Tinkertoys for the \(E_7\) theory

DOI10.1007/JHEP05(2018)031zbMATH Open1391.83104arXiv1704.07890OpenAlexW2964323683WikidataQ129894094 ScholiaQ129894094MaRDI QIDQ1651075

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Publication date: 11 July 2018

Published in: (Search for Journal in Brave)

Abstract: We classify the class $S$ theories of type $E_7$. These are four-dimensional $mathcalN=2$ 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.

Full work available at URL: https://arxiv.org/abs/1704.07890

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