S-foldings of 5d SCFTs

We explore the Z(2,3,4,6) S-foldings of some 5d superconformal field theories from the (p, q) 5-brane web perspective. The S-folding involves both a spatial quotient and an SL(2, Z) transformation on 5-branes simultaneously. The Z(2,3,4,6) S-foldings are achieved by the insertion of the D-4, E-6, E-7, E-8 7-branes, respectively. The deficit angles and monodromies of these 7-branes are exactly those necessary for the S-foldings. We explore the details of the S-folding process, especially the enhancement of global flavor symmetry in various simple cases. The characteristic of the S-folding depends sharply on whether the fixed point of the discrete symmetry is at the center of a compact face (or surface), at a 5-brane, or at a crossing point of 5 branes. The analysis of the prepotential greatly supports this view of the discrete gauging.