Tinkertoys for the E7 Theory

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.

arXiv commentFixed one entry in table of interacting fixtures with an irregular puncture

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Cited by in corpus (25)

• 2-Group Symmetries in Class S
• Compactifications of 6d $N=(1,0)$ SCFTs with non-trivial Stiefel-Whitney classes
• Relative Defects in Relative Theories: Trapped Higher-Form Symmetries and Irregular Punctures in Class S
• Revisiting the classifications of 6d SCFTs and LSTs
• 4D Gauge Theories with Conformal Matter
• Global Form of Flavor Symmetry Groups in 4d N=2 Theories of Class S
• A slow review of the AGT correspondence
• New N=2 superconformal field theories from S-folds
• Dynamical consequences of 1-form symmetries and the exceptional Argyres-Douglas theories
• Infinitely many 4d $\mathcal{N}=2$ SCFTs with $a=c$ and beyond
• Two 6d origins of 4d SCFTs: class $\mathcal{S}$ and 6d (1,0) on a torus
• Argyres-Douglas Theories in Class S Without Irregularity
• Testing our understanding of SCFTs: a catalogue of rank-2 $\mathcal{N}$=2 theories in four dimensions
• Higgs, Coulomb, and Hall-Littlewood
• Distinguishing 6d (1,0) SCFTs: an extension to the geometric construction
• Structure of Anomalies of 4d SCFTs from M5-branes, and Anomaly Inflow
• Wrapped Branes and Punctured Horizons
• The Hitchhiker's Guide to 4d $\mathcal{N}=2$ Superconformal Field Theories
• Nilpotent Networks and 4D RG Flows
• On low rank 4d $\mathcal{N}=2$ SCFTs
• Isomorphisms of 4d N=2 SCFTs from 6d
• Quiver Polymerisation
• 1-form Symmetries of 4d N=2 Class S Theories
• The Hitchin Image in Type-D
• Factorized class $S$ theories and surface defects