S-foldings of 5d SCFTs

TL;DR

This paper investigates the construction of 5d superconformal field theories using S-foldings involving discrete quotients and SL(2,Z) transformations, achieved through 7-brane insertions, revealing effects on global symmetries and fixed points.

Contribution

It introduces a novel approach to S-foldings of 5d SCFTs via 7-brane insertions and analyzes their impact on symmetry enhancement and fixed point characteristics.

Findings

S-foldings correspond to specific 7-brane insertions with matching monodromies.

Global flavor symmetry enhancements depend on the fixed point location.

Prepotential analysis supports the discrete gauging interpretation.

Abstract

We explore the $\mathbb{Z}_{2,3,4,6}$ 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 $\mathrm{SL}(2,\mathbb{Z})$ transformation on 5-branes simultaneously. The $\mathbb{Z}_{2,3,4,6}$ 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.