On the Holographic Dual of a Topological Symmetry Operator

On the Holographic Dual of a Topological Symmetry Operator

January 2024 | Jonathan J. Heckman, Max Hübner, and Chitraang Murdia
The paper explores the holographic dual of topological symmetry operators in the context of the AdS/CFT correspondence. The authors construct the topological sector associated with bulk counterparts of these operators using bottom-up considerations. They argue that the bulk counterpart has a non-topological worldvolume action, indicating that there are no global \( p \)-form symmetries for \( p \geq 0 \) in asymptotically AdS spacetimes, including non-invertible symmetries. This argument is based on the structure of entanglement wedge reconstruction and the absence of bulk global symmetries. The authors also discuss the existence of lower-form symmetries for general QFTs, both holographic and non-holographic. They provide examples to illustrate the general structure and properties of the bulk duals of topological symmetry operators, particularly for continuous 0-form symmetries like \( U(1) \) and non-abelian Lie groups. The paper concludes by discussing potential extensions to more general spacetimes.The paper explores the holographic dual of topological symmetry operators in the context of the AdS/CFT correspondence. The authors construct the topological sector associated with bulk counterparts of these operators using bottom-up considerations. They argue that the bulk counterpart has a non-topological worldvolume action, indicating that there are no global \( p \)-form symmetries for \( p \geq 0 \) in asymptotically AdS spacetimes, including non-invertible symmetries. This argument is based on the structure of entanglement wedge reconstruction and the absence of bulk global symmetries. The authors also discuss the existence of lower-form symmetries for general QFTs, both holographic and non-holographic. They provide examples to illustrate the general structure and properties of the bulk duals of topological symmetry operators, particularly for continuous 0-form symmetries like \( U(1) \) and non-abelian Lie groups. The paper concludes by discussing potential extensions to more general spacetimes.
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