S-folds and 4d N $$ mathcal{N} $$ = 3 superconformal field theories

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 garcía-etxebarria and regalado to provide the first construction of four dimensional $$ mathcal{n} $$ =3 superconformal theories. in this note, we classify the different variants of these $$ mathcal{n} $$ =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 $$ mathcal{n} $$ =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.