S-folds and 4d N=3 superconformal field theories

TL;DR

This paper classifies variants of S-folds that preserve N=3 supersymmetry in four dimensions, explores their associated superconformal theories, and analyzes their holographic duals and symmetries using cohomology techniques.

Contribution

It provides a classification of N=3 preserving S-folds, analyzes their field theories and holographic duals, and clarifies the role of discrete symmetries using cohomology methods.

Findings

Classified different N=3 S-fold variants using torsion analysis.

Connected S-fold variants to distinct superconformal field theories.

Clarified the role of discrete gauge and global symmetries in holography.

Abstract

S-folds are generalizations of orientifolds in type IIB string theory, such that the geometric identifications are accompanied by non-trivial S-duality transformations. They were recently used by Garcia-Etxebarria and Regalado to provide the first construction of four dimensional N=3 superconformal theories. In this note, we classify the different variants of these N=3 preserving S-folds, distinguished by an analog of discrete torsion, using both a direct analysis of the different torsion classes and the compactification of the S-folds to three dimensional M-theory backgrounds. Upon adding D3-branes, these variants lead to different classes of N=3 superconformal field theories. We also analyze the holographic duals of these theories, and in particular clarify the role of discrete gauge and global symmetries in holography. In the main part of the paper, certain properties of cohomology groups associated to the S-folds were conjectured and used. This arXiv version includes an appendix written by Kiyonori Gomi in 2023 providing the proofs of the required properties using the technique of Borel equivariant cohomology, whose brief review is also provided.