4d $\mathcal{N}=2$ S-folds

TL;DR

This work extends S-fold constructions to 4d $\mathcal{N}=2$ theories by combining S-folds that act on spacetime and the axio-dilaton with stacks of 7-branes, and probes this geometry with D3-branes to realize rank-one $\mathcal{N}=2$ SCFTs. It develops a systematic quotienting of Kodaira fibers under $\mathbb{Z}_k$ actions to generate a set of $\langle G, \mathbb{Z}_k\rangle$ models, maps them to known rank-one theories, and analyzes their Coulomb and Higgs branches, global symmetries, and mass parameters. The central charges are computed holographically from a combination of bulk AdS$_5$ contributions, 7-brane Chern-Simons terms, and ECB hypermultiplet content, showing consistency with rank-one data and predicting higher-rank generalizations. Overall, the paper provides a geometric, string-theoretic realization of the rank-one $\mathcal{N}=2$ SCFT classification and outlines a path toward systematic construction of higher-rank theories via D3-brane probes of $\mathcal{N}=2$ S-fold backgrounds with 7-branes.

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.