Non-Invertible Symmetries from Holography and Branes

Abstract

We propose a systematic approach to deriving symmetry generators of Quantum Field Theories in holography. Central to this are the Gauss law constraints in the Hamiltonian quantization of Symmetry Topological Field Theories (SymTFTs), which are obtained from supergravity. In turn we realize the symmetry generators from world-volume theories of D-branes in holography. Our main focus is on non-invertible symmetries, which have emerged in the past year as a new type of symmetry in $d\ge 4$ QFTs. We exemplify our proposal in the holographic confinement setup, dual to 4d $\mathcal{N}=1$ Super-Yang Mills. In the brane-picture, the fusion of non-invertible symmetries naturally arises from the Myers effect on D-branes. In turn, their action on line defects is modeled by the Hanany-Witten effect.

10 pages; published version

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• Generalized Charges, Part I: Invertible Symmetries and Higher Representations
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• Non-invertible Symmetries and Higher Representation Theory II
• Bootstrapping Non-Invertible Symmetries
• Gapped Phases with Non-Invertible Symmetries: (1+1)d
• Subsystem Non-Invertible Symmetry Operators and Defects
• Anomalies of Non-Invertible Symmetries in (3+1)d
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• Gauging Noninvertible Defects: A 2-Categorical Perspective
• Fusion Surface Models: 2+1d Lattice Models from Fusion 2-Categories
• 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
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• Remarks on Geometric Engineering, Symmetry TFTs and Anomalies
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• Generalized Charges, Part II: Non-Invertible Symmetries and the Symmetry TFT
• Non-Invertible Symmetries in Supergravity
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• Hasse Diagrams for Gapless SPT and SSB Phases with Non-Invertible Symmetries
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• SymTFT for (3+1)d Gapless SPTs and Obstructions to Confinement
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• Reading between the rational sections: Global structures of 4d $\mathcal{N}=2$ KK theories
• Higher Gauge Theory
• Symmetry Operators and Gravity
• 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
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• Noninvertible Gauge Symmetry in (2+1)d Topological Orders: A String-Net Model Realization
• Topological Manipulations On $\mathbb{R}$ Symmetries Of Abelian Gauge Theory