Tinkertoys for the \(E_{6}\) theory

DOI10.1007/JHEP09(2015)007zbMATH Open1388.81645arXiv1403.4604OpenAlexW4245102876MaRDI QIDQ2635773

Author name not available (Why is that?)

Publication date: 31 May 2018

Published in: (Search for Journal in Brave)

Abstract: Compactifying the 6-dimensional (2,0) superconformal field theory, of type ADE, on a Riemann surface,

C

, with codimension-2 defect operators at points on

C

, yields a 4-dimensional

m a t h c a l N = 2

superconformal field theory. An outstanding problem is to classify the 4D theories one obtains, in this way, and to understand their properties. In this paper, we turn our attention to the

E_{6}

(2,0) theory, which (unlike the A- and D-series) has no realization in terms of M5-branes. Classifying the 4D theories amounts to classifying all of the 3-punctured spheres ("fixtures"), and the cylinders that connect them, that can occur in a pants-decomposition of

C

. We find 904 fixtures: 19 corresponding to free hypermultiplets, 825 corresponding to isolated interacting SCFTs (with no known Lagrangian description) and 60 "mixed fixtures", corresponding to a combination of free hypermultiplets and an interacting SCFT. Of the 825 interacting fixtures, we list only the 139 "interesting" ones. As an application, we study the strong coupling limits of the Lagrangian field theories:

E_{6}

with 4 hypermultiplets in the

27

and

F_{4}

with 3 hypermultiplets in the

26

.

Full work available at URL: https://arxiv.org/abs/1403.4604

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