5d SCFTs