The Branes Behind Generalized Symmetry Operators

Abstract

The modern approach to $m$-form global symmetries in a $d$-dimensional quantum field theory (QFT) entails specifying dimension $d-m-1$ topological generalized symmetry operators which non-trivially link with $m$-dimensional defect operators. In QFTs engineered via string constructions on a non-compact geometry $X$, these defects descend from branes wrapped on non-compact cycles which extend from a localized source / singularity to the boundary $\partial X$. The generalized symmetry operators which link with these defects arise from magnetic dual branes wrapped on cycles in $\partial X$. This provides a systematic way to read off various properties of such topological operators, including their worldvolume topological field theories, and the resulting fusion rules. We illustrate these general features in the context of 6D superconformal field theories, where we use the F-theory realization of these theories to read off the worldvolume theory on the generalized symmetry operators. Defects of dimension 3 which are charged under a suitable 3-form symmetry detect a non-invertible fusion rule for these operators. We also sketch how similar considerations hold for related systems.

v3: 21 pages + references, 1 figure; clarifications added, reference added

References in corpus (19)

• Generalized Global Symmetries
• Symmetries and Strings in Field Theory and Gravity
• 6d Conformal Matter
• Comments on One-Form Global Symmetries and Their Gauging in 3d and 4d
• Fusion Category Symmetry I: Anomaly In-Flow and Gapped Phases
• The Uncertainty of Fluxes
• Heisenberg Groups and Noncommutative Fluxes
• Snowmass White Paper: Generalized Symmetries in Quantum Field Theory and Beyond
• Anomaly polynomial of E-string theories
• 6d, N=(1,0) Coulomb Branch Anomaly Matching
• Generalized symmetries and holography in ABJM-type theories
• Generalized symmetries and 2-groups via electromagnetic duality in AdS/CFT
• Higher-Form Symmetries, Bethe Vacua, and the 3d-3d Correspondence
• Maruyoshi-Song Flows and Defect Groups of $D_p^b(G)$ Theories
• Zero-form and one-form symmetries of the ABJ and related theories
• Type II Actions from 11-Dimensional Chern-Simons Theories
• Comments on compatibility between Conformal symmetry and Continuous higher-form symmetries
• Matching higher symmetries across Intriligator-Seiberg duality
• On the 6d Origin of Non-invertible Symmetries in 4d

Cited by in corpus (38)

• Unifying Constructions of Non-Invertible Symmetries
• Exploring Non-Invertible Symmetries in Free Theories
• Non-invertible Symmetries of Class $\mathcal{S}$ Theories
• Non-Invertible Symmetry Webs
• Lecture Notes on Generalized Symmetries and Applications
• Symmetry TFTs for 3d QFTs from M-theory
• Generalized Charges, Part I: Invertible Symmetries and Higher Representations
• Mixed Anomalies, Two-groups, Non-Invertible Symmetries, and 3d Superconformal Indices
• Bootstrapping Non-Invertible Symmetries
• Non-invertible Symmetries and Higher Representation Theory II
• Gapped Phases with Non-Invertible Symmetries: (1+1)d
• Subsystem Non-Invertible Symmetry Operators and Defects
• Fusion Surface Models: 2+1d Lattice Models from Fusion 2-Categories
• Gauging Noninvertible Defects: A 2-Categorical Perspective
• On the Holographic Dual of a Topological Symmetry Operator
• SymTFTs and Duality Defects from 6d SCFTs on 4-manifolds
• Comments on Non-invertible Symmetries in Argyres-Douglas Theories
• The Club Sandwich: Gapless Phases and Phase Transitions with Non-Invertible Symmetries
• On the Symmetry TFT of Yang-Mills-Chern-Simons theory
• On Triality Defects in 2d CFT
• Remarks on Geometric Engineering, Symmetry TFTs and Anomalies
• Generalized Charges, Part II: Non-Invertible Symmetries and the Symmetry TFT
• Non-Invertible Symmetries in Supergravity
• Non-invertible symmetries and boundaries in four dimensions
• The holography of non-invertible self-duality symmetries
• Hasse Diagrams for Gapless SPT and SSB Phases with Non-Invertible Symmetries
• Fermionic Non-Invertible Symmetries in (1+1)d: Gapped and Gapless Phases, Transitions, and Symmetry TFTs
• Reading between the rational sections: Global structures of 4d $\mathcal{N}=2$ KK theories
• Higher Gauge Theory
• Symmetry fractionalization and duality defects in Maxwell theory
• Symmetry Operators and Gravity
• The 3d $A$-model and generalised symmetries, Part I: bosonic Chern-Simons theories
• Generalized Symmetries of Non-SUSY and Discrete Torsion String Backgrounds
• Hitchhiker's Guide to the Swampland: The Cosmologist's Handbook to the string-theoretical Swampland Programme
• von Neumann Subfactors and Non-invertible Symmetries
• Non-Invertible Gauss Law and Axions
• Noninvertible symmetries in the B model TFT
• Refined BPS numbers on compact Calabi-Yau threefolds from Wilson loops