S-foldings of 5d SCFTs

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.

arXiv commentv1: 45 pages, 32 figures; v2: references added, minor corrections; v3: published version

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• 3d defects in 5d: RG flows and defect F-maximization
• Generalized quotients and holographic duals for 5d S-fold SCFTs
• O-vertex, O7${}^{+}$-plane, and Topological Vertex
• Coulomb branch surgery: Holonomy saddles, S-folds and discrete symmetry gaugings