Atomic classification of 6D SCFTs
TLDR
Heckman et al. as discussed by the authors used F-theory to classify possibly all six-dimensional superconformal field theories (SCFTs) and showed that all of these tensor branches have the structure of a linear chain of intersecting spheres with a small amount of possible decoration at the two ends.Abstract:
Author(s): Heckman, JJ; Morrison, DR; Rudelius, T; Vafa, C | Abstract: We use F-theory to classify possibly all six-dimensional superconformal field theories (SCFTs). This involves a two step process: We first classify all possible tensor branches allowed in F-theory (which correspond to allowed collections of contractible spheres) and then classify all possible configurations of seven-branes wrapped over them. We describe the first step in terms of "atoms" joined into "radicals" and "molecules," using an analogy from chemistry. The second step has an interpretation via quiver-type gauge theories constrained by anomaly cancellation. A very surprising outcome of our analysis is that all of these tensor branches have the structure of a linear chain of intersecting spheres with a small amount of possible decoration at the two ends. The resulting structure of these SCFTs takes the form of a generalized quiver consisting of ADE-type nodes joined by conformal matter. A collection of highly non-trivial examples involving E8 small instantons probing an ADE singularity is shown to have an F-theory realization. This yields a classification of homomorphisms from ADE subgroups of SU(2) into E8 in purely geometric terms, matching results obtained in the mathematics literature from an intricate group theory analysis.read more
Citations
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On Geometric Classification of 5d SCFTs
TL;DR: In this article, the authors studied the geometric conditions necessary for engineering 5d superconformal field theories via M-theory compactification on a local Calabi-Yau 3-fold and showed that all rank 2 SCFTs descend from 6d (1,0) SCFT compactified on a circle possibly twisted with an automorphism together with holonomies for global symmetries around the Kaluza-Klein circle.
Journal ArticleDOI
$ \mathcal{N}=1 $ theories of class $ {\mathcal{S}}_k $
Davide Gaiotto,Shlomo S. Razamat +1 more
TL;DR: In this paper, a supersymmetric index of theories with k > 1 was constructed using eigenfunctions of elliptic quantum mechanical models generalizing the Ruijsenaars-Schneider integrable model.
Journal ArticleDOI
6d N = (1,0) theories on S1 /T2 and class S theories: part II
TL;DR: In this paper, it was shown that the superconformal theory on a single M5 brane on the ALE space of type G = An,Dn,En, when compactified on T 2, becomes a class S theory of type g on a sphere with two full punctures and a simple puncture.
Journal ArticleDOI
Fibers add flavor. Part I. Classification of 5d SCFTs, flavor symmetries and BPS states
TL;DR: In this paper, a graph-based approach to 5d superconformal field theories (SCFTs) is proposed based on their realization as M-theory compactifications on singular elliptic Calabi-Yau threefolds.
Journal ArticleDOI
AdS6 solutions of type II supergravity
Fabio Apruzzi,Marco Fazzi,Marco Fazzi,Achilleas Passias,Achilleas Passias,Dario Rosa,Dario Rosa,Alessandro Tomasiello,Alessandro Tomasiello +8 more
TL;DR: Very few AdS6 × M 6 × M 4 supersymmetric solutions are known: one in massive IIA, and two IIB solutions dual to it as mentioned in this paper, which is known as the pure spinor approach to give a classification for IIB supergravity.
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