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

Antonio Amariti, Davide Morgante, Antoine Pasternak, Simone Rota, Valdo Tatitscheff

TL;DR

This work addresses the problem of identifying global one-form symmetries in non-Lagrangian $\mathcal{N}=3$ SCFTs realized via $S$-fold projections of D3-branes. The authors adapt the IR-based DelZotto method to the Type IIB brane setup by extracting the electromagnetic charges of $(p,q)$-strings, forming a charge lattice, and then quotienting by screening to obtain genuine line operators; maximal mutually local sublattices fix the possible global structures. They provide a complete classification for various $S$-folds, finding a $\mathbb{Z}_3$ one-form symmetry for $S_{3,1}$ and a $\mathbb{Z}_2$ one for $S_{4,1}$ in rank-2 cases, while many other theories exhibit trivial one-form symmetry. The results reproduce known $\mathcal{N}=4$ enhancements and illuminate the potential for non-invertible duality defects, establishing a bridge between brane constructions, lattice of lines, and generalized global symmetries in $\mathcal{N}=3$ theories. This lattice-driven approach enables systematic analysis across ranks and discrete torsion choices and paves the way for exploring non-invertible structures in broader classes of $S$-fold and exceptional $\mathcal{N}=3$ theories.

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.

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

TL;DR

This work addresses the problem of identifying global one-form symmetries in non-Lagrangian SCFTs realized via -fold projections of D3-branes. The authors adapt the IR-based DelZotto method to the Type IIB brane setup by extracting the electromagnetic charges of -strings, forming a charge lattice, and then quotienting by screening to obtain genuine line operators; maximal mutually local sublattices fix the possible global structures. They provide a complete classification for various -folds, finding a one-form symmetry for and a one for in rank-2 cases, while many other theories exhibit trivial one-form symmetry. The results reproduce known enhancements and illuminate the potential for non-invertible duality defects, establishing a bridge between brane constructions, lattice of lines, and generalized global symmetries in theories. This lattice-driven approach enables systematic analysis across ranks and discrete torsion choices and paves the way for exploring non-invertible structures in broader classes of -fold and exceptional theories.

Abstract

We classify the global one-form symmetries for non-Lagrangian SCFTs that arise by the action of -fold projections on D3-branes. Such a classification is dictated, on a generic point of the Coulomb branch, by probing the charge spectrum of -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 SCFTs.
Paper Structure (17 sections, 124 equations, 2 figures, 6 tables)

This paper contains 17 sections, 124 equations, 2 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Generalities
  3. Global structures from the IR
  4. Charged states in $S_{k,l}$-folds
  5. Dirac pairing from $(p,q)$-strings
  6. Lines in O3-planes
  7. Lines in $S$-folds with $\mathcal{N}=4$ enhancement
  8. Lines in $\mathfrak{su}(3)$ from $S_{3,1}$
  9. Lines in $\mathfrak{so}(5)$ from $S_{4,1}$
  10. Trivial line in $\mathfrak{g}_2$ from $S_{6,1}$
  11. Lines in $\mathcal{N}=3$ $S$-folds
  12. Lines in $S_{3,1}$-fold
  13. Lines in $S_{4,1}$-fold
  14. Trivial line in $S_{6,1}$-fold
  15. Trivial line in the discrete torsion cases
  16. ...and 2 more sections

Figures (2)

  • Figure 1: A pictorial representation of two D3-branes probing the $O3^+$ orientifold on a generic point of the Coulomb branch. The light blue shaded area is a possible choice of fundamental domain under the spacetime identification induced by the orientifold. Black (gray) dots represent (images of) D3-branes. Black lines correspond to $(p,q)$-strings stretched between D3-branes. In particular, we drew $(p,q)$-strings generating the $\mathcal{W}$-bosons corresponding to simple roots $\mathcal{N}=4$$\mathfrak{usp}(4)$ SYM.
  • Figure 2: A pictorial representation of two D3-branes probing the $S_{3,1}$-fold. The transverse directions to the $S$-fold are shown. The light blue dot represents the position of the $S_{3,1}$-fold. The light blue shaded area is a possible choice of fundamental domain under the spacetime identification induced by the $S_{3,1}$-fold. Black (gray) dots represent (images of) D3-branes. Black lines correspond to $(p,q)$-strings stretched between D3-branes. In particular, we drew $(p,q)$-strings corresponding to $\mathcal{W}$-bosons of $\mathcal{N}=4$$\mathfrak{su}(3)$ SYM.