All 5d balanced (ADE-shaped) SU quivers with no Chern-Simons level have UV completions as 5d conformal matter SCFTs realized by explicit local Calabi-Yau threefolds in M-theory.
Tinkertoys for the Z3-twisted D4 Theory
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abstract
Among the simple Lie algebras, $D_4$ is distinguished as the unique one whose group of outer-automorphisms is bigger than $\mathbb{Z}_2$. We study the compactifications of the $D_4$ (2,0) Theory on a punctured Riemann surface, $C$, with outer-automorphism twists around cycles of $C$ lying in $\mathbb{Z}_3\subset \text{Aut}(D_4)= S_3$. The resulting 4D $\mathcal{N}=2$ SCFTs have a number of new and interesting properties. As byproduct, we discover a new rank-1 $\mathcal{N}=2$ SCFT with flavour symmetry group $SU(4)$.
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A comprehensive introduction to spectral networks that develops higher-rank Teichmüller theory in parallel with class S gauge theory and BPS spectra.
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From Quivers to Geometry: 5d Conformal Matter
All 5d balanced (ADE-shaped) SU quivers with no Chern-Simons level have UV completions as 5d conformal matter SCFTs realized by explicit local Calabi-Yau threefolds in M-theory.
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Spectral Networks: Bridging higher-rank Teichm\"uller theory and BPS states
A comprehensive introduction to spectral networks that develops higher-rank Teichmüller theory in parallel with class S gauge theory and BPS spectra.