Non-invertible Symmetries of Class $\mathcal{S}$ Theories

Abstract

We study the non-invertible symmetries of class $\mathcal{S}$ theories obtained by compactifying the type ${\mathfrak{a}}_{p-1}$ 6d (2,0) theory on a genus $g$ Riemann surface with no punctures. After setting up the general framework, we describe how such symmetries can be classified up to genus 5. Of central interest to us is the question of whether a non-invertible symmetry is "intrinsic," i.e. whether it can be related to an invertible symmetry by discrete gauging. We then describe the higher-dimensional origin of our results, and explain how the Anomaly and Symmetry TFTs, as well as $N$-ality defects, of class $\mathcal{S}$ theories can be obtained from compactification of a 7d Chern-Simons theory. Interestingly, we find that the Symmetry TFT for theories with intrinsically non-invertible symmetries can only be obtained by coupling the 7d Chern-Simons theory to topological gravity.

85 pages; v2: references corrected

References in corpus (45)

• Generalized Global Symmetries
• Duality and defects in rational conformal field theory
• Kramers-Wannier-like duality defects in (3+1)d gauge theories
• Non-Invertible Higher-Categorical Symmetries
• Universal Non-Invertible Symmetries
• Asymptotic density of states in 2d CFTs with non-invertible symmetries
• Theory of Twist Liquids: Gauging an Anyonic Symmetry
• Non-Invertible Symmetries from Holography and Branes
• Non-Invertible Symmetries of $\mathcal{N}=4$ SYM and Twisted Compactification
• The Branes Behind Generalized Symmetry Operators
• Construction of two-dimensional topological field theories with non-invertible symmetries
• Non-invertible Time-reversal Symmetry
• The Global Form of Flavor Symmetries and 2-Group Symmetries in 5d SCFTs
• Branes and Non-Invertible Symmetries
• 5d and 4d SCFTs: Canonical Singularities, Trinions and S-Dualities
• Exploring Non-Invertible Symmetries in Free Theories
• On Continuous 2-Category Symmetries and Yang-Mills Theory
• Non-invertible self-duality defects of Cardy-Rabinovici model and mixed gravitational anomaly
• Non-Invertible Defects in 5d, Boundaries and Holography
• 2-Group Symmetries in Class S
• Decomposition, condensation defects, and fusion
• Symmetry TFTs for 3d QFTs from M-theory
• Coulomb and Higgs Branches from Canonical Singularities, Part 1: Hypersurfaces with Smooth Calabi-Yau Resolutions
• 2-Group Symmetries and M-Theory
• Higher Symmetries of 5d Orbifold SCFTs
• Generalized symmetries and holography in ABJM-type theories
• Non-Invertible Symmetries from Discrete Gauging and Completeness of the Spectrum
• Mixed Anomalies, Two-groups, Non-Invertible Symmetries, and 3d Superconformal Indices
• Holography, 1-Form Symmetries, and Confinement
• Mean string field theory: Landau-Ginzburg theory for 1-form symmetries
• Generalized symmetries and 2-groups via electromagnetic duality in AdS/CFT
• Higher Form Symmetries TFT in 6d
• Topological axion electrodynamics and 4-group symmetry
• Higher-Form Symmetries, Bethe Vacua, and the 3d-3d Correspondence
• Relative Defects in Relative Theories: Trapped Higher-Form Symmetries and Irregular Punctures in Class S
• Maruyoshi-Song Flows and Defect Groups of $D_p^b(G)$ Theories
• Duality Defects in $E_8$
• Gauged 2-form Symmetries in 6D SCFTs Coupled to Gravity
• 1-Form Symmetry, Isolated N=2 SCFTs, and Calabi-Yau Threefolds
• Global Form of Flavor Symmetry Groups in 4d N=2 Theories of Class S
• The holography of duality in $\mathcal{N}=4$ Super-Yang-Mills theory
• Zero-form and one-form symmetries of the ABJ and related theories
• M5-branes Probing Flux Backgrounds
• Topological Orders in (4+1)-Dimensions
• Matching higher symmetries across Intriligator-Seiberg duality

Cited by in corpus (28)

• Unifying Constructions of Non-Invertible Symmetries
• Non-Invertible Symmetry Webs
• Obstructions to Gapped Phases from Non-Invertible Symmetries
• Generalized Charges, Part I: Invertible Symmetries and Higher Representations
• Non-invertible Symmetries and Higher Representation Theory II
• Gapped Phases with Non-Invertible Symmetries: (1+1)d
• Anomalies of Non-Invertible Symmetries in (3+1)d
• Subsystem Non-Invertible Symmetry Operators and Defects
• Fusion Surface Models: 2+1d Lattice Models from Fusion 2-Categories
• Comments on Non-invertible Symmetries in Argyres-Douglas Theories
• SymTFTs and Duality Defects from 6d SCFTs on 4-manifolds
• The Club Sandwich: Gapless Phases and Phase Transitions with Non-Invertible Symmetries
• On the Symmetry TFT of Yang-Mills-Chern-Simons theory
• Remarks on Geometric Engineering, Symmetry TFTs and Anomalies
• Non-invertible symmetries along 4d RG flows
• Generalized Charges, Part II: Non-Invertible Symmetries and the Symmetry TFT
• Holographic duals of symmetry broken phases
• Hasse Diagrams for Gapless SPT and SSB Phases with Non-Invertible Symmetries
• Topological defects
• Fermionic Non-Invertible Symmetries in (1+1)d: Gapped and Gapless Phases, Transitions, and Symmetry TFTs
• SymTFT for (3+1)d Gapless SPTs and Obstructions to Confinement
• Non-Invertible T-duality at Any Radius via Non-Compact SymTFT
• Symmetry fractionalization and duality defects in Maxwell theory
• Hitchhiker's Guide to the Swampland: The Cosmologist's Handbook to the string-theoretical Swampland Programme
• The 3d $A$-model and generalised symmetries, Part I: bosonic Chern-Simons theories
• One-form symmetries and the 3d $\mathcal{N}=2$ $A$-model: Topologically twisted indices and CS theories
• Non-Invertible $SO(2)$ Symmetry of 4d Maxwell from Continuous Gaugings
• Non-Invertible Gauss Law and Axions