The authors construct 5d SCFT trinions and tetraons with D flavor symmetry via M-theory, producing non-linear quivers with instanton symmetry enhancement and ruling out E-type cases.
Tinkertoys for the E7 Theory
3 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We classify the class $S$ theories of type $E_7$. These are four-dimensional $\mathcal{N}=2$ superconformal field theories arising from the compactification of the $E_7$ $(2,0)$ theory on a punctured Riemann surface, $C$. The classification is given by listing all 3-punctured spheres ("fixtures"), and connecting cylinders, which can arise in a pants-decomposition of $C$. We find exactly 11,000 fixtures with three regular punctures, and an additional 48 with one "irregular puncture" (in the sense used in our previous works). To organize this large number of theories, we have created a web application at https://golem.ph.utexas.edu/class-S/E7/ . Among these theories, we find 10 new ones with a simple exceptional global symmetry group, as well as a new rank-2 SCFT and several new rank-3 SCFTs. As an application, we study the strong-coupling limit of the $E_7$ gauge theory with 3 hypermultiplets in the $56$. Using our results, we also verify recent conjectures that the $T^2$ compactification of certain $6d$ $(1,0)$ theories can alternatively be realized in class $S$ as fixtures in the $E_7$ or $E_8$ theories.
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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.
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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5d Trinions and Tetraons
The authors construct 5d SCFT trinions and tetraons with D flavor symmetry via M-theory, producing non-linear quivers with instanton symmetry enhancement and ruling out E-type cases.
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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.