Abstract
We propose a generalization of S-folds to 4d $\mathcal{N}=2$ theories. This construction is motivated by the classification of rank one 4d $\mathcal{N}=2$ super-conformal field theories (SCFTs), which we reproduce from D3-branes probing a configuration of $\mathcal{N}=2$ S-folds combined with 7-branes. The main advantage of this point of view is that realizes both Coulomb and Higgs branch flows and allows for a straight forward generalization to higher rank theories.
Highlights
The classification of superconformal field theories (SCFTs) with 8 supercharges has seen immense advances in the past years
Starting with the chiral supersymmetric theories in 6d, where a classification framework has been developed in F-theory on elliptic Calabi-Yau threefolds [1,2,3], recent years have seen a concerted effort to establish a classification of 5d N 1⁄4 1 super-conformal field theories (SCFTs) constructed from M-theory on singular Calabi-Yau threefolds [4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20]
A complementary approach to the geometric one in 5d are the five-brane webs, which cover a large class of 5d SCFTs and their nonperturbative properties [21,22,23,24,25,26,27,28,29,30,31,32,33,34]
Summary
The classification of superconformal field theories (SCFTs) with 8 supercharges has seen immense advances in the past years. Some of these rank one theories have been constructed from twisted torus compactification of 6d/5d SCFTs [52] As this analysis is entirely developed from a bottom-up point of view, making no direct reference to a string theoretic construction, it is natural to ask whether this classification approach can be reproduced from a geometric setup, and ideally extended to higher rank. To obtain all rank one SCFTs in 4d with 8 supercharges, we have to slightly extend the notion of S-folds to quotients that preserve N 1⁄4 2 on a probe D3-brane, and include 7-branes in the background of the S-folds This approach has several advantages: first, it provides a straightforward generalization to higher rank theories by considering stacks of D3branes, which are more difficult to study from the Coulomb branch picture. VI we compute the a and c central charges of the 4d theories, using insights from holography, and discuss the extension to higher rank theories
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