One-form symmetries in $\mathcal{N} = 3$ $S$-folds

TL;DR

This paper classifies the one-form symmetries of non-Lagrangian $ =3$ SCFTs derived from $S$-folds, using brane charge spectra and line lattice analysis, and discusses potential non-invertible symmetries.

Contribution

It provides a systematic classification of global one-form symmetries for $ =3$ SCFTs from $S$-fold constructions, including non-invertible symmetries.

Findings

Charge lattice of lines determined by brane analysis

Maximal mutually local line sub-lattices identified

Non-invertible symmetries potentially present

Abstract

We classify the global one-form symmetries for non-Lagrangian $\mathcal{N}=3$ SCFTs that arise by the action of $S$-fold projections on D3-branes. Such a classification is dictated, on a generic point of the Coulomb branch, by probing the charge spectrum of $(p, q)$-strings in the brane setup. The charge lattice of lines is then obtained by finding the ones that are genuine modulo screening by dynamical particles. The one-form symmetries are then extracted from the maximal sub-lattices of mutually local lines. We further comment on the existence of non-invertible symmetries for some of these $\mathcal{N}=3$ SCFTs.