On the Holographic Dual of a Topological Symmetry Operator

Abstract

We study the holographic dual of a topological symmetry operator in the context of the AdS/CFT correspondence. Symmetry operators arise from topological field theories localized on a subspace of the boundary CFT spacetime. We use bottom up considerations to construct the topological sector associated with their bulk counterparts. In particular, by exploiting the structure of entanglement wedge reconstruction we argue that the bulk counterpart has a non-topological worldvolume action, i.e., it describes a dynamical object. As a consequence, we find that there are no global $p$-form symmetries for $p\ge 0$ in asymptotically AdS spacetimes, which includes the case of non-invertible symmetries. Provided one has a suitable notion of subregion-subregion duality, our argument for the absence of bulk global symmetries applies to more general spacetimes. These considerations also motivate us to consider for general QFTs (holographic or not) the notion of lower-form symmetries, namely, $(-m)$-form symmetries for $m\ge 2$.

29 pages, 10 figures

References in corpus (12)

• Generalized Global Symmetries
• Symmetries and Strings in Field Theory and Gravity
• Holographic representation of local bulk operators
• Surface/State Correspondence as a Generalized Holography
• Non-Invertible Symmetries from Holography and Branes
• The Branes Behind Generalized Symmetry Operators
• Branes and Non-Invertible Symmetries
• Lecture Notes on Generalized Symmetries and Applications
• 2-Group Symmetries in Class S
• Generalized Symmetry Breaking Scales and Weak Gravity Conjectures
• Disorder Averaging and its UV (Dis)Contents
• Coarse-Graining Holographic States: A Semiclassical Flow in General Spacetimes

Cited by in corpus (14)

• Holographic duals of symmetry broken phases
• 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
• Asymptotic safety, quantum gravity, and the swampland: a conceptual assessment
• 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
• U(1) Gauging, Continuous TQFTs, and Higher Symmetry Structures
• (-1)-Form Symmetries and Anomaly Shifting from SymTFT
• Subregion duality, wedge classification and no global symmetries in AdS/CFT
• Global symmetry violation from non-isometric codes
• Gravitational Background of Alice-Vortices and R7-Branes
• Center Symmetry Breaking in Calabi--Yau Compactifications
• Topological Manipulations On $\mathbb{R}$ Symmetries Of Abelian Gauge Theory